Profit Maximization in Perfectly Competitive Markets, Lecture notes of Business

Download Profit Maximization in Perfectly Competitive Markets and more Lecture notes Business in PDF only on Docsity! These notes essentially correspond to chapter 10 of the text. 1 Perfectly Competitive Markets The …rst market structure that we will discuss is perfect competition (also called price-taker markets –I will use the terms interchangeably throughout the notes). We study this theoretical market for two main reasons. First, there are actual markets that meet the assumptions (listed below) necessary for perfect competition to apply. Many agricultural and retailing industries meet these assumptions, as well as stock exchanges. Second, the perfectly competitive market can be used as a benchmark model, as there are many desirable properties of this model. We will compare the perfectly competitive model (discussed in this chapter) with the monopoly model after we have completed the monopoly model. 1.1 Assumptions of perfectly competitive markets We will list 4 assumptions in order for a market to be perfectly competitive. 1. Consumers believe all …rms produce identical products. 2. Firms can enter and exit the market freely (no barriers to entry). 3. Perfect information on prices exists (all …rms and all consumers know the price being charged by each …rm, and this knowledge is common knowledge). 4. Large numbers of buyers and sellers (so that each buyer and seller is small relative to the market) 5. Opportunity for normal pro…ts (or zero economic pro…t) in long run equilibrium. If these 5 assumptions are met (note that textbooks di¤er in both the number of assumptions, as well as the precise wording of the assumptions, but the underlying idea is the same across textbooks), then each …rm in the market will face a perfectly elastic demand curve. Recall that a perfectly elastic demand curve is a perfectly horizontal line, like: We will return to the …rm’s demand curve shortly. 1 2 Pro…t Maximization The goal of the …rm is to maximize its pro…t (economic pro…t). Recall that economic pro…t equals total revenue minus explicit costs minus implicit costs, or  = TR TC (we will use  as the symbol for pro…t). Now, we know that TR = P  q and that TC is some function of q. So we can rewrite pro…t as: (q) = PqTC (q). Price is a function of Q, so (q) = P (Q)qTC (q). Now, pro…t is solely a function of quantity. There is a subtle di¤erence between Q and q. When Q is used, this refers to the market quantity. When q is used, this refers to a speci…c …rm’s quantity. We will typically consider the market quantity as the sum of all of the individual …rm quantities. Assuming there are n …rms in the market, the market quantity, Q, would then equal q1 + q2 + ::: + qn1 + qn or Q = nX i=1 qi, where X is the summation operator. Thus, Q is implicitly a function of q, so that price is implicitly also a function of q. While a …rm’s total cost depends only on how much it produces, q, the market price depends on how much all of the …rms produce, Q, which depends on q. We can “derive”the pro…t function from the …rm’s total revenue function and total cost function. We know that the …rm’s demand curve in a price-taker market is perfectly elastic – this means that it will charge the same price regardless of how many units it sells. The …rm’s total revenue function, TR (q), is then TR (q) = Pq, where P is a constant at the level of the …rm’s demand curve. Suppose that P = 15, then TR (q) = 15q. Plotting this will yield a straight line through the origin with a slope of 15. We know that the …rm’s total cost curve, TC (q), is a function that “looks like a cubic function”. Let’s assume that TC (q) = 10 + 10q 4q2 + q3. If we plot the two functions below we get (where the TR is the straight line and the TC is the curved line): 0 2 4 6 0 20 40 60 80 100 Quantity Price Plot of TR (q) and TC (q). Because (q) = TR (q)TC (q), then (q) = 15q 10 + 10q 4q2 + q3
. If we plot this relationship, we get: 2 4 6 ­20 ­10 0 10 20 30 Quantity Profit Plot of (q) 2 For this particular problem the math does not work out so nicely –we would need to use the quadratic formula to …nd q: q = 8 p 64 4 (3) (5) 2 (3) q = 8 p 124 6 q = 8 2 p 31 6 q = 8 + 2 p 31 6 ; 8 2 p 31 6 The …rst possible answer, 8+2 p 31 6 , is  0:52, which is not a realistic quantity. The second possible answer, 82 p 31 6  3:19. So the only viable solution is q = 4+ p 31 3 . From here we can …nd the …rm’s maximum pro…t by substituting our solution, q = 4+ p 31 3 , into the pro…t function, (q) = 15q 10 + 10q 4q2 + q3
