Appunti completi di Behavioural Economics 2020/2021 prof. Zirulia, Appunti di Economia

Scarica Appunti completi di Behavioural Economics 2020/2021 prof. Zirulia e più Appunti in PDF di Economia solo su Docsity! Clara Corona Introduction to Behavioral Economics Behavioral economics can be broadly defined as the attempt to understand economic behavior by applying insights from psychology (and other social sciences), also relying on laboratory and field experiments. 
 Daniel Kanheman, in his book Thinking fast and slow, makes reference to “System 1” and “System 2”. System 1 is mostly involved in the activities of the left side, it’s a cognitive system involved in automatic decisions. It’s the system for simple operations. System 2, instead, characterizes our brain activity, our decision processes. It’s involved in decision making, mental activities like giveing somebody your phone number, reading books. Its characteristics are: it’s low, deliberate, effortful. 
 They are always active in humans when we are awake. System 1 is most of the time absorbing impressions, insights, and gives these imputes to System 2 which transforms them into actions without further elaborations. 
 However, System 1 may get in trouble if the first impression is not fully correct; System 2, if it’s asked to make a decision, it can produce the correct answer, taking a more active role (at a cost of greater effort). This dual system is efficient because it saves on cognitive costs. How is this connected to economics? The traditional model of rational decision making by economists is exclusively concerned with System 2 type of decisions (deliberate reasoning, people making decisions in a fully rational way), which often makes sense for economic applications. 
 However, research in behavioral economics and psychology show that System 1 (perceptions, impressions, intuitions) does have an impact on how real people take decisions and behave. This knowledge has mainly being obtained through experiments. This is also true for consumers and firms, and more over the distinction between System 1 and 2 is important to understand other’s behavior, but also our own. Reference to Microeconomics 
 The traditional, «neoclassical», approach to consumer behavior starts from the notion of preferences (or tastes). Suppose for simplicity that there exists only two goods, apples (A) and bananas (B), which can be consumer in different quantities. A basket (denoted with E) is any combination of the two goods. 
 Given two baskets E′ and E′′, consumers can prefer E to E′ (E ≻ E′), E′ to E (E ≺ E′), or be indifferent (E ∼ E′). 
 Behavioral Economics 1 Clara Corona Preferences have three characteristics: completeness, transitiveness and non-satiation. When consumers can always express a judgment comparing E and E′, they have complete preferences. Instead, preferences are transitive if E ≻ E′ and E′ ≻ E′′ implies E ≻ E′′. 
 Preferences satisfy non satiation if the consumer prefers a higher quantity of a good. 
 When preferences are complete and transitive we call them rational. When preferences are rational, we can represent them through the so-called utility function u(E), such that if E ≻ E′ then U(E) ≻ U(E′). The notion of utility in economics is a convenient way to represent preferences. If a consumer can choose within a set of baskets, maximizing utility means picking up the preferred basket given the preferences. 
 What does determine the set of baskets? Typically, consumer choice is affected by the fact that consumers have to pay a price to buy a good, and they have a limited income to spend. We call Pa and Pb the prices of A and B and I the income. paA + pbB = is the budget constraint. Suppose that we have a consumer that is fully rational (= complete and transitive preferences = utility function = idea of indifference curve). The latter is the set of baskets yielding the same utility, for instance baskets judged as indifferent by the consumer. Indifference curve Here, we have two indifference curves (u = 20, u = 10). In the higher one, E′′, the utility is also higher. In u = 10, there are E and E′, which are judged as indifferent by the consumer. 
 The shape comes from the idea that we start from point E, and then we start reducing the quantity of the good B, but at the same time we want to keep the utility fixed. We have to increase the quantity of good A to remain in the same indifference curve. 
 Behavioral Economics 2 Clara Corona Lesson 2 Gains, losses and reference points We are going to talk about the importance gains, losses and reference points have in decision making. On the one hand, there is an issue of what are the objects of preferences, and on the other, there is an issue on where these preferences come from. 
 
 Two persons get their monthly report from a broker. Carol is told that her wealth went from 4 million Euro to 3 million Euro. Amanda is told that her wealth went from 1 million to 1.1 million. Who is happier? 
 The answer depends on the argument of the utility function. If utility is defined on wealth (u(x)), we should say Carol is happier. However, we may thinks also as «natural» to say that Amanda is richer, while Carol is poorer. Relative evaluations, in addition to absolute evaluations, matter. 
 From a mathematical point of view, we can define in addition to the standard utility function, a value (increasing) function v(x-r) (the higher is the argument, the happier is the person) that measures the utility of outcome x with respect to a reference point r. A reference-dependent utility function is given by: 
 u’(x) = ρu(x) + v(x-r) 
 with ρ > 0 The higher is the value for ρ, the more is the absolute evaluation important. This is an example of a modification of the utility function, justified by evidence. 
 The reference point r leads to distinguish between gains (x > r) and losses (x < r). Gain is an outcome above the reference point; losses are below the reference point. 
 A lot of (experimental) evidence show that individuals tend to be “loss averse”. In words, loss aversion means that individuals dislike losses more than they like gains. The “x-r” is an increasing function; the idea is that, in general, people are happier with a gain than with a loss. With loss aversion, the dislike associated to loss tends to be higher than the increasing utility associated with a gain of the same level. 
 Fix a positive quantity g, the variation in income, or the quantity of the good. The idea that individuals are loss averse is the idea that, mathematically, v(-g) < -v(g) for g > 0. If g is positive, - Behavioral Economics 5 Clara Corona g is negative. It’s a loss of amount g. So v(-g), in general, is a loss and we can assume it’s a negative quantity; it’ll be smaller than -v(g). v(g) is the increasing utility due to the gain; if we punt in front of it a -, it becomes a negative quantity. If I consider losses for 10 in my wealth, the reduction in value would be higher more important than the increase in value associated with an increase of 10. 
 This loss aversion is considered as coming from a typical property of our individual preferences. In this definition, they are both negative quantities. If you put an absolute value, which is the way in which you can talk about importance, you get that the left term is lower than the right one. If you put a plus in front of the quantities g, then the left term would be greater than the right one. “More important” means a higher absolute value. 
 What affects r?
 - History (current wealth, past purchase experience) 
 - Expectations 
 - Framing effects, with which (essentially) equivalent descriptions of the same problem lead to different choices. 
 Consider the following problem: Your country is preparing to face a disease which is going to kill 600 persons, according to forecasts. There are two possible plans to implement: 
 Plan A: 200 persons will be saved for sure 
 Plan B: with probability 1/3 600 persons will be saved, with probability 2/3 no one will be saved 
 Most people chooses A. So far, just comparing A and B, you can’t talk about biases, because A is fine, B is fine as well. 
 Consider now the following problem: Your country is preparing to face a disease which is going to kill 600 persons, according to forecasts. There are two possible plans to implement: 
 Plan C: 400 persons will die for sure 
 Plan D: with probability 1/3 no person will die, with probability 2/3 600 persons will die 
 Most people choose D. Once again, there is nothing wrong in choosing between the two, it’s just a matter of preference. However, the two questions are simply a different formulation of the same choice. A=C and B=D! The difference lies in the fact that in A and B outcomes are expresses as gains, in C and D as losses. The idea is that individuals tend to be risk avers when it comes to gains, and risk lovers when loss is involved. 
 These were examples in which the reference point was manipulated by the framing. Sales, for instance, aim at modifying the consumer’s preferences because they could not know the initial price (= reference point). 
 Behavioral Economics 6 Clara Corona Risk, uncertainty and economic behavior Many economic situations involve lack of certainty (from the point of view of the decision maker) about the consequences of actions and the realized outcome. A good could be of high quality or low quality; in a holiday, the weather can be good or bad; financial investments can be profitable or not. 
 Usually, a distinction is made between situations of uncertainty and situations of risk. A situation of uncertainty occurs when the individual is unaware of all possible outcomes and/or he cannot exactly assess how likely are the different outcomes, i.e. he cannot assign (or is not given) probabilities. 
 In a situation of risk, instead, individuals know the possible outcomes and the corresponding probability. Although, most real world situations are of uncertainty, starting with decision under risk is a natural starting point. 
 
 We are going to talk about expected utility. The standard to way to represent choices under risk is through expected utility. Consider the following choice: 
 Alan has to make a choice about his car insurance. His wealth is 20 Euro, and his car has a value of 50 Euro. He has three possible actions: 
 - Full (theft + accident) insurance: costs 9 Euros, protects car against theft and accident 
 - Theft insurance: costs 6 Euros, protects car against theft 
 - No insurance: costs 0 Euros, no protection and a fine of 40 Euros if discovered by the police 
 
 We are talking about situations of risk, so the probability is given, objected and know by Alan. 
 Probability («car is stolen») = 0.05; 
 Probability («car is in an accident») = 0.05 
 Probability («stopped by police») = 0.10; 
 Probability («no theft, accident, police») = 0.80 The following table is the visual representation of the decision process of a situation under risk. Behavioral Economics 7 Clara Corona Often, individuals give too much importance to small probability events (overweighting of small probability). We buy lottery tickets; We avoid useful medical treatments, even when the probability of seriously negative consequences is very small. 
 Lesson 3
 
