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# m07 - UNIVERSITY OF TORONTO Faculty of Arts and Science...

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Unformatted text preview: UNIVERSITY OF TORONTO Faculty of Arts and Science APRIL/MAY 2007 EXAMINATIONS ECO 200Y Duration - 2 hours Examination Aids: Non-Programmable Calculators Instructions: Choose FIVE questions among seven (each question is equally weighted and worth 20 points). Question 1 A monopolist currently has a total production cost TC01d=0.015Q2 and a marginal cost MCold=0.03Q. The market demand is P=50-0.01Q. The monopolist could invest 20000 to upgrade its technology so that the total production cost will be TCnew=10Q and a the marginal cost MCnew=10. A) Will the monopolist upgrade its technology? (6 points) B) Now the government regulates the market price so that the monopolist can not charge a price higher than 33. Will the monopolist upgrade the production technology? Will consumer be better off with the price regulation? Why? (7 points) C) A government agency proposes to lower the price ceiling from 33 to 15. Is this a good suggestion? (Compare this policy to case A) and B) and use consumer surplus to illustrate it.) (7 points) » Question 2 A Canadian ﬁrm sells its product to both domestic and US. consumers. Its total cost is MC=3, where Q is the total output (amount sold domestically plus amount exported and sold abroad). Domestic demand is P =15 — Q and US. demand is PA = 25 — 2Q A . Cost C for storage and transportation is negligible, so exporting to US. from Canada or exporting to Canada from US. has no additional cost other than tariff t: anyone can pay t for each unit to pass the border and sell to the market on the other side of the border. A) Before NAFTA, t=12, How does the ﬁrm sell in both markets? (8 points) B) With NAFTA, the tariff is reduced to zero, i.e., t=0. What is the price? What is the quantity the ﬁrm sells in Canada? In the U.S.? Are Canadian consumers better off with NAFTA? Are US. consumers better off with NAFTA? (12 points) Question 3 For many people, the wage rate varies with the number of hours that they work. Overtime work, for example, oﬂen commands a higher wage rate. John has smooth convex indifference curves between leisure and income. He can work as many hours as he chooses. In his current job, John is paid \$5 per hour for the ﬁrst 8 hours he works, and \$20 for each hour over 8. Under this payment schedule, John chooses to work 12 hours per day. a. Assuming John has no non-labor income, graph his budget constraint. On your graph, also show John’s current choice of work and leisure. (6 points) b. At this choice, what is John’s marginal rate of substitution? Explain. (7 points) 0. John is offered a new job that pays \$10 per hour for every hour he works. On a new diagram, show the old and new budget constraint? Will John take the new job? Explain. (7 points) Question 4 Arsenal Energy (AEI) is a junior oil exploration company based in Alberta. AEI is considering purchasing one of two concessions for oil exploration near Evi, Alberta. Concession A is already developed and AEI knows that will generate \$100 of proﬁt. Concession B is not yet developed and its proﬁtability depends on the amount of oil AEI will be able to extract. AEI estimates that there is a 30% chance the concession will generate \$25 of proﬁt and a 70% chance it will be generate a proﬁt of \$144. AEI’s utility ﬁlnction is given by U(7r) = 27; where 7: denotes AEl’s proﬁt. a) What is the expected proﬁt from concession B? (5 points) b) Which of the two concessions will AEI purchase? Explain clearly. (5 points) Before making its decision, the seller of concession B allows AEI to perform a test drill. By performing a test drill, AEI learns the value of concession B. A test drill costs \$10. c) What will AEI decide to do now? Explain clearly. (5 points) (1) Write down the equation that determines the highest price AEI is willing to pay to perform a test drill. (5 points) leant’d . .. Question 5 A ﬁrm produces widgets using labor (L) and capital (K). You know the following: i) When the ratio of labor to capital employed exceeds 2 (i.e. L>2K), the marginal productivity of labor (MPL) is 0 while the marginal productivity of capital (MPK) is 1; ii) When the ratio of capital to labor employed exceeds 2 (i.e. K>2L), MPL is l and MPK is 0; iii) When the ratio of labor to capital employed is in between V2 and 2 (i.e. 0.5KSLS2K ), MPL=MPK=1; a) In a clearly labeled diagram, draw one or more isoquants consistent with the information above. (8 points) b) What is the ratio of labor to capital at the cost minimizing input combination if the cost of one unit of labor, w, is \$3 and the cost of one unit of capital, r, is \$5 ? Explain clearly. (7 points) c) Give the formula of a production function that satisﬁes properties i), ii) and iii) above. (5 points) Question 6 Consider the following utility function of a consumer, U(x,y)==ln(x)+y, where the marginal utilities of x and y are given by MUx=1/x and MUy=1 respectively. Let px and py be the price of good x and good y, respectively. Let M be the income of the consumer. a) What is the marginal rate of substitution? (3 points) b) Suppose that M=100, px=10 and py=5. What is the optimal consumption bundle? (4, points) , 0) Suppose that the government rations purchases of good x such that the consumer is limited to 1 unit of it. Assuming that the consumer chooses to spend her entire income, how much units of good y will the consumer buy? (f 8' points) (1) Show by how much the consumer utility decreases after the government restrictions? (.5 points) COﬂt'd . . . Question 7 The professional baseball league on the planet Economus allows team owners to draft players for life. Once a player 15 acquired 1n the draft, team owners may trade players to other teams The demand fosr high quality players 13: QHD = 2000— PH/ 1000 The supply of high quality players 18 QHS — —-500 + Ps/3000. a) What is the lowest price necessary to induce an owner to trade a high quality player? Determine the equilibrium price and quantity of high quality players. (4 points) The demand for low quality players 13: QLD = 400—- PL/ 1000 The supply of low quality players IS QLS = -125 + Ps/3000. b) Determine the equilibrium price and quantity of low skill players. (5 points) Now, suppose that only the team that has the rights to the players knows the quality of the player. This implies the new demand for players of uncertain quality IS QD — —1200 — PLs/l 000. The supply of players becomes: Q3 = -625 + P/3000 ifP<\$1, 500, 000 = -125 + P/1500 ifP>\$1, 500, 000 c) Derive the equilibrium price and quantity for players of uncertain ability. (5 points) (1) Do you believe any high quality players are being traded at this new market price? (6 points) ...
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m07 - UNIVERSITY OF TORONTO Faculty of Arts and Science...

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