, and directly calculating the pro…t. While the general rule for pro…t maximization isMR =MC, recall that in perfectly competitive markets that MR = P . Thus, in perfectly competitive markets, P =MC is an equivalent pro…t-maximization rule. 3 Shutdown Rule In the short-run, the price-taking …rm has a decision to make regarding its quantity choice. If the …rm can earn a positive pro…t at some quantity level, then it will obviously produce the pro…t-maximizing quantity. If the …rm is earning zero pro…t (again, this is economic pro…t), it will still produce because a zero economic pro…t means that the …rm is earning as much as it could if it shifted its resources to their second best use. So, if the maximum pro…t a …rm could earn is zero, then the …rm would produce the quantity that corresponds to zero economic pro…t. However, should the …rm make a loss in the short-run the …rm has 3 choices that it could make. I will describe them …rst and then discuss the conditions under which the …rm would make each decision. 1. Continue to produce –this is just what it sounds like; even though the …rm is making a loss, it still continues to produce at the pro…t-maximizing (or in this case, loss-minimizing) quantity 2. Shutdown – the term shutdown has a very speci…c meaning in economics; it means that the …rm produces a quantity of zero (stop production), but it still stays in the industry. Technically, the …rm continues to pay its …xed costs (like rent) but pays zero variable costs (because it produces zero quantity). 3. Go out of business –in this case the …rm decides to leave the industry altogether; not only does it stop producing, but it breaks all of its contracts (leases, wage contracts, supply contracts) and completely leaves the industry. 3.1 Going out of business A …rm will choose to go out of business if it is currently making a loss (recall that this is an economic loss, so the …rm could actually be earning positive accounting pro…t) and it does not ever expect to make a pro…t again. Firms do not want to go out of business if they have a bad day or a bad week, so it may be the case that the …rm is making a loss and still stays in business because it believes it will make a pro…t again in the future. Thus, in order to know whether or not a …rm will go out of business we need to know (1) whether or not it is currently making a loss and (2) whether or not the …rm expects to earn a pro…t some time in the future. Assuming that the …rm is currently making a loss and that it does expect to make a pro…t in the future, the …rm now has two choices: to continue to produce or shutdown. 5 3.2 Continue to produce vs. shutdown The decision to continue to produce or shutdown comes down to whether or not the …rm’s total revenue from producing is greater than its total variable costs of production. We already know that TR < TC because the …rm is making a loss; thus, the key decision is whether the …rm can pay its variable costs. The shutdown rule is then: Shutdown rule: Assume that the …rm is making a loss and that it expects to make pro…ts in the future. The …rm will shutdown if the total revenue at the pro…t-maximizing (or loss-minimizing in this case) quantity is less than the pro…t-maximizing total variable cost, or TR < TV C. If TR > TV C, then the …rm will continue to produce. Alternatively, the shutdown rule can be written as: the …rm will shutdown if P < AV C, since TR = P Q and TV C = AV C Q. Why does the …rm only consider variable costs, and not …xed costs, when making its shutdown decision? If the …rm has decided to stay in the industry, it must pay its …xed costs regardless of whether or not it produces. Thus, these costs should not enter into the decision to either produce or shutdown (but they would enter into the going out of business decision). The following table shows a chart of a Dairy Queen which makes a loss during the winter months. Operate Shutdown TR $250 $0 TFC $300 $300 TVC $200 $0 Pro…t $250 $300 In this example, the Dairy Queen would decide to operate (assuming that it has decided NOT to go out of business) because it only loses $250 if it operates as opposed to $300 if it shuts down. Notice that if we change the amount of TFC (and hold TVC and TR constant), that the amount of TFC does not a¤ect the …rm’s decision – it will always lose $50 less when it operates than when it shuts down. Now, if we change TVC (and hold TR and TFC constant), notice that the …rm’s decision may change. If TV C < $250, then the …rm will decide to continue to operate because the pro…t to operating is greater than the pro…t to shutting down. If TV C > $250, the …rm will decide to shutdown because the pro…t to shutting down is greater than the pro…t from operating. 