 Choosing when to act People are making evaluations not only absolute, but also relative to a reference point. Time matters in many economic situations (and decisions), because benefits and costs are spread over time. Several decisions are about when to do a certain thing: Should I study for the behavioral economics exam tonight (to get a high mark tomorrow), or should I go out with my friends? Should I eat healthy (and go to the gym), or go to McDonald’s (and watch the football match on the sofa)? Should I save, or should I spend all my income? 
 What these decisions have in common is that different actions are associated to benefits and costs over different periods. 
 More formally, suppose that there are T periods. In each period, and individual is getting a utility Ut in period t = 1, 2, ... , Y, which can be positive or negative (cost side of the decision process). The issue is to transform a sequence of utilities to overall intertemporal utility. Example
 Maria receives her homework on Friday morning, and must hand it in on Morning afternoon. She must decide when to do it. Assume that per-period utilities are defined by the following table: 
 This is a complete representation of Maria’s preferences, and for each there is the utility associated to it. Utility on Friday Utility on Saturday Utility on Sunday Utility on Monday Do it on Friday -5 5 10 4 Do it on Saturday 0 -5 10 10 Do it on Sunday 0 5 -5 10 Do it on Monday 0 5 10 -5 Behavioral Economics 10 Clara Corona The standard approach is to use a (intertemporal) utility function with exponential discounting, i.e: 
 The utility in each period is multiplied by a number (the discount) which is given by the discount factor (parameter of the model, delta) to the power of the number of periods from today up to the moment in which the utility is obtained. 
 0 ≤ δ ≤ 1 is the discount factor (“it is better an egg today, that a chicken tomorrow”): 10 Euro tomorrow are equivalent to δ10 Euro today. Small means impatience. 
 The higher is the exponent, the lower the quantity. The more distant is the future, the less importance is given in that specific period. 
 Often, we refer to the discount rate p, with δ = 1 / (1 + p) 
 This is the interest rate the individual would like to delay until the next period. Clearly δ and p depend on what a period is (e.g. a day, a year, etc). The higher is the discount factor, the lower will be the discount rate. We need first to compete the intertemporal utility and then look for the decisions giving the highest utilility. Moving to the right, we can see that the individual is getting more impatient, so he/she is giving higher importance to the presence than to the future. The best moment to do her homework, for Maria depends from the discount factor. When δ = 1, the highest number is 15, “do it on Saturday”. Intertemporal utility δ = 1 δ = 0.9 δ = 0.7 Do it on Friday 14 10.5 4.7 Do it on Saturday 15 10.9 4.8 Do it on Sunday 10 7.7 4.5 Do it on Monday 10 9.0 6.7 Not very impatient. Do it soon Not very impatient. Do it soon Impatient. Do it later Behavioral Economics 11 Clara Corona Why does it seem contradictory when we say “not very impatient” and Maria does her homework immediately? Doing the homework is a cost, is reducing utility. “Impatient” means getting the benefits as soon as possible; here, getting the benefits means postponing the actions. At a first glance, it could seem that Maria doing her homework on Monday would mean procrastinating; but it doesn’t go against her interests, because she is, in fact, maximizing utility. Doing the homework on Monday is perfectly rational if the discount factor is low. How real-world discount factors look like? 
 Consider the following questions: 
 - (Postpone receipt) You have just earned 200 Euro but have the possibility to delay receiving it by one year. How much money would you need to get after a year in order to want to delay the payment? 
 - (Postpone payment) You need to pay back a debt of 200 Euro, but have the possibility to delay payment by one year. How much money would you be willing to pay back after a year if payment is delayed? 
 - (Expedite receipt) You will get 200 Euro in one year, but have the chance to receive the money immediately. How much money would you accept now rather than have to wait a year? 
 - (Expedite payment) You need to pay back a debt of 200 Euro in one year but can pay it now. How much would you be willing to pay now rather than pay off the debt after one year? From questions like these, we can infer individuals’ discount factor. 
 These are the main results of a research (Benzion et al. 1989), five effects of the discount factor, which tell us how people think about their intertemporal preferences: 
 1. On average, the discount factor is relatively low (0.8/0.9) 
 2. The discount factor is higher, the longer it is necessary to wait: this is called short-term impatience
 3. The larger is the sum of money, the larger is the estimated discount factor: absolute magnitude effect 
 4. The estimated discount factor is smaller for gains than for losses: gain-loss asymmetry 
 5. The estimated discount factor is higher to postpone than to expedite payment, and higher to expedite than postpone receipt: delay-speed-up asymmetry 
 To sum-up: context effects matter! 
 Behavioral Economics 12 Clara Corona So we need to introduce quasi-hyperbolic discounting or (β, δ). For β < 1, individuals exhibit present bias. 
 β is the parameter measuring the degree of the present bias of the individual, the importance of all the future outcomes. β = 1 is the standard exponential discounting. β < 1 means you have a present bias; the future outcomes are multiplied by β which is smaller than 1, so you’re giving less importance, in the same way, to any outcome in the future. We have two parameters for two different aspects of discounting: treat differently the presence and the future independently from the moment of the future we’re talking about (β) The discount effect, captured by the parameter δ, if it’s close you are giving more importance. While when talking about Maria’s homework we had one parameter, now we have two, β and δ: 
 
 We consider δ fixed at 0,9; there are parts of the story in which individuals are discounting the future in the exponential discounting way according to the parameter δ = 0,9; then, we consider different values of the β parameter: 
 β = 1 (standard exponential discounting story, no present bias). The numbers are what you get when intertemporal utility is computed on Friday or Saturday. If Maria is given her homework on Friday, Friday is the present and Maria has an optimal choice on doing the homework on Saturday. On Saturday, Maria can again compute the intertemporal utility, because Saturday now becomes the present. The optimal choice is still to do the homework on Saturday, because the value of the intertemporal utility function is the highest on Saturday. The ranking is really important, and it’s always the same. β = 1; δ = 0,9 β = 0,9; δ = 0.9 β = 0,8; δ = 0.9 Plan On Friday On Saturday On Friday On Saturday On Friday On Saturday Do it on Friday 10.5 (-) 9.0 (-) 7.4 (-) Do it on Saturday 10.9 12.1 9.8 10.4 8.7 8.7 Do it on Sunday 7.7 8.6 7.0 8.2 6.2 7.9 Do it on Monday 9.0 10.0 8.1 9.5 7.2 9.0 Behavioral Economics 15 Clara Corona Each time in which you don’t have a present bias preference, choices are always time-consistent: you expect individuals, when they make a plan, they are always stick to the plan. This is an implication of full rationality according to exponential discounting; you have a plan and, when you arrive to the moment in which you are supposed to do something, you do it. 
 β = 0,9. Again, the optimal moment to do the homework is on Saturday. And when Saturday comes, for this parameter equal to 0,9, you see that there isn’t change. Even if there is a bit of present bias preference, there is no time inconsistency. Maria makes the plan, and then stick to the plan. 
 β = 0,8. On Friday, the optimal choice is to do the homework on Saturday. When Saturday comes, you re-compute everything and what you see is that the optimal choice is to do the homework on Monday (which has the highest number). We have time inconsistency: in intertemporal choice, in a moment of time you make a plan about the future in which you assume to do something, but when the moment comes, then it’s optimal for the individual to make another choice. In order to get time inconsistency, you must have present bias preference and quasi-hyperbolic discounting, and β < 1. 
 Consequences of time-inconsistency
 Consequences of time inconsistency will depend on whether people know they are time inconsistent or not. We define someone as “naive” if he is unaware to have present-biased preference. In our example, would plan on Friday to the homework on Saturday, without expecting to think differently on Saturday. Instead, someone is “sophisticated” if he knows to have present-biased preference. 
 Suppose that Maria is naive. In the homework example, she ends up doing the homework later than she expected and later than she would have done without a present bias. This is a case of procastination. 
 
 Imagine it costs 10 Euro to go the movies and Maria only has 11 Euro spending money. There are movies on Friday, Saturday, Sunday. Suppose her preferences are summarized in the following table. The movie on Sunday is preferred to the movie on Saturday, the one on Saturday to the one on Friday: 
 Payoff on Friday Saturday Sunday Go on Friday 5 0 0 Go on Saturday 0 6 0 Go on Sunday 0 0 8 Behavioral Economics 16 Clara Corona What’s the optimal choice for Maria? Let’s assume we are using the quasi-hyperbolic discounting model. 
 If we start with β = 1; δ = 0,9, on Friday the best movie is to wait until Sunday. When Saturday comes, again the optimal choice is to wait until Sunday. Once again, with exponential discounting, with the full rationality model, there can’t be time inconsistency. 
 What about β = 0,8? When Saturday comes, Saturday becomes better than waiting until Sunday. Saturday is the present, so the movie on Saturday becomes far more attractive than the movie on Sunday, because it’s in the present. While on Friday, both Saturday and Sunday are on the future and what prevails is the fact that movie on Sunday is preferred. Once again, we observe time inconsistency for a present bias preference because Maria on Friday has a plan, but then when Saturday arrives, she does something different than planned. 
 Now Maria is actually doing something earlier than expected and earlier that she would have done without the present bias. The plan is changing in another direction: it’s called prepoperation (the act of anticipating something), the opposite term for procrastination. Suppose now Maria is sophisticated, i.e. she knows it has a present bias. In the homework case (delayed benefits), sophistication solves the problem: Maria will do her homework on Friday, because she knows that the actual choice is between Friday and Monday, and the outcome is the same as if time consistent. 
 In the movie case (delayed costs), with sophistication the actual choice is on Friday between Friday and Saturday, so she will choose Friday. Therefore she will preproperate even more, getting lower utility! The problem is with sophistication without commitment (say, Maria pre-orders Sunday movie ticket). Commitment is the possibility for the individual to restrict completely the set of future actions, limiting the possibilities. Suppose Maria has the possibility to preorder and buy in advance for a movie. She would buy and pay for the price of the movie on Sunday; she’s β = 1; δ = 0,9 β = 1; δ = 0,9 β = 0,8; δ = 0.9 β = 0,8; δ = 0.9 Plan On Friday On Saturday On Friday On Saturday Do it on Friday 5.0 (-) 5.0 (-) Do it on Saturday 5.4 6.0 4.3 6.0 Do it on Sunday 6.5 7.2 5.2 5.8 Behavioral Economics 17 Clara Corona We now look at a model to understand preferences over sequences. 
 Consider a sequence x1, x2, x3, xt. Define now the sequence x over bar 1, x over bar 2… where This is the smoothed sequence. 
 
 For every period we define which is the total difference in utility between the smooth sequence and the actual sequence. 
 We consider the following utility function: 
 We say that the anticipated utility of receiving sequence is given by AU = ∑( − 1) 
 If Maria is going to receive payoff x at t, she spends t-1 periods anticipating this. 
 We say that the recollected utility of receiving sequence is given by IU = ∑( − ) 
 If Maria is going to receive payoff x at t, she has T-t periods recollecting this. 
 Individuals not only care about the utility in the present, but also care about expectations about future events and memories about past events. 
 We can show that ∑ =0.5(AU-RU). This means that:
 > 0 is a preference for improving sequence 
 > 0 < 0 is a preference for one-sided (smooth) sequence 
 Evidence suggest a preference for > 0 and < 0. Behavioral Economics 20 Clara Corona Lesson 5 Game theory 
 So far, we discuss behavior and choice of individuals in isolation. 
 Given preferences (over absolute or relative outcomes) and (budget) constraints, the problem to be solved is a (relatively simple) maximization problem. 
 In the next few classes, we will instead consider the behavior of interacting agents. What the theory predicts. What experiments tell us about the behavior of interacting agents. 
 
 Game theory deals with strategic interaction. There is strategic interaction when the utility of an individual (or the profit of a firm) depends on the actions chosen by other agents (and not only by the action he/she chooses), and the agents are aware of this interdependence. 
 Oligopolistic markets (where few firms are active) are examples of strategic interaction. Game theory can apply to «real» games (e.g. chess) or many other social situations (such as manager- workers interaction). 
 Players: the set of agents taking decisions and interacting strategically. 
 Actions: the set of “moves” available to players. 
 Strategies: a strategy assigns an action for each possible situation in which the player has to take a decision (strategy=complete plan of action). 
 Pay-offs: the outcome of the game for each player as a function of all players’ strategies. In general, payoffs are to be defined in terms of utility. 
 In simultaneous games, all players choose their actions without knowing the actions of the other players. Otherwise, the same is sequential. We consider only complete information games, in which all players know what are the possible set of strategies and the payoffs for all players. 
 
