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Unformatted text preview: UNIVERSITY OF TORONTO Faculty of Arts and Sciences April May Examinations 2009 ECO 204 Y1Y Duration: 3 hours Total Points: 200 points Examination Aid: Only Regular Calculators. Instructions: This test consists of 12 questions in 30 pages, singlesided. The last page is a "worksheet" Write answers only in the space provided for that question Last Name: ____________________ First Name: ______________ Student Number: _______________________________ Question (Points) 1. 20 points 3. 25 points 5. 15 points 7. 25 points 9. 5 points 11. 20 points Score Question (Points) 2. 10 points 4. 10 points 6. 20 points 8. 30 points 10. 5 points 12. 15 points TOTAL (200 Points) Score Question 1 (20 points) Alma's preferences over goods 1 and 2 are given by the utility function: U = Q1 Q2 where Q1 and Q2 are units of goods 1 and 2 respectively. Suppose + = 1. Denote Alma's weekly income by Y. Denote the price of good 1 by P1 and the price of good 2 by P2. (a) (5 points) Derive Alma's demand functions for goods 1 and 2. Show your calculations. Page 2 of 30 (b) (5 points) True or false: for a company selling good 1 to Alma, any price will maximize revenues. Show your reasoning. (c) (5 points) [This part can be answered without answering parts (a) & (b)]. True or false: a 10% increase in all prices and Alma's income will not change her optimal consumption of goods 1 and 2. Briefly explain your reasoning. Page 3 of 30 (d) (5 points) Suppose = 0.25 and = 0.75. Evaluate the statement: "a 100% increase in Alma's income leads to a 25% increase in the consumption of good 1 and a 75% increase in the consumption of good 2". Page 4 of 30 Question 2 (10 points) Your utility is a function of three goods: U = min(Q1 , Q2 , Q3 ) Denote income by Y and the price of good 1 by P1, the price of good 2 by P2 and the price of good 3 by P3. (a) (5 points) Derive the demand equations for goods 1, 2 and 3. Explain your reasoning and show all calculations. Page 5 of 30 (b) (5 points) What is the income elasticity for good 1? Show your calculations. Page 6 of 30 Question 3 (25 points) Jenn Inc. is a perfectly competitive firm with a capacity of 100 units. She uses labor (L) and capital (K) as variable inputs to produce output (q). Jenn's production function is given by: q = K1/2 L1/2 Suppose the price of labor is $160/worker and the price of capital is $10/machine. Denote the price of output by P. (a) (5 points) Does Jenn's technology have increasing, constant, or decreasing returns to scale? Prove your answer. Page 7 of 30 (b) (5 points) Derive Jenn's cost function and show that it exhibits the returns to scale from your answer in part (a). Show your calculations. Page 8 of 30 (c) (5 points) If Jenn is a "rational" producer, what is the equation of her supply curve? Show all calculations and graph the supply curve below: Page 9 of 30 (d) (5 points) Ettore Inc. is a "rational" producer and has the same technology as Jenn (i.e. q = K1/2 L1/2). Ettore proposes a merger with Jenn arguing that the merger will benefit from economies of scope. Is Ettore correct? (e) (5 points) [This part can be answered without answering parts (a) - (c)]. Assume Jenn is an "irrational" producer. Graph her supply curve below and briefly explain your reasoning. Page 10 of 30 Question 4 (10 points) Fuelled by easy access to drugs from the USA (United States of Addicts) the citizens of the Canadian town Crackotoa are fast becoming drug addicts. The mayor of Crackotoa, Ms. Cindy Bong, has started a drug treatment program which uses police officers (P) and drug counselors (D) as complementary "inputs" in 1:1 ratio to treat drug addicts (A) as the "output". (a) (5 points) The program currently has 1,000 police officers and 1,000 drug counselors. If Cracko toa's government doubles the budget for the drug treatment program, how many more police officers and drug counselors should Ms. Cindy Bong hire? Assume the price of police officers and drug counselors is constant. Page 11 of 30 (b) (5 points) Repeat part (a) for the case where the price of police officers and drug counselors also doubles. Page 12 of 30 Question 5 (15 points) The Table below reproduces Table B from the DHL case: International Air