Intermediate Theory: Price and Distribution - Final Exam Paper | ECON 410, Exams of Microeconomics

Download Intermediate Theory: Price and Distribution - Final Exam Paper | ECON 410 and more Exams Microeconomics in PDF only on Docsity! Name _______________________ Honor Code ________________________ Econ 410-007 Fall 2007: Final Exam You must show all of your work to receive full credit for an answer. This exam will be graded on a 100 point scale, with the value of each question indicated below. Good luck! 1. Joey gets utility from consuming two goods: hot dogs (X) and root beer (Y). His utility function is ))(1(),( YXYXU += , with corresponding marginal utilities YMU X = and )1( += XMUY . His income is $90. a. (3 pts) Suppose the price of hot dogs is $10 and the price of root beer is $5. What choice of hot dogs and root beer maximizes Joey’s utility? b. (3 pts) Suppose the price of hot dogs decreases to $5. What is Joey’s new optimal choice of hot dogs and root beer? c. (4 pts) What is the substitution effect and income effect of the price change on consumption of hot dogs? d. (2 pts) Based on your answer to part (c), are hot dogs a normal good or an inferior good? Explain why. 2. (8 pts) Suppose consumes water and a composite good (with price equal to $1). Due to the recent drought, the price of water increases by $0.50 per gallon. Prior to the price increase, Sally consumed 100 gallons of water per week. To offset the price increase, the government gives Sally a lump sum payment of $50. Will Sally be better off, worse off, or neither after the price change and lump sum payment? Will she consume more or less water? Explain your answer (NOTE: for full credit you should use a sketch to illustrate your answer). 5. Suppose the market for latex is perfectly competitive, with a market supply curve of SQP )5(.20 += and market demand curve of DQP −= 80 . a. (3 pts) What is the equilibrium price and quantity in this market? b. (3 pts) Compute consumer surplus and producer surplus in this perfectly competitive market. c. (3 pts) Suppose Vandalee Industries buys out all the individual latex producers and forms a monopoly in the latex market. Vandalee’s marginal cost curve is SQMC )5(.20 += , and market demand for latex is still DQP −= 80 . Assume that Vandalee Industries is able to set only one price in the market. What is the new market equilibrium price and quantity? d. (3 pts) Compute consumer surplus and producer surplus in this monopoly market. What is the deadweight loss relative to the perfectly competitive scenario? e. (3 pts) Suppose Vandalee Industries is able to first-degree price discriminate. What is producer surplus and consumer surplus in this case? What is the deadweight loss relative to the perfectly competitive scenario? 6. Amtrak has a monopoly on train service between Baltimore and Washington DC. Suppose that they have two types of customers: elderly and non-elderly. Demand for this train service among the elderly is ee QP )5(.30 −= and demand for this train service among non- elderly is nn QP 250 −= . Suppose Amtrak’s marginal cost per ticket sold is 10. a. (4 pts) Suppose Amtrak is allowed to third degree price discriminate. What prices would Amtrak charge for tickets? b. (4 pts) Suppose the government made it illegal for Amtrak to price discriminate. Would this make all consumers better off? Explain why or why not. 7. Suppose Roy and Dean are the only producers in the market for widgets, and that widgets are a homogeneous good. The market demand for widgets is QP 10500 −= , and Roy and Dean each has marginal cost of producing widgets of 200=MC . a. (2 pts) What is Roy’s reaction function? b. (1 pts) Given that Dean produces 25 widgets, how many widgets will Roy produce? c. (3 pts) If Roy and Dean simultaneously choose a quantity to produce as in the Cournot model, what is the equilibrium quantity of widgets produced by Roy and Dean? What is the market price of widgets in equilibrium? 9. It’s the 2010 World Cup and the U.S. soccer team is in a penalty shootout against Mexico. The shooter can choose to aim right or left, and the goalie may dive to the shooter’s right or left. The payoffs from this game are listed in the following matrix. Right Left Right -5,10 5,0 Left 5,0 -5,10S h o o te r Goalie a. (2 pts) Are there any pure strategy Nash Equilibria? If so, list them. b. (6 pts) Is there a mixed strategy Nash Equilibrium? If so, what is it? 10. Lucy and Charlie Brown are on the football field. Lucy asks Charlie Brown if he wants to kick the football. If he declines, nothing happens (each gets a payoff of 0). If he accepts, Lucy chooses whether to pull the ball away or to let Charlie Brown kick the ball. If Lucy pulls the ball away, she gets a payoff of 5 and Charlie Brown gets a payoff of -5. If Lucy does not pull the ball away, she gets a payoff of 0 and Charlie Brown gets a payoff of 5. a. (4 pts) Write down a game tree that corresponds to this story b. (4 pts) Should Charlie Brown accept Lucy’s offer? Explain why or why not.