 Two suspects in a crime are put into separate cells. If they both confess, each will be sentenced to six years in prison. If only one of them confesses, he will be freed and used as a witness against the other, who will receive a sentence of seven years. If neither confesses, they will both be convicted of a minor offense and spend one year in prison. 
 
 THIS IS AN EXAMPLE OF A SIMULTANEOUS GAME Behavioral Economics 21 Clara Corona Players: the two criminals (1 and 2) 
 Strategies (=actions): “confess" “not confess" 
 Payoffs: 
 A solution for a game is a procedure giving you a prediction about what the players will do in a specific setting. The first solution is the Nash equilibrium (for a game with two players): a pair of strategy such that the choice of each player maximizes his payoff given the choice of the other player. 
 A dominant strategy for a player is a strategy which is optimal (=maximizes the payoff) for any strategy by the opponent. 
 If both players have a dominant strategy, the pair of these strategies is a Nash equilibrium in dominant strategies. 
 
 In a NE, all players have expectations about the actions chosen by the other players, which turn out to be correct. A NE can be interpreted as: 
 - A self-enforcing agreement. 
 - The outcome a learning process. 
 - The consequence of a high degree of knowledge and rationality on the players’ side. Behavioral Economics 22 Clara Corona In order to be a credible threat, I would need some form of commitment, «forcing» it to play low price in case of entry. 
 Although the theory expresses payoffs in terms of utility, traditionally most applications equate payoffs with the individual, material payoff. 
 If this assumption is incorrect, predictions of game theory may be wrong. 
 Indeed, experimental evidence has suggested deviations from the «standard» predictions which suggest an important role for «social preferences». 
 We will consider the case of the ultimatum game. 
 
 
 A game can have multiple Nash equilibria. A particular important case is when players play coordination games, in which it is advantageous for players to choose the same action. 
 For this case, game theorists have developed theories to select specific equilibria through refinements of Nash equilibrium. An alternative approach is to assume that factors outside the game may help the players to pick up a specific equilibrium. 
 We will consider the example of the «battle of sexes» game. A couple needs to decide what to do in the evening. There are only two options: going to a football match, which is the preferred option by the man, and going to the cinema, which is the preferred option by the woman. They could also prefer to do the same thing, rather than going alone to the preferred alternative. It implies there are two Nash equilibria (in pure strategy): one in which the two players play the strategy preferred by player 1, one in which they play the strategy preferred by player 2. 
 
 There is also mixed strategy equilibrium, for which players are choosing strategy with a certain probability, they are randomizing. In this game, the equilibrium in mixed strategy is a situation in which each player is peaking at random one of the two options. What happened in the game? It was built to make coordination very, very difficult. Basically, most of us start playing completely at random; and when it happens, mixed strategy equilibrium is at stake. What is then the expected payoff? If you play at random, with a probability 0.5, you don’t coordinate, so you get 0. 
 At the beginning, the average payoff was 1.5, because you were trying to coordinate but it was difficult. Then, after a while, especially in groups that were playing on Friday, they were able to get a bit of coordination and the payoff was moving to 2, because some pair of players were actually Behavioral Economics 25 Clara Corona getting a coordinated choice. 
 It is not surprising, because the number of times in which you were repeating the game was relatively short, and you were not given the elements in terms of the description of the game, to get coordinated choice. Coordination games like the battle of sexes are very common: Should we drive on the right or on the left? Coordination with many players and many actions is difficult. 
 Some equilibria (i.e. some strategy/action) might be focal and be a natural outcome for a coordinated choice. But where do focal points come from? It depends on salience, which means that “something is important”. 
 - Primary salience hypothesis: when people need to choose one option among many in order to coordinate, they peak the option that is most salient to them, and since there are situation in which the same option is simultaneously salient to many people, then coordinated choice emerges. 
 - Secondary salience hypothesis: people expect others to use primary salience and so choose the option they think will have primary salience for others. 
 - Schelling salience hypothesis: people ignore what is primary or secondary salient and look for some key or clue to coordinate. “Schelling” comes from the man who developed the Battle of The Sexes game, a nobel prize in Economics for his contribution in game theory. Suppose that two friends should meet in a big city. They can’t talk and agree for a specific space, but suppose they agree for the time, maybe the afternoon. Suppose the city it’s Milan. Primary salience hypothesis means they both think about the most natural place to visit; suppose they think about Piazza del Duomo, and then they meet. 
 Secondary: If I am a football fan, maybe my first idea is San Siro. But since I expect my friend, not a particular fan of football to go to Piazza del Duomo, then I go there as well. 
 Schelling: idea that people are not thinking about salience, but try to think about general ideas to Behavioral Economics 26 Clara Corona solve the coordination problem. In the example, could be that since we are both coming to Milan by train, each of us think that is quite natural when you go to a city you don’t know to go the main station, so they go to the central station in Milan. Ask people to play very simple coordination games, in which players don’t have a preference for a equilibrium after the other, they just want to coordinate. 
 The two problems are “write down any year” or “write down any positive number”. There were 2 scenarios in the experiment: players were not given any incentive to match (here the payoff was fixed, they were given some money to partecipate and they gave the answer they wanted). This scenario is useful to get the primary salient option. In the “No incentive to match” column, you see there is no answer emerging in both cases. Then, in the “Incentive to match” scenario, players were rewarded to obtain coordination; in this case, most people were giving a specific answer (1990) and 1 in the case of numbers. 
 Why 1990? The research was conducted in 1990, even if the paper was published in 1994. This yeas was thought as a natural solution to the program. People actually are not using the primary salience hypothesis; when you say people “just say the first thing in your mind”, they say different thing and, when they have to coordinate, they use other types of salience. 
 It’s not simple to say if they are using the second or the Schelling here. For instance, if you look at the question “Write down any positive number” you see that people are using Schelling salience Behavioral Economics 27 Clara Corona Consider two employees, senior (S) and junior (J) involved in a team activity with two required actions (to guarantee firm’s positive profit): one pleasant (P) - one unpleasant (UP). If the team activity is for students to prepare a presentation, there are several tasks to do, and maybe of them are funny, or preparing the presentation, writing down could turn to be boring. 
 The payoff is positive because is guaranteeing a positive profit for the firm, when one player is choosing the pleasant while the other is choosing the unpleasant action. All the actions are chosen, and so are all the steps required; however, the two players disagree on what is the best outcome because they both prefer the outcome in which they do the pleasant action. There are two Nash equilibria here. The firms needs to rely on the coordination by the team. In this case, the risk is form the company that there is not coordination. How could it be got? Share at the company level a norm which is saying who should do the pleasant or unpleasant action; in this case, there is a natural way to think about norms, because of the different age of the employees. There is a senior one, and a junior one. We could think about two norms: 1) seniors are more important, so juniors should peak up the unpleasant action; 2) seniors should defer to juniors, who are more important than seniors. 
 If you share one of the two norms, this is creating a focal point to solve the game. From the point of view of the firm, in this specific example, two corporate cultures are exactly equal, because in the end they produce the same outcome: each player is choosing one specific action (the problem of coordination is solved). 
 Behavioral Economics 30 Clara Corona Focal points can come from intentional strategy from firms, or can take the form of culture. They don’t come from elements of the game! 
 
 
 The Ultimatum Game
 In the traditional game theory approach, payoffs are thought in terms of utility. Concretely, when you move to applications the assumption is that for players, what really matters is the material payoff. If this assumption is incorrect, predictions of game theory may be wrong. 
 Indeed, experimental evidence has suggested deviations from the «standard» predictions which suggest an important role for «social preferences». We will consider the case of the ultimatum game. 
 There are two players who play sequentially; one is a proposal, who is given a certain amount of money, then he is asked he wants to give to a second player, the receiver, who has a strategy set which is very simple: he can say yes or no. The receiver either accepts or rejects the offer. If she accepts both receiver and proposer get their share. If she rejects both get nothing. 
 If you assume that a receiver which is indifferent between accepting and rejecting accept, then in a subgame perfect equilibrium the proposer proposes 0 (and keep 100), and the receiver accepts. 
 
 Results of an experiment. In this image, we have the summary of a game played in reality. In the horizontal axe, we have the same of the proposal; the size of the circle is the frequency of the proposal. Behavioral Economics 31 Clara Corona For any amount of money, the higher circle is the 0.5 proposal, which means sharing the amount of money. The second one is around 0.4. Rejecting offers in ultimatum game It seems that individuals are inequality averse: they get a disutility if they get less than the others. Therefore, they may sacrifice some of her material payoff to obtain a more equitable offer. Notice that if the receiver is inequality averse, the proposer may not propose 0 even if she is not inequality averse (since she does not want her offer to be rejected), expecting an «unfair» offer to be rejected. 
 This may be the case of firms making take-or- leave-it offers by fixing posted prices (or wages) 
 
 Kanheman, Knetch and Thaler, 1986. When is a firm price increase (or wage decrease) considered «fair»? (by consumers, workers or the general public). 
 They refer to the theory of dual entitlements, based on the notion of reference transaction. A reference transaction is a precedent, which determines a reference price (wage) for consumers (workers) and a reference profit for firms. An increase of profits above the reference level is unfair if it is obtained by increasing price (reducing wage) above (below) the reference point. 
 Instead, if something happens so that a reference profit of the firm is threatened, the change of price or wage is perceived fair. 
 