Express Market Shares by $ Revenues (1988) Company Market Share DHL 44% Fedex 7% TNT 18% UPS 4% Others 27% Source: Table B in DHL case. (a) (5 points) Calculate the CR4 in the international air express market. State any assumptions. (b) (5 points) Estimate the HHI from the data in the Table above. Brief explain whether the estimate overstates or understates the true HHI. Page 13 of 30 (c) (5 points) If Fedex and UPS merge what is the change in the global HHI? Show your reasoning. Page 14 of 30 Question 6 (20 points) The following table reproduces portions of Exhibit 11 from the DHL case. Exhibit 11 Revenue and Cost Lane Examples: DOX and WPX U.K. to United States (1990) DOX WPX Revenue $5,723,000 $2,342,000 Outbound Cost 2,392,915 667,712 Hub Cost 596,608 490,436 Line Haul 1 1,121,882 647,915 Delivery 1,376,953 386,049 Gross Margin 234,642 149,888 Gross Margin % 4.1 6.4 Shipments 231,139 68,580 Revenue/Shipment $24.76 $34.15 Note: Please see footnote at the bottom of this page. (a) (10 points) Suppose DHL's headquarters in Brussels sets prices to maximize profits. If Brussels raises the price of a document from $24.76 to $25.01 how many documents will be sent from the U.K. to the U.S on this lane? State any assumptions. 1 Line haul refers to the air segment of the shipment Page 15 of 30 (b) (5 points) Compute the price elasticity of the WPX segment. Show your calculations. (c) (5 points) Suppose DHL lowers the cost of shipping packages through learning by doing. Assuming the elasticity in part (b) is constant, what must the MC of packages be in order for the price of a document to be equal to the price of a package on the U.K. to U.S. lane? Show all calculations. Page 16 of 30 Question 7 (25 points) Proctor and Grumble (P&G), a risk neutral decision maker, must decide whether to develop and release a new shampoo "Shine on you" targeted at bald men. If P&G does not develop the shampoo the outcome is $0m. If P&G develops the shampoo, R&D costs will be $100m and when released into the market it will be a success (S) with probability 0.6 or a failure (F) with probability 0.4. If the shampoo is a success, gross revenues (before R&D costs) are estimated to be $500m. On the other hand, if the shampoo is a failure, gross revenues (before R&D costs) are estimate to be $0m. (a) (5 points) Draw P&G's decision tree and indicate whether the shampoo should be developed. Page 17 of 30 (b) (5 points) P&G's statistics consultant thinks the probability of success may not be accurate: i.e. there is a margin of error in the probability of success. The consultant worries that within the margin of error, the decision in part (a) may be change. For what range of the probability of success will P&G make the decision in part (a)? (c) (5 points) [This part can be answered without answering parts (a) - (b)]. Suppose a marketing company has developed a perfect (100% accurate) test for new products. The test results can be positive (+) or negative (). Fill in the entries in the two way classification table below. S F Total + Total 100 Briefly explain your answer below. Page 18 of 30 (d) (5 points) Draw P&G's decision tree if it makes the decision with the perfect test in part (c). What is P&G's decision with the perfect test? (e) (5 points) What is the value of a "perfect test"? Show your calculations. Page 19 of 30 Question 8 (30 points) Lee Hao, a private investor, has at T = 0 purchased a perpetual annuity (bond) issued by the BMO (Bank of Many Odors). The purchase price is $500 and the annuity will, starting at T= 0, pay an annual coupon payment of $100 forever. (a) (5 points) Calculate the yield to maturity of the BMO bond. What can you say about Lee Hao's opportunity cost of capital? In case you need it, the sum of an infinite series [1 + x + x2 + x3 + .. ] is 1/(1 x). Page 20 of 30 Lee Hao is a risk averse investor with utility function U = X. The recent economic downturn has led Lee Hao to believe that there is a chance BMO will default on the bond: he expects the annual coupon payment to be $40. (b) (5 points) What does Lee Hao think the probability of BMO defaulting is? Show your reasoning. (c) (5 points) What is Lee Hao's expected utility from facing the uncertainty that BMO might default? Page 21 of 30 (d) (5 