3.3 Firm’s short run supply curve Recall that a supply curve is a price and quantity supplied pair. What we want to see is if we can …nd the …rm’s supply curve. We will use the …rm’s picture. The picture below has the …rm’s MC and AVC, as well as 3 demand curves, d1, d2, and d3. Notice that when the demand curve shifts upward it intersects the MC curve at a new quantity level. Since the demand curves shift parallel to one another, each quantity level corresponds to only one price (which is the de…nition of a function). Thus, the …rm’s supply curve in a perfectly competitive market is simply the …rm’s MC above the minimum of AVC. 6 3.4 Firm’s long run supply curve In the long run the …rm will need to make at least zero economic pro…t. In this case, the analysis is similar to that for the …rm’s short run supply curve, only now we must have price above the minimum of ATC. Market Supply Curve The market supply curve can be found by …xing a price and determining the quantity that each …rm will supply at that price. When we add the quantities each …rm will supply at a given price together, we get the total market quantity that will be supplied at that price. Notice that the market supply curve will be more elastic than the individual …rm supply curves. 4 LR vs. SR equilibrium in perfectly competitive markets In the short-run (SR), perfectly competitive …rms may make an economic pro…t or loss. The SR equilibrium simply requires …rms to produce their pro…t-maximizing quantity, which is described in detail in the preceding sections. However, long-run equilibrium in perfectly competitive markets requires …rms to earn zero economic pro…t when they produce their pro…t-maximizing quantity. Recall that the term equilibrium means “to be balanced”or “to be at rest”. If …rms in a perfectly competitive market are earning positive economic pro…ts, then other …rms with similar resources will enter that market. If …rms in a perfectly competitive market are making losses, then some of those …rms will exit the market. Clearly, …rms entering and exiting the market is not a situation where all things are “at rest”. While an individual …rm may be at rest (since it can do no better than to produce its pro…t-maximizng quantity), the market itself is not at rest. However, when all …rms in the perfectly competitive market are earning zero economic pro…ts at their pro…t-maximizing quantities, then the market is in LR equilibrium because there is no incentive for any of the …rms to exit, nor is there any incentive for other …rms to enter the market. A picture of LR-equilibrium looks like the following picture. You should note that in the …rm’s picture the MC, ATC, and MR all intersect at the …rm’s pro…t-maximizing quantity. Since P = ATC at q, the …rm is earning zero-economic pro…t. 7 4.1.3 Decreasing cost industry A decreasing cost industry is an industry in which input prices decrease (increase) as the quantity produced in the market increases (decreases). Thus, there will be a downward sloping LR market supply curve. Decreasing cost industries typically occur when the resource providers have not yet begun to experience diseconomies of scale. Consider the calculator market in the 1970s. When demand for calculators was low, the resource providers did not need large facilities and likely did not utilize mass production methods to their fullest extent. However, as demand for the calculators increased, the demand for the resources increased. As resource providers increased production, the prices of the resources fell as the resource providers were able to take advantage of economies of scale, and possibly learning curves, to lower costs. These resource price decreases could be passed along to the calculator manufacturer, which could then be passed along to the …nal consumer. Thus, as the market output expands, the price of the …nal product actually falls due to the decrease in resource prices. The following picture illustrates the decreasing cost industry. The explanation is essentially the same as the increasing cost industry, except that now costs and MR are both falling. The process again stops when the …rm is earning zero economic pro…t. 10 mee Prise ao Go oy ql a Diy Merket Rapeeeendallye 1 11