 Behavioral Economics 32 Clara Corona declines with age, which means that the younger people are actually the groups who is less happy (maybe because they spend their time attending university courses…). To what extent life-changing events have an impact on happiness? In this research by Brickman et al. (1978), which is quite old now, they have presented declarations of happiness of people in three situations: the “control group”, for which nothing relevant happened recently; the “lottery winners” were people that recently were lucky to win at the lottery a significant amount of money; the “accident victims”, affected by a significative negative event. 
 First, we look at the “control group”, nothing particularly relevant happened. There are three bars on the vertical axe, which is moving on a 0-5 scale. The bar on the left is referring to past evaluations; in the middle the evaluations of the present; in the right, evaluations for the future. In this group it can be said that there is a natural tendency of people considering themselves happier in the present than they were in the past, and more over they expect to be even happier in the future. It’s a kind of benchmark. And what about lottery winners? The tendency is the same, for the present to be better than the past, but comparing the two groups, you see that there is a small present effect. Lottery winners tend to be happier than the Control group in the present. The other result is that if you compare the white bars of the two groups, it’s a bit higher for Lottery winners, but the difference is pretty small. It means that the present effect is small, but the future one is even smaller for good events. 
 Behavioral Economics 35 Clara Corona If you look at bad events, paying attention to the Accident victims category, you see that the present effect is much more significant; the reduction in declared happiness is much higher for Accident victims compared to the increase in happiness for Lottery winners. Loss aversion appears here, for the present. But if you look at the future, the Accident victims are those actually expecting the higher level of happiness in the future. It means that following bad events, people tend to be more optimistic, they think they now they are very unhappy but life will be better in the future. 
 Accident victims tend to have an evaluation of the past which is very high, the highest compared to the other groups. So accident victims tend to remember the past as a period in which, compared to present, there was a period which turned to be particularly happy. This is clearly related to the fact that people tend to make relative evaluations. 
 It’s like what we have been thinking during this whole pandemic situation, because if we think about the past, before the start of the Covid-19 era, we were much happier than we are today, but probably we also consider ourselves much happier than we were in reality. Another point to focus on is the correlation between life satisfaction and relative income. In the vertical axe, we see the percentage of respondents that were giving a particular answer; the six bars, instead, are related to different levels of income. For each income category, we have the percentage of people who declared themselves “very happy”, “fairly happy”, “not very happy”. The percentage of the latter is getting lower and lower with higher level of income, while the fraction of very happy people is getting higher. 
 Behavioral Economics 36 Clara Corona If you compare the life satisfaction across individuals in a given moment of time, through the so- called “cross section”, you are considering a group of people in a specific moment, in a specific country, and you look at the answers. Here we see that the higher is the income, the higher is the relative happiness. 
 However, things are slightly different when you look at life satisfaction and national income. So there is a positive correlation between the level of income and the mean life satisfaction of people in the country. Living in a richer country, on average, plays a great role in life satisfaction. 
 What is surprising, instead, is what we discover comparing life satisfaction and changes in national income in a specific country. Here, we compare the data about income and happiness over time. On the vertical axe on the right, we have the median income, and the line corresponding is a positive slope. If you look, instead, at the proportion of people that declared to be very happy (represented by the crosses), there is not any evident trend. There are variations over time, but after all, there was much less clear behavior. If you draw a correlation between income and the proportion of happy people, it is basically absent, because one line is getting higher, whereas the other (the crosses) are moving up and down. Behavioral Economics 37 Clara Corona Kanheman calls it), whereas total utility is the accumulated instant utility of an activity. More over, remembered utility is the perception of total utility from the past activity, and is likely to influence decision utility. 
 If we think of an event occurred through time, like a holiday, typically it can be thought as a sequence of moment, in each of which we have utility satisfaction positive or negative. This is the sequence of instant utility. Total utility, instead, is the sum of these moments If we think about decision utility in situations like these, it may be the case that you can’t predict everything (uncertainty ex ante), and more than that, the total utility you have from an experience should be equal to a remember utility. 
 
 The latter idea is not always true. An experiment like the one that follows is sometimes called “hand in the cold water experiment”. The story is that: suppose you have a group of people, and you ask them to put their hands in cold water. The water is sufficiently cold so that it’s a bad experience; the instant utility is so negative. On the vertical axe we have instant utility and a minus, and a scale because people were asked to express the “disutility” of their experience. The individuals were actually asked to run two different experiments, each one with a different hand, and they turned out to be slightly different. The first one was organized as following: they were asked to put their hand underwater at 14 degrees for 60 seconds. We can see from the graph that the curve corresponds from 0 to almost -9 (instant utility). For the second experiment, the situation was almost the same up until 60 seconds had passed (for instant utility, for the time of one minute the situation was equal between the two scenarios). Then, there is an addition of 30 seconds which, in terms of instant Behavioral Economics 40 Clara Corona utility, produces a lower disutility, perfectly understandable because the temperature is a bit higher (15 degrees). If we compare the two situations in terms to the total utility attached, we can say that the act of adding 30 seconds in the 2nd trial, we are adding 30 seconds of bad experience, and producing a lower total utility. This means that individuals should clearly have a preference for the first one (60 second trial). What did Kanheman et al. do? They collected data for instance utility and then ask, at the end, a number of questions trying to infere the evaluation of the overall experience in terms of Remember utility. On the vertical axe is the relative answer to the four questions, between the 90 seconds compared to the 60 seconds trial, on the -5 +5 scale. The positive measures mean that individuals were answering more frequently yes for the 90 seconds rather than the 60 second trials; the negative measures mean exactly the same. 
 The first three questions are directly an evaluation of the pain or disutility created by the two experiences, and are “which of the two caused the greatest discomfort?”, “which was the tougher to cope with?” and others like these, as it can be seen from the graph. Behavioral Economics 41 Clara Corona In all the three cases, individuals were answering that the 60 seconds trial was the most significant. For most individuals, it was that experience which caused more discomfort, and also colder, and tougher to cope with. And it’s surprising that, contrary to what we should expect from their own evaluation of instant utility, they were saying the first experiment had been the hardest to deal with. 
 The important point to stress is that these answers are in contradiction with those given by the same individuals in terms of instant utility. If we look at the second question, the 90 seconds trial wasn’t colder. Finally, the last question is interesting: the answer is positive, so people said that the 90 seconds trial had been longer. In this case, they are correct. It turns out that the problem is not that people don’t understand which experience was longer or shorter; however, there is systematic difference between the remember and total utility for the two cases. This is what is called the “peak- end evaluation”, that Kanheman was mentioning. It seems that individuals are not using the integration principle to determine their remember utility; the latter is not the total utility of an experience. 
 But there is another way for individuals to map the sequence of instant utility, called the “peak-end evaluation principle”: for individuals, not all the moments are equally important. In fact, there are two types of moments that really determine remember utility: 1) the peak, the most significant and intense moments in positive or negative sense; 2) what is happening at the end of the story what really matters. 
 Duration neglect, instead, is the idea for which it’s not the length which is determining the total utility. If we look at the graph paying attention to the peak-end evaluation, why the 90 seconds trial was considered less negative by individuals? Because the peak isn’t in the ends of the trial. If you think about restaurants, the end is the dessert, the moment to which you pay the most attention! Behavioral Economics 42 Clara Corona Secondly, they would have had the consumption. Obviously, the moment of the consumption in the future should matter, because if you consume the good after lunch, you are probably less hungry. Instead, the moment in which the question is asked should be irrelevant. 
 It turns out, instead, that the moment in which you ask the question is important. We should expect that the two bars on the left should be higher than the two on the right; people are able to put themselves in decision utility at the moment, and to ask for the unhealthy snack when they are more hungry. What is instead surprising, is that the moment of asking the question is important; if you ask it in late afternoon, people tend to say more frequently that they want the unhealthy snack independently from the moment in which it will be consumed. The idea is that current mood has an impact on future choices. 
 
 We have seen evidence that people are time-inconsistent in choice (present day bias); that people may not know that is good for them (different between remembered and total utility; projection bias). So to what extent people value choices? 
 Let’s talk about commitment by asking people what they are going to do. People were asked to have a plan about the future, but then they were asked to make the actual choice when the moment has come. It turns out that their answers, when they were initially asked, have an impact on their actual choice. Behavioral Economics 45 Clara Corona Remember than when people were asked late afternoon, they were more incline to consume the unhealthy snack. How we should read these bars? “Actual” is the whole bar, whereas the “predicted” is the yellow/green part. It turns out that the actual choice of the unhealthy snack is always higher than the predicted choice. 
 If you look at the actual consumption, there is a difference if the individual was asked late afternoon and after lunch. The bars are not so different for “Chose late afternoon”; however, the difference is more visible is we look at the choice after lunch. The fact that you are saying “no, I don’t want junk food” is a very light form of commitment but has some impact. What people say are going to do in the future HAS an impact. Look at how things change when people write down things. Having a muffin before going shopping reduces unplanned purchases. Behavioral Economics 46 Clara Corona Lesson 12 Last time, we saw how commitment can occur even relatively with light interventions like answering telling in advance what you are going to do or write down. Now we are going to see the complementary point to what extent this can actually have a significant impact on consumers’ satisfaction. 
 Here we are proposing a couple of examples, showing that even if the individual has a very small size of present bias, still the impact on utility can be large because of the tendency of time inconsistency to accumulate its effects over time. This is an elaboration of the example of managing deadlines. There is an action to take referring to the homework, and it can be taken each day before the deadline. In this example, in the day in which you do the homework or you take your action, you get 0 because of the immediate cost associated to the action; while, on the other days, you get 100. If you don’t do the homework immediately, in the day before you are doing the homework, your utility is not 100 but 99. 
 Given these values, first we can compute the total utility. Let us assume, for simplicity, that here is no standard discounting, so the parameter delta is 1; however, the individual is associated with some degrees of present bias, so there is a parameter beta which is 0.98. The model we are using is the standard model beta-delta (the quasi hyperbolic discounting model). The individual is very close to be fully rational and not have present bias. Behavioral Economics 47 Clara Corona Another way to see the value of commitment is to show that commitment can be good even if it’s actually reducing flexibility. This is an experiment by Dan Ariely. He asked a grouped of students to do their homework (read a number of texts and find grammar errors and alike); a simple task but which regarded attention. There were different scenarios in terms of how the work could be managed by the students; since there were more than 1 text, they were assigned different rules about the time in which to send the work to the Professor. In one case, the students were just given all the texts to look through and the deadline was just at the end of the period for everyone. In the second case, the students were given separate deadlines for the texts, and they were evenly spaced in time (like 10 texts to read and each text was given a deadline in a specific way). Then there is the situation of self imposed deadlines, in which students were asked to announce in advance their own deadlines. 
 We have three different situations. Then, Ariely was looking at the performance in the three scenarios: 1) looking at errors detected; 2) delays in submission; 3) earnings, because there were incentives to do the homework. 
 In a standard setting of rationality, it should not be any difference. In fact, why the management of the deadline should matter? After all, the deadline is just an external constraint. 
 
