ECON 201-2017 Spring Final suggested answers 1. (32 points, 7 points each unless specified)suppose that all firms in a constant-cost industry have the following long-run cost curve: c(q) = 3q2 + 100q + 75 The demand in this market is given by QD = 1280-2p. To produce firms need to have a permit and there are only 60 permits a) Derive the supply curve in this situation. Find the market equilibrium price and quantity with the restriction. Solution: In the condition of MC=P, P = 6q + 100 q = P 100 6 We know that there are 50 firms out there, Q S = 60q = 10P 1000 Equate to demand: 10P 1000 = 1280 2P P = 190, Q = 900 Partial: To find out right eqution ; 4 points, any calculation mistake ; -1 b) If firms are allowed to buy and sell these permits in an open market, what will be the rental price of permits? Will firm s that own permits make profit? Solution: Firms will not earn profits but RENTS. The rent will equate the firm s profits to zero: q = 900 60 = 15 Profit = P q TC Rent = 600 Partial: To find out right eqution ; 4 points, any calculation mistake ; -1 c) (10 points) Due to deregulation policy of the new government the permit requirement in this market has been abolished. What will be the new price in this market? What will be the market equilibrium quantity? Solution: Without permits, the market price will fall to the break-even price: AC = 3q + 100 + 75 q MC = 6q + 100 In the condition of AC=MC, 1
Q = 1020 q = 5, P = 130 Partial: To find out right eqution ; 4 points, any calculation mistake ; -1 d) (8 points) How much deadweight loss is generated by the permit system? Show your work Solution: DWL = 0.5 (190 130) (1020 300) = 21600 Partial: any calculation mistake ; -1 2. (38 points) Joe s Utility function is given as follows. UU(XX, YY) = XX 11 33YY 22 33 Joe s income is 81,000 won and Price of X is 1,000 won and Price of Y is 2,000 won. a. (7 points) Calculate consumption quantity for X and Y which will maximizes Joe s utility Joe s utility maximization problem can be represented as follows (the unit of price and income is 1,000 won). mmmmmm XX,YY XX1 3YY 2 3 ss. tt. XX + 2YY = 81 The utility maximization problem can be solved by Lagrangian approach. The utilitymaximizing consumption bundle is (27, 27) and the solving process is shown below. LL = XX 1 3YY 2 3 + λλ(81 XX 2YY) FF. OO. CC = 0 1 2 3 XX 3YY 2 3 = λλ (1) 2
= 0 2 3 XX1 3YY 1 3 = 2λλ (2) = 0 XX + 2YY = 81 (3) (1), (2) XX = YY wwwwwwh (3), (XX, YY ) = (27, 27) (2 pts) Setting up correct utility maximization problem (5 pts) Correct process and correct solution b. (7 points) Joe s parents decided to reimburse 50% of price for good X. Find the new equilibrium for Joe. Because of his parents reimbursement, the real price of X for Joe becomes 500 won. Joe will increase X consumption to 54 and consume 27 units of Y as before. Therefore, new optimal consumption bundle will be (54, 27). The solving process is shown below. mmmmmm XX,YY XX1 3YY 2 3 ss. tt. 0.5XX + 2YY = 81 LL = XX 1 3YY 2 3 + λλ(81 0.5XX 2YY) FF. OO. CC = 0 1 2 3 XX 3YY 2 3 = 1 λλ (1) 2 = 0 2 3 XX1 3YY 1 3 = 2λλ (2) = 0 0.5 XX + 2YY = 81 (3) (1), (2) XX = 2YY wwwwwwh (3), (XX, YY ) = (54, 27) (3 pts) Setting up correct utility maximization problem (4 pts) Correct process and correct solution c. (7 points) How much Joe s parents should pay as reimbursement? Calculate Joe s 3
utility under the new equilibrium in part b. Joe s parents should pay 500 won per 1 unit of X consumption as reimbursement. Thus, the total amount of the reimbursement is 54 500 = 27,000 won. The utility level of Joe under the new equilibrium can be figured out by plugging the new optimum into Joe s utility function. The solving process is shown below. UU(54, 27) = 54 1 327 2 3 = (2 27) 1 327 2 3 3 = 27 2 (3 pts) Calculation of correct amount of reimbursement (4 pts) Calculation of correct level of utility d. (10 points) Joe s parents decided to transfer money for the same amount needed for reimbursement. Calculate the utility for Joe after receiving money transfer. When Joe s parents transfer money for the same amount needed for reimbursement in c, the utility maximization problem of Joe becomes as follows. mmmmmm XX,YY XX1 3YY 2 3 ss. tt. XX + 2YY = 108 LL = XX 1 3YY 2 3 + λλ(108 XX 2YY) FF. OO. CC = 0 1 2 3 XX 3YY 2 3 = λλ (1) = 0 2 3 XX1 3YY 1 3 = 2λλ (2) = 0 XX + 2YY = 108 (3) (1), (2) XX = YY wwwwwwh (3), (XX, YY ) = (36, 36) In this case, we can calculate the utility level of Joe under the money transfer by plugging the new optimum into Joe s utility function. U(36, 36) = 36 1 336 2 3 = 36 4