points) Express Lee Hao's utility from facing the uncertainty of a default as an equivalent risk of facing the uncertainty of receiving either $10,000 or $0. Show your calculations. Page 22 of 30 (e) (5 points) How can Lee Hao use credit default swaps to hedge against the risk of BMO defaulting? Please describe how the credit default swap contract will be structured and how the counter party expects to profit from the swap. (f) (5 points) [This part can be answered without answering parts (a) - (e)]. Why have credit default swaps become a problem recently? Page 23 of 30 Question 9 (5 points) As you walk through Toronto's Pearson airport to catch a flight to Paris, you see a booth selling flight insurance for $12. If you die on the flight, the insurance company will pay your family $200,000. As of 2009 the probability of dying flying was 1 in 1.1 million. Should you buy the policy? State any assumptions. Hint: What is the price per dollar of insurance? Page 24 of 30 Question 10 (5 points) When booking a one way flight on Air Canada, you have the option of purchasing a travel insurance policy "On My Way" for $25. Here is the description on Air Canada's website: Get extra protection in case of flight delays or disruptions that are beyond the airline's responsibility or control. On My Way offers aroundtheclock priority rebooking service, a hotel if needed, and much more for only a small fee. Under actuarially fair insurance, what is the "benefit" of the On My Way travel insurance program for a passenger traveling one way from Toronto to NYC? According to Flightstats.com, 86% of flights from Toronto to NYC are on time. Page 25 of 30 Question 11 (20 points) Lb. Cake Corporation is a cake franchisor. Under the terms of the current contract with a restaurant on the U Toronto campus, Lb. Cake takes a fraction of the restaurant's revenues (R) and incurs a fraction of the restaurant's total cost (C). Lb. Cake supplies ingredients to the restaurant with a markup over AC: assume AC is constant and the restaurant has no other costs besides the cost of ingredients. Suppose the restaurant has a capacity of 700 cakes a day. Daily demand is given by the equation: P = 100 10 Q P is in dollars per cake and Q is in hundreds of cakes. Suppose = 0.2, = 0.25, AC = $8 per hundred cakes, and, Lb. Cake charges the restaurant a 100% markup over AC. (a) (10 points) If Lb. Cake chooses the price and quantity at the UT location, solve for the optimal P and Q. Show all calculations. Page 26 of 30 (b) (10 points) Lb. Cake has an opportunity to renegotiate the contract: it can change either by 0.1 or by 0.1 or the markup by 10%. (i.e. Lb. Cake can only change one of these). What do you think they should do? Show your reasoning below. Page 27 of 30 Question 12 (15 points) "Capital None", a credit card company, has to decide today (T = 0) whether to make a credit card offer to a particular consumer. There is no cost of making this unsolicited offer. If Capital None does not make an offer, the value of this decision is $0. If it makes an offer, assume the consumer always accepts. The terms of the Capital None credit card are: Issued for two periods only (T = 1, 2) Maximum limit of $1,000 in each period 2 (The "2" here is a footnote, not "squared"). Let i denote the interest rate charged by Capital None on the ending balance in each period. In any period the consumer has the credit card, she always "maxes out" it out: i.e., she charges the maximum limit of $1,000. In any period, the consumer can default on the credit card with probability p. If the consumer defaults in T = 1, Capital None swallows the loss and cancels her credit card in T = 2. If the consumer defaults in T = 2, Capital None again swallows the loss. In any period, if the consumer does not default Capital None profits from interest rate charges on the balance: i*(balance). Denote the opportunity cost of capital by r. Show that for Capital None to make a credit card offer to this consumer, the interest rate on the balance must be at least the odds of default: i.e. i p/(1 p). Hint: discount all figures to T = 0. 2 That is, $1,000 limit in T = 1 and $1,000 limit in T = 2. Page 28 of 30 Page 29 of 30 WORKSHEET Page 30 of 30 ...
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