 What we can see is that there is clearly not a similar scenario. What is interesting is that the best scenario for students and the Professor, in a sense of earning for students and errors detected and no delays, is when deadlines were evenly spaced in time, and externally given. The worst situation is when deadlines are all together in the end. 
 Behavioral Economics 50 Clara Corona This means that, for students, having less flexibility was actually better. Having external constraints about what to do was improving their performance; having more flexibility and freedom was actually reducing their performance. This is an example made using students, but you can see immediately the applications to companies and business employees. One mechanism because reduction of freedom works here is because individuals tend to be time-inconsistent. Let’s see the video “The paradox of choice https://www.youtube.com/watch?v=VO6XEQIsCoM” by the famous psychologist Barry Schwartz, who explains why for individual it is better to have less alternatives to choose among. 
 More choice is not necessary better. Schwarz was giving a number of reasons why; one of the paper showing these results through experiment is this quite famous by Iyengar and Lepper (2000), a field experiment (run with people who aren’t aware in being in a psychological experiment). It was organized in a supermarket and involved chocolate. Consumers were proposed a set of alternatives (different types of chocolate), and then they were allowed, if they wanted, to buy this. First, there was limited and extensive choice; second, some consumers were allowed to choose the type of chocolate to try, whereas others were given pieces of chocolate at random. It turns out that people were much more likely to choose the piece of chocolate if they were given limited choice, so if the number of alternatives was small, and actually they were allowed to try the chocolate they selected. The two things together are important. The story is that if you are in charge of making a decision, it’s better to have less alternatives: the lower possibility of regret, the lower expectations Behavioral Economics 51 Clara Corona towards what we haven’t tried. When you aren’t responsible of the choice, then the size of the alternative set is not important. 
 In the same experiment, there were some questions posed to individuals the importance to different type of mechanisms. On the vertical axe we have, according to the questions, the time spent in making the choice (in seconds) and the type of questions that can be answered on a “likert scale”. When choice was extensive, this was requiring more time for the individual to make a choice, and individuals were much more likely to answer “too many choice” or “process was difficult”. What is interesting is that, at the end, people were much less likely to feel satisfied with the sample chocolate they tried. In this table, we see that in extensive choice there was one answer in contrast with the others: the fact that more people were actually enjoying the process. All this literature is not saying that people “don’t like to make choice”. However, what people don’t like on average is to make complicated choice. There is this trade-off: they would like to be in charge of the choice, but when alternatives are wide, they don’t like it. 
 1) For people, having an extensive amount of alternatives is particularly negative, is disliked, when they are facing a choice that is unfamiliar for them. So if I’m put in a context I know well, for me it’s not a problem to face alternatives, because I know that I expect. However, in other situations, when choice is unfamiliar it is not appreciated. 
 2) Since people do like to make a choice, but they want to deal with relatively simple choices, it turns out that people tend to be less dissatisfied with extensive set of alternatives when the options that are given, are grouped in different categories. Suppose you are going to watch a movie on Behavioral Economics 52 Clara Corona Suppose the firm decides k first (long run choice), and then p (short run choice). When the firm decides k (long run), the relevant costs are those associated both to capacity and production (fixed and variable), since the firm will base its choice on its expectation about the level of production. 
 When the firm decides p (short run), the relevant costs are only those associated to production (fixed and variable), since the decision about capacity has already been made (“sunk” costs are associated to investments choices you made in the past and currently you can’t change). 
 This is the standard view based on rationality; the idea that everything than can’t be changed, shouldn’t be relevant in your choice. 
 Experiments suggest that people tend to behave in a different way, i.e. sunk costs affect their decision (“sunk cost fallacy”). Suppose you decide to start going to the gym every week; you pay immediately for 6 months. According to the standard view of rationality, what you pay for getting the 6-month membership to the gym should be irrelevant in you choice because that money is gone. However, people sometimes think that if they don’t go, they are losing something. This is a psychologically common thought, but it’s not rational in a standard sense, because once the money is gone, you shouldn’t pay attention to it anymore. The idea here is that given this relationship between the cost and the notion of production and capacity, we can define cost functions, defined with respect to production and the capacity levels. The total cost function is defined as follows: total cost (fixed + variable) associated to a given level of production C(q;k). 
 The average cost function, instead, is defined as the average cost of production as a function of q: AC(q;k)=C(q;k)/q. 
 The marginal cost function is the cost to produce an additional unit of a good, as a function of q: 
 Any notion of cost function (total, average and marginal) can be defined as for long and short run. We’ll have a total long run cost function (the total cost associated with a given level of production and capacity); and the same is for average and marginal. 
 Behavioral Economics 55 Clara Corona Suppose that building a hotel of size k (its capacity) implies a fixed cost F and unit cost equal to r. The bigger the hotel, the larger the number of rooms, the higher will be the cost associated to capacity. Moreover, serving q customers implies a cost cq (for example, the cost for cleaning rooms, serving breakfast in the morning etc). 
 The long run total cost function is given by: Look at q < or equal to k. Why? These are the costs if you produce the quantity up to the capacity level. For producing higher than the capacity level, you have a cost which is equal to infinity. This formulation is written like this because is saying that you can’t produce more than the capacity level. 
 The short run total cost function, instead, is given by: Here, k doesn’t enter into the cost, because in the short run, F and rk are sunk, so the only elements we have are cq. The latter is the cost if q < k since we can’t produce more than k, and the total cost would be infinite if q > k.
 So, in the long run capacity costs are relevant together with production costs, whereas in the short run only production costs are relevant. 
 The total cost function (both long run and short run) can be classified according to returns to scale: 
 • Returns to scale are constant if AC(q) is constant. Ex: C(q) = cq. If returns to scale are constant, your average cost of production is independent from production; the cost to produce one unit of the good is always the same. 
 • Returns to scale are increasing if AC(q) is decreasing. The bigger you are, the lower is the average cost. Ex: C(q) = F + cq. The bigger is q, the lower will be the average cost, and the intuition is that if there’s a fixed cost of production which is independent from the production level, it means that Behavioral Economics 56 Clara Corona the more you produce, the more you can spread these fixed costs over your production, so theaverage cost will be lower. 
 • Returns to scale are decreasing if AC(q) is increasing. The bigger you are, the less efficient you are. Ex: C(q) = cq^2 
 If there are increasing returns to scale, we also say there are economies of scale. Instead, if there are decreasing returns to scale, we also say there are diseconomies of scale. 
 It is possible for a cost function to have different returns for different levels of production. For instance, you may have both a fixed cost and the variable part which is quadratic. In this example, if we compute the average cost and we draw it, we get a U-shaped function: C(q) = F + cq^2. At the beginning, the average cost is going down (there are increasing returns), but after a while there are decreasing returns. Let’s assume the firm can assume a single price (uniform or linear prices, which means the price is the same for all the consumers and for all the units bought by the same consumer). If that is the assumption, than the total revenue function (TR) is mapping the quantity demanded or produced into the level of the total revenues: TR(q) = pq. Instead, marginal revenues function (MR) maps the quantity into the revenues from selling an additional unit: MR = dTR/dq. Mathematically, it’s the derivate of the total revenue function respect to the quantity. Notice that the average revenue, if the price is uniform, is simply equal to price (because all the units are sold at the same price). 
 
 The monopoly model
 There is a single firm in the market, and we’re going to focus first on short-run analysis, and the capacity will be given but also large: k can not be changed by the firm, and it’s large enough that it's never a constraint. In the monopoly, the firm is choosing the price and the latter defines the quantity, or the firm is choosing the quantity to sell and then the price is determined by the demand function in order to have that quantity demanded. It’s one to one correspondance, given by the demand function. 
 What are the behavioral assumptions? The idea is that given the demand and cost function, the firm is willing to maximize its profits: 
 The choice of optimal (= profit maximizing) quantity follows the profit maximization rule [MR = Behavioral Economics 57 Clara Corona However, there are limits to the market power which are associated with demand elasticity: 
 
 It is possibile to show that mathematically, in equilibrium, that there’s a very important relationship between the degree of market power and demand elasticity: 
 So if a firm wants to maximize profits, it must satisfy this condition. The Lerner index is a measure of market power because is increasing in the difference between the price and the marginal cost, and then it’s divided by the price. The lower value of the Lerner index we can expect is 0, because we can expect that the firm is not fixing a price below the marginal cost (because it has always the possibility not to produce). If the firm fixes a price below the marginal cost, it will get a loss. The maximum value for the Lerner index, instead, is 1, because if the price is getting larger and larger, p* - c becomes irrelevant. 
 The rich term, instead, is the inverse of demand elasticity. 
 The most important claim from the monopoly analysis is that there exists and inverse relationship between market power and elasticity of demand. The lower is elasticity, the higher is market power. Behavioral Economics 60 Clara Corona So, for firms, market power comes from the fact that they are able to face a demand elasticity which is low. 
 In addition to preferences of consumers, there may be also some cognitive factors related to the level of rationality that can affect how big or small is demand elasticity. However, from the point of view of the firm, low demand elasticity is good, whereas high demand elasticity is bad. 
 If elasticity is large, the firm cannot increase the price too much without reducing the quantity sold. So it’s true that a monopolist has control over price but, first of all, he’s willing to maximize profits. So if increasing the price is creating a big negative jump in the quantity demanded, it’s something that the monopolist doesn’t want. 
 The elasticity of demand limits the monopolist’s market power.
 
 The monopoly in the short run: the role of capacity 
 Let’s consider a numerical example with large k.
 Inverse demand: P(q) = 10 − q
 Costs: C(q) = 2q 
 k = 5 
 
 
 q = 4 is smaller than the capacity: if the firm is just applying the profit maximization rule ignoring capacity it gets 4. 
 Large capacity means that it’s a capacity you can safely ignore, you can maximize profits as if there aren’t errors, no problems in terms of capacity constraints, because the quantity which is maximizing profits is below your capacity. Behavioral Economics 61 Clara Corona Let’s consider a numerical example with small k.
 Inverse demand: P(q) = 10 − q
 Costs: C(q) = 2q 
 k = 2
 The firm can’t produce 4, because it’s greater than k = 2. So you must get as close to 4 as possible, because it’s the quantity you would produce. So you must produce 2 (q=k=2) fixing a price equal to 8 (=10-k). The following is the graphical representation between profits and quantity. The profit function is given by TR - marginal cost, so 10q - q^2 - 2q = 8q - q^2. Why? Because at the beginning, when you increase quantity, the profit goes up to a quantity equal to 4. But then, if you want to sell more, your profits start going down (because we need the price to be reduced. 4 is the maximum point. If the capacity is above the quantity which is maximizing the profits, I can just ignore and not produce all my capacity. 
 