(2 pts) Setting up correct utility maximization problem (2 pts) Correct process and correct solution (3 pts) Correct calculation of utility level. e. (7 points) Illustrate in the graph for b and d s situation. Explain intuitively the results. The budget constraint of case b and d are different from that of case a. The slope of budget constraint in case b is flatter than that of in case a since only the price of X is decreased. The budget constraint in case d is a parallel shift to the right of that of in case a. At the same time, the budget constraint in case d passes through the equilibrium of case b. The initial equilibrium is mark by (1). The equilibria in case b and d are marked by (2) and (3), respectively. The levels of utility in case a, b, and d are marked by UU 1, UU 2, and UU 3, respectively. The level of utility of Joe under money transfer, UU 3 is higher than the level of utility of Joe under reimbursement, UU 2. Under the reimbursement, Joe consumes more units of X which is relatively cheaper than Y. On the other hand, under the lump-sum transfer, there is no change in relative price between X and Y so Joe consumes less X than the reimbursement case and chooses (3) which gives higher utility. 5
(4 pts) Illustration with correct graph (2 pts) Correct 3 budget constraints (2 pts) Correct 3 indifference curves (3 pts) Intuitive explanation 3. (51 points) SBC, the monopoly satellite company, broadcasts TV to subscribers in New York and Washington D.C. area. The demand functions for each of these two areas are Qdc=60-0.25Pdc Qny=100-0.50Pny where Q is the number of subscriptions per year and P is the subscription price per year. The cost of providing Q units of service is given by C= 40Q where Q=Qdc+Qny (If you need rounding do it at the second digit. ex) you can use 123.35 instead of 123.3456.) a. (7 points) What are the marginal revenue for the New York and DC markets? (1) *** DC Market *** Qdc=60-0.25Pdc Pdc=240-4Qdc TR=240Qdc-4Qdc 2 MR=240-8Qdc MC=40 MR=MC then Qdc = 25 then plug into demand function Pdc=140 Profit=TR-TC=240(25)-4(25) 2 1000-40(25)=2500 (2) *** NY Market*** Qny=100-0.5Pny Pny=200-2Qny TR=200Qny-2Qny 2 MR=200-4Qny MC=40 MR=MC then Qny = 40 then plug into demand function Pny=120 Profit=TR-TC=200(40)-2(40) 2 40(40)=3200 6
MR for DC=240-8Q dc MR for NY=200-4Q ny (3.5 pts) MR for DC (3.5 pts) MR for NY b. (7 points) What are the profit maximizing prices and quantities for the New York and DC markets? Profit maximizing price/quantity for NY: P dc =140, Q dc = 25 Profit maximizing price/quantity for DC: P ny =120, Q ny = 40 (3.5 pts) Pdc=140, Qdc = 25 (3.5 pts) Pny=120, Qny = 40 c. (10 points) What are the maximized profit for the New York and DC markets? As a new technology people in New York receives SBC's DC broadcasts and people in DC receives SBC's New York broadcasts. As a result, anyone in New York or DC can receive SBC's broadcasts by subscribing in either city. Thus SBC can charge only a single price. (5 pts) Profit DC:2500 (5 pts) Profit NY:3200 d. (10 points) What price should he charge? (3) *** combined market*** P=Pdc = Pny Q=Qdc+Qny horizontal summation Q=100-0.5P+60-0.25P Q=160-0.75P P=213.33-1.33Q Profit DC: 2500, NY: 3200. 7
TR=213.33Q-1.33Q 2 MR=213.33-2.66Q MR=MC then Q=65.16 P=126.67 Profit=TR-TC=213.33(65.16)-1.33(65.16) 2 40(65.16)=5647.23 P=126.67 (9 pts) P=126 or P=126.6 or P=126.7 etc (5 pts) Correct the equation & Incorrect the answer e. (10 points) How much quantities can SBC sell in New York and DC altogether? Q=65.16 (9 pts) Q=65 or Q=65.1 or Q=65.2 etc (5 pts) Correct the equation & Incorrect the answer f. (7 points) What will be the profit? Profit=5647.23 (9 pts) Q=65 or Q=65.1 or Q=65.2 etc (5 pts) Correct the equation & Incorrect the answer 4. (21 Points) The domestic demand curve, domestic supply curve, and world supply curves for a good are given in the above figure. All the curves are linear. Initially, the country allows imports. Then imports are banned. 8
a. (7 points) Calculate consumer and producer surplus without imports ban. Consumer surplus before the ban :.5 * 75 * 75 = $2812.5. Producer surplus before the ban :.5 * 25 * 25 = $312.5. Total social welfare : $3125. (3.5 pts) CS=$2812.5. (3.5 pts) PS=$312.5. b. (7 points) Calculate consumer and producer surplus after the ban. Consumer surplus after the ban :.5 * 50 * 50 = $1250. Producer surplus after the ban :.5 * 50 * 50 = $1250. Total social welfare : $2500. (3.5 pts) CS=$1250 (3.5 pts) PS=$1250 c. (7 points) Is the country better off with the ban on imports? Explain why? Consumer surplus has decreased by $1562.5 and producer surplus has increased by $937.5 because of the ban. Total social welfare has decreased by $635. The country is worse off because the total social welfare has decreased. 5. (28 points) Write down the definition of the following terms. a. (7 points) Negative Externality (5 pts) It has a negative effect on third parties. (7 pts) 3pts + Explain Cost & Supply of negative externality 9
b. (7 points) Moral hazard (3 pts) hidden behavior, The probability or magnitude of action that don t explain full attempts. (5 pts) Asymmetry of information c. (7 points) Principal-Agent problem (3 pts) Agents act to achieve their own goals not for principal s (5 pts) Asymmetry of information d. (7 points) Nash Equilibrium (3 pts) They are trying to maximize their payoff (5 pts) Once the players have settled on strategies that form a Nash equilibrium, neither player has incentive to deviate 10