 About long run analysis, if there is no uncertainty about demand, capacity will be chosen by the monopolist exactly equal to the quantity the firm will produce. Therefore, the firm maximizes its profit with respect to q, using the long run cost function (which includes capacity cost), instead of the short run one. Since long run and short run cost functions usually differ, short and long run decisions will differ as well. 
 Moreover, in the long run, the decision to stay in the market or exit becomes relevant. The firm stays in the market if its profits are non – negative. Behavioral Economics 62 Clara Corona In a market, total surplus is maximized when demand function and marginal cost functions cross. Here, FB stands for First Best. 
 Why is this the point where we want to get the maximum surplus? Because on the inverse demand function, we have the willingness to pay of consumers, and it would be decreasing in the quantity. As long as the willingness to pay is above the marginal cost, this means that consumers are evaluating the good more than the good costs to the firm. So, we want to produce up to the point where the price is equal to the marginal cost, because if you produce more than qFB, the inverse demand function (the willingness to pay) is below the marginal cost. In the latter case, you would destroy value. What happens in monopoly? The point on which the marginal cost and the inverse demand function cross is where we maximize total surplus. The area that is not obtained under monopoly with respect to the area that would be First Best is called the “welfare loss”, the best possibile situation in which the price is equal to the marginal cost. In that case, the total surplus would be equal to these three areas (green, red and violet). But then, if we are in monopoly, this triangle is loss. It’s a welfare loss in the sense it’s an area not obtained neither by the firm, nor by the consumers. Behavioral Economics 65 Clara Corona This means that the monopoly outcome is inefficient from the social point of view. Why there is this welfare which is lost? From the social point of view, you want to produce when the price is greater than the marginal cost. If you are a monopolist, you only care about your profits; and produce whenever the marginal revenue is above the marginal cost. The problem is that marginal revenue is below the price because actually whenever you want to produce more, if you are using a single price, you are actually forced to reduce the price with respect to the initial situation, so you are losing profits from the units of the good you were already selling. 
 If you consider points to the right of q*, you can see that the demand function is above marginal cost. Consumers are evaluating the good more than marginal cost; it would be socially efficient to produce. However, for the firm, the marginal revenue is below marginal cost, so for her its not convenient. We have units of the good which are not produced so the value is not obtained by anybody. The clear point is that there can’t be value if there’s not production (and here there’s not because it’s not convenient). In the previous class we analyzed the optimal price strategy of a monopolist firm that is constrained to fix a linear price given a certain demand functions. We saw how the firm market power (ability to fix a price above marginal cost and so appropriate part of the value created for consumers) is limited by demand elasticity. Firms can increase its profit by using various forms of price discrimination. The latter includes a lot of commercial practices; it occurs when firms fix different prices to different consumers that are not justified by differences in costs. In this way, we can analyze the products that are offered by the firm to consumers are not exactly equal, but the price fixed to different consumers is not just reflecting the difference in prices. 
 The traditional taxonomy: 
 • First-degree price discrimination: a situation in which each consumer pays a price equal to his willingness to pay for each unit of the good. The ides is that each unit of the good is treated differently by the firm … 
 • Second-degree price discrimination: each consumer faces the same price scheme, but price varies with the quantity bought. 
 • Third degree price discrimination: consumers are classified according to observable characteristics, and consumers belonging to different groups pay different prices. 
 
 There is an alternative taxonomy using more modern terminology: 
 • Full price discrimination (personalized pricing): each consumer pays a price equal to his willingness to pay for each unit of the good (=first-degree price discrimination). 
 Behavioral Economics 66 Clara Corona • Direct price discrimination (group pricing): consumers are classified according to observable characteristics, and consumers belonging to different groups pay different prices (=third-degree price discrimination). 
 • Indirect price discrimination (menu pricing): the firm offer different «variants» of its product (in terms of quality, quantity, time of delivery) and each consumer chooses its preferred variant as a function of non-observable (by the firm) characteristics (includes second-degree price discrimination). 
 
 Full price discrimination 
 It implies that different prices to different consumers are not justified by difference in costs, because within the class of “discrimination” we also want to include other situations in which the firm is offering slightly different variants of the good. If we think about first class and second class of a train service, they are not the same services. There are differences in costs; on the first class, what we get “extra” is basically some drinks’ offers, or more comfortable seats, but there are differences in services that are offered and the costs, and the price you pay for the first or second class is not just reflecting this difference. The price of the first class is much higher. 
 Example 1: Suppose consumers demand at most one unit of the good. The willingness to pay is equal to v, where v is uniformously distributed between 0 e vmax. The marginal cost is equal to 0. The mass of consumers is m. If the price is above v max, nobody buys; if the price is 0, the number of consumes buying is m. What is the profit with no price discrimination? Marginal cost is 0, it coincides with the horizontal axe; the marginal revenue would be the line below the inverse demand function, and the first would cross in some moment the horizontal axe, so we have the quantity produced by the monopolist and the price. Pmon is the monopoly price which for sure would be greater than 0 (in equilibrium, the Behavioral Economics 67 Clara Corona Lesson 15 and 16
 
 Up until this moment, we discussed the theory of full price discrimination, in which each consumer is paying a price which is equal to his/her willingness to pay. It allows the firm to get full consumer surplus and we also saw that this is bad for consumers, because they are left with 0 surplus, but it’s also socially efficient because it increases the quantity produced; under monopoly, or under any circumstance in which firms have market power but have the possibility just to use linear prices, prices tend to be too high and quantity too low. 
 Price discrimination can be both direct or indirect. Direct is observed whenever the firm is using observable characteristics of the consumer to discriminate in order to create groups (and within these groups, prices are different). Examples of observable characteristics used to discriminate: 
 • Age (like discounts for children and the elderly); 
 • Gender (free entry for women in disco); 
 • Motive (for instance honeymoon cruises); 
 • Professional status;
 • Place of origin or residence; 
 
 Let’s assume that there are two groups of consumers (1 and 2) characterized by demand function with different elasticities: e1 > e2. The same service is offered to the two groups. The key assumption is that no arbitrage is possible (it’s not possible to have consumers selling the product to the other group). Arbitrage is quite difficult to avoid when we are referring to manufacturing goods, for example; however, it’s difficult to practice arbitrage in the service world (how could consumers re-sell an airplane ticket?). So, in our example, if the consumers can’t resell, then the firm can treat the two groups as two different markets; the firm maximizes profit fixing two prices, one for each group. 
 Let’s assume that marginal cost is equal to c (the product is the same, and so is the marginal cost). p1 and p2 are the prices for the two groups. In monopoly, in equilibrium, prices that maximizes profits are: 
 
 
 Behavioral Economics 70 Clara Corona The prices in the two groups are connected by this first equality involving price and elasticity. Looking at this, we assume that e1 > e2, and it means that (1/e1) < (1/e2), so (1 - 1/e1) > (1 - 1/e2), so if they must be equal, p1 must be lower than p2. If elasticity is different in the two groups, then optimal price should be different (in particular, the higher the elasticity, the lower should be the price). In the group for which elasticity is high, it’s optimal to fix a low price. 
 In behavioral economics terms, one concern is about fairness perception of consumers. It may be the case the consumers paying a higher price because of lower demand elasticity are actually unhappy to see that somebody else is paying a lower price (and this could have an impact of their willingness to pay). 
 For the firm, the complicate part is identifying the observable characteristics leading to different elasticity. In general, you want to create groups of consumers for which you have different elasticity. A case which is similar to direct discrimination is pricing under demand seasonality. Here, we define as season a time interval during which demand is stable. A cycle, instead, is the time interval including all the seasons. 
 If the cycle is the year, “seasons” are summer, autumn, winter and spring. In terms of market, this distinction is important for instance for the electricity market. 
 If the cycle is the week, “seasons” may be the weekend and the working days. This is important for airlines. 
 If the cycle is the day, “seasons” are different hours in a day. One example is the public transport services. 
 The firm has to i) fix capacity; ii) fix the price in each season. The similarity with direct price discrimination is that prices differ for an observable characteristic, i.e. the time of delivery. There can be markets in which more than one seasonality is at the core. 
 
 Suppose there are two seasons: high (A) and low (B). The (inverse) demand functions for the firm are linear: p A = 200 − q A p B = 100 − q B. 
 Both capacity and production marginal costs are equal to 20. Without demand uncertainty, for the firm it will be optimal to choose a capacity level equal to quantity demanded in the high season, because there is no sense in having a capacity level that you aren’t using fully in the period of time when the demand level is the highest. 
 Behavioral Economics 71 Clara Corona What can we expect the firm to do? In order to determine the optimal capacity level, we expect that the high season marginal revenue is equal to the overall marginal cost (capacity + production). 
 Capacity will be used completely only in high season. Therefore, the decision concerning the optimal capacity takes into account only high season demand. In our case: In the low season, profit maximization implies that low season marginal revenues is equal to production marginal cost (therefore, capacity will be not utilized completely). In our case: Low season underutilization of capacity is optimal! 
 In the long run choice of monopoly, you want to use your full capacity, otherwise you’re wasting money (long run would be equal to high season); in the short run, once capacity is given, it may be the case that you’re not using fully your capacity (short tun wold be equally to the low season). 
 
 Indirect price discrimination, firms are offering a menu of products or variants of the good for which prices of the different variants are different as well and then consumers are selecting their preferred variant based on unobservable characteristics by the firm. So there is self-selection of variants by the consumer. Of course there must be etherogenerity among consumers. A few examples are: 
 • Quantity discounts (price different according to the quantity you buy); 
 • Different «variants» for consumer products (like eletronic goods); 
 • Full-board and half-board tariffs in hotels; 
 • First (business) and second class (standard) services in trains and flights. 
 
 It must be remarked that there is price discrimination every time price differences are not justified by differences in cost.
 
 Let’s consider a hotel with two types of rooms, standard and suites. The hotel has to decide the prices and the level of quality q for each type of room. 
 The cost to provide a quality q is C(q) = q2 / 2 
 Behavioral Economics 72 Clara Corona One interesting result is that in this case price discrimination is leading to higher profits than no price discrimination (it would mean that you can only produce one product). It may be also beneficial to some groups of consumers, in particular high-evaluation consumers since they get the rent. Here, indirect price discrimination is even less perfect than direct price discrimination because of asymmetric information. 
 More over, the quality of the standard room is lower than the case of perfect information. Sometimes, in literature, we talk about what is know as “damage goods”: products offered in the market with technical characteristics which are inferior to the basic product, and firms need even to sometimes pay a cost to reduce the quality of a product. An example is the free trial version of softwares; you have a basic version with all the functionalities, and then you have often the version which less technical features with a price of 0. Sometimes it’s a free trial, sometimes a free version. 
 Why firms should actually invest or think about ways to reduce the quality of the product? The motive is related to the logic of menu pricing and second-degree price discrimination. The reason why you are deleting some features of the product is because you want to make it less attractive for those consumers who are willing to spend more to have standard version with all the functionalities. The analysis we had so far is basically equivalent to the quantity discount model. Suppose there are two types of consumers. One type has a high marginal utility for each day at the hotel; the other type a low marginal utility. In the previous model, it is sufficient to relabel q as holiday lenght. 
 The optimal offer implies a quantity discount (i.e. a lower price for the second week) to induce the tourist with a higher marginal utility to choose the longer holiday. 
 
 Temporal price discrimination, instead, is a particular form of price discrimination is the one under which prices differ according to the moment in time where the transaction occurs. It’s a common strategy in the service industry, where they have advance booking (used by hotels, airlines, events, etc). In temporal price discrimination, the firm treats differently customers that buy the service in different moment of time. We distinguish: 
 • Last minute strategy: the price is lower the closer the transaction date is to the date when the service is consumed. 
 • First minute strategy: the price is lower the more distant the transaction date is to the date when the service is consumed. Behavioral Economics 75 Clara Corona A model of temporal price discrimination 
 We have again a monopolist; we assume that marginal cost is 0; there is given capacity (K); there is linear demand function p = a - bq for consumers in a given moment of time. The idea is that consumers can buy the product in three moments before the product is delivered: 2 months before delivery: 1 month before delivery; 1 week before delivery. 
 
 First period The firm chooses the quantity and the price in order to have the marginal revenue equal to 0 (the marginal cost). 
 All consumers with a willingness to pay higher than p1 book in the first period. The hypothesis is that they are naïve consumers: they are not able to make any reasoning about the future development of prices. There remains K-q1 consumers with a willingness to pay that is higher than the marginal cost (=0), who could be still served by the firm, because because there is capacity left. 
 So, in the first period, with p1 as the price, all the consumers with a willingness to pay higher than p1 buy, so they exit the market, buy their good and are happy with it. This q1 consumers go out of the market and what is left? Only the consumers with willingness to pay below p1. Behavioral Economics 76 Clara Corona Here we have drawn a new vertical axe starting from q1. The first consumers are gone, so we have only the new inverse d e m a n d f u n c t i o n ( q u e l l a n o n tratteggiata). The vertical intercept is p1 and the rest of the inverse demand function are all the consumer with a willingness to pay below p1. 
 In the second period, the firm has the possibility to fix a new price which is maximizing the profits in the second period given the new demand function, Q2 is the additional quantity in the second period and p2 is the price. The latter is lower because the consumers have lower willingness to pay compared to that in the first period. Still, if the firm has not used fully its capacity, then it has the possibility to sell additional units, and once again it would be convenient because the willingness to pay of consumers is higher than the marginal cost. 
 The only inverse demand function left is the one at the right of the yellow line. If you draw the marginal revenue line and you look at the points where the line crosses the horizontal axe, this means that the firm is not able to sell all those units. It follows that the optimal choice is not to fix a price such that the quantity is equating marginal revenue and marginal cost. So what is optimal in the last period is to fix a price p3 such that the demand is equal to the capacity left. In the last period we don’t have much capacity, so it isn’t so true that marginal revenue is equal to marginal cost in equilibrium because that isn’t visible, so the price is fixed as equal to the capacity. P3 is lower than p2 which is lower than p1. Behavioral Economics 77 Clara Corona There are two basic reasons why airline companies may change prices over time. The first motive is related to time-based theories (consumers are etherogeneous so you want to exploit time in order to have different consumers buying different prices). Such theories can predict increasing (as in first minute strategies) or decreasing (as in last minute strategies) price profiles. 
 The second motive is related to capacity-based theories, that rely on uncertain demand, and predict fares decreasing in the remaining capacity at that specific moment in time. 
 
 In order to test the relative relevance of the two theories, one needs information on available capacity, which is in general difficult to get. However, in the sample period (January 2004-June 2005), Ryanair allowed purchases up to 50 seats. Through a «spider», repeatedly asking seats from 1 to 50 seats on a given flight, the number of available seats, up to 50, can be known. 
 The authors collected information on fares and capacity for all flights leaving from a UK airport (both domestic and international). 
 This is the data. The rows are booking days in advance, and the column correspond to available seats on a specific flight. We find the average price for all the combination. We can separate the effect of inter-temporal price discrimination form the impact of capacity. Suppose you fix the day before departure (the row), and if you move to the right you can see that the price is getting lower. It means that the larger is the number of available seats, the lower is the price. 
 If you compare, instead, different columns, there is a strong tendency towards first-minute pricing: the price is getting higher and higher as you are getting closer to the departure date. Behavioral Economics 80 Clara Corona Lesson 17, 18 From preference-based to naivetè-based discrimination 
 In the previous lectures we analyzed monopoly linear pricing and forms of price discrimination based on the heterogeneity of consumers’ preferences. From linear price models we learnt that market power is limited by demand elasticity, and that market outcomes are socially inefficient because price is «too high» and quantity «too low». From the «traditional» forms of price discrimination we learnt a number of lessons: 
 - Price discrimination allows firms to increase profits by extracting more value from consumers and expanding quantity. 
 - Some consumers are typically worse off (those who end up paying a higher price), but some may be even better off (if they pay a lower price). 
 
 In this lecture we will analyze three models, which assume «behavioural» consumers (i.e. consumers whose behaviour departs from standard rational behaviours). 
 • Model 1: (monopoly) pricing with loss averse consumers. 
 • Model 2: Anticipating future preferences – the case of time-inconsistent consumers - optimal pricing and naivetè-based discrimination. They may actually change their mind in the future compared to the present. This was the main model in inter-temporal choice analysis. 
 • Model 3: Anticipating future preferences – the case of overoptimistic consumers – optimal pricing and naivetè-based discrimination. This type of consumers are “wrong” about the future preferences. Let’s consider with the analysis of monopoly behavior of consumes who are loss-averse. We need to make a premise; if we think carefully about the optimal linear pricing model, we get that actually linear pricing is equivalent to mark-up pricing: firms should fix a mark-up over marginal cost, which should depend on demand elasticity. 
 Behavioral Economics 81 Clara Corona We saw that the optimal pricing rule can be re-written in terms of the Lerner index and demand elasticity, which is determined on the left. Starting from the equation on the left, we can move to that on the right isolating the price. With the mark-up rule, the price is equal to the cost multiplied by 1 plus a term which is the mark-up. This means that elasticity, in equilibrium, must be greater than 1. Mark-up pricing implies that prices should vary proportionally with marginal cost, both when cost increases or decreases. 
 So, when we have consumers who are loss-averse, there is an asymmetry depending on what depends on marginal cost if this is changing over time. Suppose consumers have a marginal evaluation of the good (willingness to pay) which is: 
 where pe is the reference price. 
 We consider the simplest cases in which demand can be 0 or 1. L > 0 implies loss aversion. If we face a price which is greater than our reference price, we get a dis-utility, because we suffer from this loss. 
 v is distributed uniformously between 0 and 1. There is a unit mass of consumers equal to 1. Given this assumption, the demand function is given by: 
 
 In order to do this, we use statistical property of the distribution function. The story is the following: suppose we put all the consumers on a line between 0 and 1, using the willingness to pay v. Suppose there is a price p. Who is going to buy? The consumers with v higher than p (they are the consumers on the right of p in the following image). The length of the segment from p to 1 is 1 - p. Behavioral Economics 82 Clara Corona elastic. Loss aversion has the consequence of making consumers to have a more elastic demand for high price, in which “high” means “higher than expected”. The main message here is that loss aversion is a preference parameter; if consumers are loss averse, the firm can just influence the expected price, because the problem with loss aversion is that the price can be higher than expected. 
 For which value of the reference price we are getting back to the original model? When we discussed the paper of Kanheman about fairness of eliminating a discount and getting the price back to normal, we have that if we can convince consumers that the high price is the normal price, the consumer is not facing any loss whenever the price is high because, thanks to our communication, he was considering it as a standard price. 
 Model 2 - Anticipating future preferences 
 In many markets, consumers choose at time t a contract which determines the prices associated to goods/services that will be object of choice at time t+1. For instance: 
 1. Telecommunications (you decide at t + 1 how many calls you make, how many giga you use); 
 2. Media services (maybe for the contract you must pay a fixed price for a certain period of time); 
 3. Restaurants, because if you see, for instance, the prices outside on the menu and then you enter, you are signing a contract that you’re going to pay for those things you order. Choice at time t is made based on the expected preferences at time t + 1. These preferences may be not known if: consumers have time-inconsistent preferences and are naive; consumers are over- (or under-) optimist. Time-inconsistent consumers 
 Suppose a monopolist firm proposes at time 1 a contract (pL; pH) for the goods L and H, among which the consumer will choose at time 2. Preferences at time 1 and 2 differs: 
 • At time 1, valuation for L (H) is uL (uH) with uH > uL. This means that the good H is the good you prefer at time t + 1, in the moment in which you sign the contract. 
 • At time 2, valuation for L (H) is vL (vH) with vL > vH. A time 2, consumers prefer good L to good H; this is the instability in preferences. 
 Suppose you go to the restaurant and there are two variants of a food. Suppose that before you go, the self prevealing is to stay healthy (and have a small portion and healthy, whereas the bigger one is unhealthy). However, when you are there, you can’t resist the temptation and you buy the large portion and unhealthy one. H can be the small portion or the healthy version. 
 Behavioral Economics 85 Clara Corona The idea is that the firm and the sophisticated consumer know that the change of preferences will occur! The naive consumer does not predict the variation, he believes he will prefer the H version also at time 2. Finally, we assume that the utility of no consumption is zero, and for the firm we assume that both goods H and L have zero cost of production. 
 What are the optimal contracts for firms? It depends if consumers are sophisticated or not. If they are, they are making a decision today knowing that in the future they will have this tendency to do something different from what is optimal for them today. What they actually want for the firm is a commitment, they are asking the firm to offer a contract for which the L alternative will be not convenient for them in time 2. Why? Because they are making the choice in time 1, so their evaluations are uH and uL. They want to wait to choose H. Notice that the firm actually is not in contrast with them, because uH > uL so evaluation is higher; the firm would be happy to help the consumers in committing to buy the good which is preferred to them in period 1. 
 What is so the optimal contract to do that? pH = uH because the firm wants to maximize utility. It must be pL > uH + (vL - vH) to induce the consumer not to choose L; we have, in fact, that vL - vH is the temptation, the extra utility they can get in period 2 whenever they choose L which is the best good in period 2. This is the incentive compatibility constraint for firm for H to be chosen instead of L also in time t = 2. 
 
 If consumers are naive, they expect the preferences to be uL, uH also at time 2. Consumers will be offered a contract they will accept believing they will choose H, but they will actually choose L (and the firms know that). The primal contract would be pH = uH, which is the participation constraint, because like this the firm can convince the consumers to accept the contract. 
 In the second period, the firm would be very happy with consumers choosing L because L is the good for which they have a higher evaluation in period 2, so the optimal price will be that for which the consumer is indifferent between L and H. And when he’s indifferent, he’s going to choose L. 
 In this case, pL = uH + (vL - vH) to induce the consumer to choose L. 
 Firm profit is then equal to uH + (vL - vH) > uH. The contract offered to the consumer is exploitative: the consumer is paying a higher price, the firm is getting a higher profit, and the consumer utility is negative when evaluated at time 1 utility. The story is, the consumer made a choice in time 1 based on wrong preferences; at the end of the day he chose L, and going back he would have dove another choice. Because evaluating based on preference of the initial type is actually getting the consumer a negative utility. 
 Behavioral Economics 86 Clara Corona The naive consumer accepts it because it’s a “bet” on an event over which he as different priors compared to the firm (but the firm is right). The sum of the profit and consumer surplus doesn’t change, because this is always the case when demand is perfectly inelastic - zero or one. Now we move to naivetè-based discrimination: suppose that in the market there are both naive and sophisticated consumers. Suppose that the firm proposes the two contracts determined before: 
 • pH = uH and pL > uH + (vL - vH) (Sophisticated). uH is the evaluation at time t = 1, when signing the contract. In the case of sophisticated consumers, “pL > uH + (vL - vH)” allows them not to choose L in the second period. 
 • pH = uH and pL = uH + (vL - vH) (Naive). pH = uH is the price for which naive consumers are willing to accept the contract because they wrongly think they’re going to accept H. “pL = uH + (vL - vH)” is the condition which allows the firm to induce the consumers to buy the L good, the preferred under the second period preferences. 
 Suppose you can find both types of contracts in the market, and that have the same price for H, and a different price for L. For both consumers, the net evaluation for contract S is zero, while for sophisticated consumers, N is a contract which gives a lower utility when is evaluated at time 1 preferences, because in the second period you choose L. If you are sophisticated, you can predict this, and since L is not preferred under time 1 preferences, as a sophisticated consumer, this contract will give you a negative utility, when evaluated at time 1 preferences. For naive consumers, instead, this contract is equivalent as the S contract, because they think they aren’t going to choose L in any case. 
 We can assume that if S and N are considered equivalent by consumers N, they are going to choose the N contract, while consumers S are going to choose the S contract. This assumption that when consumers are indifferent they choose the contract the firm has designed for them, it looks like strange, because you can always think that for N contracts pH will be slightly below uH. 
 Therefore, the firm can perfectly screen the two types. Notice that the presence of sophisticated consumers does not advantage (nor disadvantage) naive consumers. 
 Suppose that pH, in the case of naive consumers, is equal to uH or very close. In the market, we have two contracts, one of the two prices is basically the same and the other one is higher, so contract N should be better. Naive consumer doesn’t infer anything from the fact that the firm offers one contract (N) that is apparently dominant over the other (S). 
 
 Behavioral Economics 87 Clara Corona Therefore, the firm cannot perfectly screen the two types, and must reduce pH (creating an informational rent as in standard menu’ pricing). The presence of sophisticated consumers advantages overoptimistic consumers, because is leading the firm to reduce the price for them. So, summing up, the introduction of behavioral consumers provides new insights in monopolistic pricing. If consumers use relative evaluations and are loss averse, they will react negatively to price (upwards) variation (as if demand becomes more elastic). Prices get «sticky», and profits would be lower than with standard preferences. For firms, using framing effects to increase the reference price becomes crucial. If consumers have cognitive biases, firms can exploit them offering contracts that transfer additional surplus from firms to consumers. 
 Firms can offer menus of contracts to discriminate based on cognitive biases. In case of overoptimistic behaviour, the presence of rational (unbiased) consumers can protect biased consumers. 
 
 We now present empirical evidence on behaviour that cannot be (easily) reconciled with fully rational models. We discuss at lenght the paper by Della Vigna and Malmendier (2006), “Paying not to go on the gym”, and additional evidence/arguments in favor of an important role of behavioural biases in explaining certain types of contracts, which would be difficult to justify otherwise. 
 A dataset from three health clubs located in New England (clubs 1, 2, and 3). The dataset contains information on the contractual choices and the day-to-day attendance of users (sample period 1997-2001). The sample is composed of 7,752 individuals. The membership options offered by health clubs belong to one of these groups: 
 • A monthly contract, with the monthly fee automatically debited each month to a credit card 
 • An annual contract, both monthly and annual contracts have an initiation fee but no per-visit fee 
 • A pay-per-visit option, often in the form of a ten-visit pass. 
 
 In addition to the data on behavior, the authors also conducted a survey on users’ forecast. Which where the findings? 
 • (price per expected attendance at enrollment) Users who choose a flat-rate contract pay a price per average attendance of over $17 in the monthly contract and over $15 in the annual contract. The share of users who pay ex post less than $10 per visit (price for visit) is 20 percent in the monthly contract and 24 percent in the annual contract. 
 Most users choosing a flat-rate contract made the wrong choice. 
 Behavioral Economics 90 Clara Corona • (forecasts of attendance) The average forecasted number of monthly visits, 9.50 is more than twice as large as average attendance, 4.17. 
 Users are overoptimistic on their future attendance. 
 • (cancellation lags under the monthly contract) On average, 2.31 full months elapse between the last attendance and contract termination for monthly members, with associated membership payments of $187. This lag is at least four months for 20 percent of the users. 
 Cancellation occurs too late. 
 • (survival probability) The survival probability after 14 months for the monthly contract is 17 percent higher than for the annual contract. 
 Cancellation is too rare. 
 • (average attendance over time in annual contracts) In the annual contract, average monthly attendance for the initial group in the first year, 4.36, is significantly lower than for stayers in the second year, 5.98 
 • (average attendance over time in monthly contracts) Average monthly attendance in the first six months of a monthly contract, 4.36, is 20 percent higher than in the next six months and is significantly higher than in any of the later six-month periods among stayers. 
 Users choosing monthly and annual contracts behave in a systematically different way. The authors suggest an explanation including both overestimation of attendance and overestimation of cancellation. Overestimation of future attendance leads consumers to choose flat-rate contracts. 
 Overestimation of future cancellation leads consumers to delay cancellation in the monthly contract, but not in the annual contract which requires no cost to cancel. Consumers seems heterogenous in their degree of overestimatation. 
 Firms offering flat-rate contracts (and “pushing” for them) can profit from higher price per visit and late cancellations (with automatic renewal). In the economics and marketing literature, there is significant evidence on flat-rate bias. 
 
 In many markets, notably telecommunications, firms offer three-part tariffs, consisting of three components: a fixed fee; an included allowance of units for which marginal price is zero; a positive marginal price for additional usage beyond the allowance. The difference with the two-part tariff is that only one price is fixed, which is the same for the first unit of consumption and for all the remaining units. 
 
 Behavioral Economics 91 Clara Corona Explaining this type of contract is difficult assuming standard rationality. In order to justify three- part tariff, we need to make some weird assumption like the one for which marginal cost has a jump somewhere, so from 0 it becomes positive after a certain level. The paper by Grubb (2009) introduces a model based on consumers’ overconfidence, and we use this term instead of “overoptimism”, because we are referring to a phenomenon defined as the underestimation over uncertainty about their future behavior. The story is the following: in many cases, consumers don’t know in advance what will be the level of consumption, there may be elements of uncertainty. Overoptimism is related to the average level: if you think you’re going to spend more than actually the case, in that case you are overoptimistic. Instead, here, we have overconfidence because we underestimate the variance of our future behavior. 
 Grubb and Osborne (2011), in a related paper, conducted an analysis using a sample of US students, and it shows that the students underestimate their own uncertainty about their average demand by 82% and that consumers underestimate the monthly volatility of their demand by 54%. 
 If you include these types of bias into consumer behavior, then the optimal response for firms is to provide a three-part tariff. In the paper, there is an example. Assume that we are on the side of a telephone firm, and that the marginal costs are 5 cents per minute and fixed costs are $50 per customer. Consumers value each minute of calling at 45 cents up to some satiation point, beyond which they have no additional value for calling. 
 Suppose there is a time 1 period where consumers sign contracts, and they are homogeneously uncertain about their satiation points (they don’t which is the number of minutes of call after which there will be 0 value attached to calls). Then, at time 2, consumers actually learn their satiation points and make their consumption choices. In particular, one third of consumers learn that they will be satiated after 100 min, one third after 400 min, and the remaining third after 700 min. 
 What happens if consumers are not overconfident? It’s optimal for the firm to charge a marginal price equal to the marginal cost of 5 cents per minute. A monopolist can extracts all the surplus via a fixed fee of $160, earning profits of $110 per customer. 
 If consumers are overconfident, however, marginal cost pricing is no longer optimal. For instance, if all consumers are extremely overconfident and believe that they will be satiated after 400 minutes with probability one, then it is optimal to charge 0 cents per minute for the first 400 minutes, and 45 cents per minute thereafter. In other words it is optimal to have 400 “included” minutes in the tariff. Behavioral Economics 92 Clara Corona 
 Which are he characteristics of the demand level? It is discontinuous, because when we move from a price just above p2 to a price just above p2, we move form a quantity which is 0 to a quantity which is 0. Instead, the market demand function is continuous (the straight line). 
 
 Players: the firms 
 Strategies: prices 
 Payoffs: profits 
 Equilibrium: the Bertrand - Nash equilibrium is given by a pair of price (p * 1 ,p * 2 ) such that each firm maximizes profits given the other firm’s price. How to solve the game? Through the representation of the “best response function”. In the Bertrand model, the possible strategies of the opponents are on a continuous set, because they can fix any price. We need to compute, in order to have the best response function, what is the optimal price (for firm 1) for any price fixed by the rival. 
 Behavioral Economics 95 Clara Corona The 45° line is that for which the two prices are equal. PM stands for the monopoly price. 
 Suppose you are firm 1, and you think firm 2 is fixing a price below marginal cost: it doesn’t make any sense, because it’s losing money, but if you think so, the optimal thing to do for you is - since you don’t want to serve the same price in the market - to fix a price exactly equal to marginal cost (the lowest price for which you aren’t losing money). 
 The horizontal red line is when the price of firm 2 is below the marginal cost. Instead, when the price is above marginal cost, for firm 1 it’s optimal to fix a price just below firm 2, the rival. Consumers will buy from you and you are maximizing profits. 
 But what happens when the price of the rival is above the monopoly price? In that case, you are not fixing a price below that of your rival, because with the monopoly price you get the maximum level of profits; if your rival is again “crazy” and fixing a price above the monopoly price, what it’s optimal for you as firm 1 is to fix the monopoly price, because it’s lower than that of the rival - but at the same time you’re maximizing your profits. The unique Nash equilibrium in the Bertrand game is: p*1,p * 2 = c In equilibrium, firms make zero profits, because the price is equal to marginal cost. 
 Behavioral Economics 96 Clara Corona The intuition is very simple. We start from verifying this is an equilibrium; suppose the rival is fixing a price equal to marginal cost. For you, there is nothing better than fixing a price equal to marginal cost, because if you fix a price above it, you don’t sell; if you reduce it, you sell everything in the market so you lose money. This to verify we are in a Nash equilibrium. 
 For each different pair of prices, at least one firm has a profitable deviation. In particular, if prices are equal but above marginal cost; in that case, if you fix a price equal to your rival you share the market and you get the profit. But suppose you reduce the price a little bit; you get the whole market by doubling your sales. So, firms find convenient to do “undercutting” (a price which is slightly lower than the rival) and double sales. 
 
 If we daw the two best response functions, we get this graph. The point in which the two cross, is the Nash equilibrium , in which the price is equal to marginal cost. 
 The Bertrand is sometimes called a “paradox” : two firms in the market reproduce exactly the outcome of perfect competition (no market power because there are a lot of firms, maximal social welfare). 
 Another word attached to the Bertrand is “trap”: price reductions are “temptations” firms cannot resist, leading to “price wars”. When we considered the word “temptation” so far, we considered it as regarding individual choices. Here, it’s related to the fact that the firm is reducing the price, which is clearly optimal given the price of the rival. However, it’s a temptation because the reaction Behavioral Economics 97