ECO204_2009_Final_Exam - UNIVERSITY OF TORONTO Faculty of...

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Unformatted text preview: UNIVERSITY OF TORONTO Faculty of Arts and Sciences April Examinations 2010 ECO 204 Y1Y Duration: 3 hours Total Points: 200 points Examination Aids: Single 8.5” by 11” (Size A4) Double sided paper and calculator. Instructions: ‐ This test consists of 5 questions in 28 pages, single‐sided. Please give your name as it appears in ROSI Last Name: ____________________ First Name: ______________ Student Number: _______________________________ Question 1 2 3 4 5 Points 35 40 40 55 30 Scores TOTAL (200 Points) All questions in this exam are based on the information in Question 1 Please read and do Question 1 before doing other questions In case you can’t solve question 1 note that it gives information required for other questions Question 1 [35 points] Founded in January 2010, Dulce & Havana (D & H) designs and manufactures high end men’s jackets right here in Toronto. The inputs for D & H jackets are fixed labor (tailors), fixed capital (machines), and variable materials. Once manufactured, the jackets are sold at a uniform price to 10 individual customers in NYC; at a uniform price to 5 individual customers in Boston; and at a uniform price to the Harry Boor‐son store on Bloor Street in Toronto. The marginal cost of distribution to NYC is $300; the marginal cost of distribution to Boston is $100; and the marginal cost of distribution to Toronto is $0. The following graph depicts D & H’s business model: MCDistribution = $300 Fixed Labor Toronto Factory NYC Fixed Capital MCDistribution = $100 Boston MCDistribution = $0 Materials Inputs T. O. Jackets Manufactured D & H manufactures jackets according to the production function: Here is number of jackets manufactured, is fixed labor, is materials, and is fixed capital. Currently, in 2010, the Toronto factory currently employs 32 tailors ( 32) who work on 8 machines ( 8). D & H hires tailors and purchases materials from competitive markets. D & H purchased the machines in January 2010 for $100 each and the machines have a lifetime of 20 months. In each month: $10, $10, $100 D & H has signed a 1 year contract with Harry Boor‐son: in each month of 2010 D & H will sell Harry Boor‐ son 20 jackets a month at a fixed price of $100. This contract expires in December 2010. Page 2 of 28 Label the NYC market “market 1”, the Boston market “market 2” and the Toronto market “market 3”. The following exhibit contains some key figures for January – March 2010: Dolce & Havana: January – March 2010 January Units Sold in NYC: February March 10 30 20 Units Sold in Boston: 20 10 10 Units Sold in Toronto: 20 20 20 $9,000 $21,000 $16,000 NYC Revenues: Boston Revenues: $5,000 $3,500 $3,500 Toronto Revenues: $2,000 $2,000 $2,000 50 40 50 10 10 10 5 5 5 Available (Unused) Capacity Number of individual customers in NYC Number of customers individual customers in Boston Page 3 of 28 1,000 10 and from this calculate the (a) [5 points] Show that the NYC market demand curve is price elasticity in March 2010. Show all calculations and state any assumptions. [You will need this demand curve for other questions in this exam]. Answer: Page 4 of 28 450 10 and from this calculate the (b) [5 points] Show that the Boston market demand curve is price elasticity in March 2010. Show all calculations and state any assumptions. [You will need this demand curve for other questions in this exam]. Answer: Page 5 of 28 (c) [10 points] Show that the monthly cost function for manufacturing the target output is: 400 25 [You will need this cost function for other questions in this exam. From the cost function above note that the total variable cost of serving the NYC market is 25 , the total variable cost of 300 25 and the total variable cost of serving the Toronto 100 serving the Boston market is 25 ]. market is Answer: Page 6 of 28 (d) [5 points] Does D & H have increasing, constant, or decreasing returns? Provide an argument for your answer. Answer (e) [10 points] Recall that D & H owns machines and that in each month: $10. What is D & H’s monthly opportunity cost rate of capital? Show all calculations and state any assumptions. Answer Page 7 of 28 Question 2 [40 points] [For this question, use information from Question 1 only] Recall that D & H has 10 individual customers in NYC (“market 1”). (a) [5 points] Recall from question 1 (a) that the NYC market demand curve is: 1,000 10 Assuming all NYC customers are identical, use this market demand curve to derive the individual NYC customer’s demand curve. Show all calculations and state any assumptions. Answer: Page 8 of 28 (b) [5 points] [This part should be answered independently of part (a)] Suppose each individual NYC customer has the utility function: , 2 Here is savings in dollars and is the number of D & H jackets. Denote income by and the price of good 1 (D & H jackets) by . Solve the UMP and derive expressions for and in terms of the parameters , , and (i.e. don’t use numbers for ). Answer: Page 9 of 28 (c) [5 points] Use your answers in parts (a) and (b) to deduce the parameters and in the utility function. Does this consumer have monotonic preferences over D & H jackets (good 1)? Show all calculations and state any assumptions. Answer (d) [5 points] For what price of D & H jackets will a NYC customer maximize or minimize savings? Prove whether savings are maximized or minimized. Show all calculations and state any assumptions. Hint: Use the expression for from part (b). Answer: Page 10 of 28 (e) [10 points] Suppose in April 2010, D & H sells jackets in NYC through a two part tariff where each customer pays an access fee for the right to buy jackets and a “usage” price for each jacket. Use the individual demand curve in part (a) and calculate the optimal and (answers with decimal places are OK). Graph your solution below. Hints: Allow for the possibility , and choose and to max Π . [Do two part tariff pricing in this part only]. Answer: Page 11 of 28 $ q Page 12 of 28 (f) [5 points] Now suppose that in April 2010 D & H sells jackets in NYC through 1st degree price discrimination. Use the individual demand curve in part (a) to calculate the optimal prices and number of jackets (answers with decimal places are OK). Graph your solution below. [Do 1st degree price discrimination in this part only]. Answer $ q Page 13 of 28 (g) [5 points] [This part assumes uniform prices] Suppose that in April 2010, NYC consumer with the utility function: , 2 $800. Consider a typical Here is savings in dollars and is the number of D & H jackets. Suppose this consumer has an income of $5,000. Using values for and from part (c), solve the UMP for the optimal , and (any) Lagrange multipliers given that $2,600. Calculate the marginal utility of relaxing the savings limit constraint. Show all calculations and state any assumptions. Answer Page 14 of 28 Question 3 [40 points] [For this question use information from question 1 only] (a) [10 points] Use the Kuhn‐Tucker/Lagrangian method to calculate D & H’s profit maximizing outputs, prices and (any) Lagrange multipliers for all 3 markets in April 2010. Show all calculations and state any $100, 20. assumptions. Hints: Don’t forget the constraint that total output capacity, and that Answer: Page 15 of 28 Page 16 of 28 (b) [15 points] Now suppose there is a possibility of arbitrage between (i) NYC and Boston and (ii) between Boston and Toronto. Assume the cost of arbitrage between NYC and Boston is $300, and the cost of arbitrage between Boston and Toronto is $200. Use the Kuhn‐Tucker/Langrangian method to calculate the optimal outputs, prices and (any) Lagrange multipliers for all 3 markets in April 2010. Answer Page 17 of 28 Page 18 of 28 (c) [10 points] [This part is based on your answer to part (b)] Suppose D & H can choose to raise the cost of arbitrage either between NYC‐Boston or between Boston‐Toronto. Which one would D & H choose? Show all calculations and state all assumptions. Answer: (d) [5 points] Give two examples of how companies in prevent or inhibit arbitrage. Answer: Page 19 of 28 Question 4 [55 points] [For this question, use information from question 1 only] D & H jackets have become a prized fashion item ‐‐ everyone wants one. Seeking to cash in on D & H’s success, another company, Canadian Moose (CM), sets up a manufacturing facility in Toronto and starts producing jackets identical to D & H’s jackets. CM competes with D & H in the Boston market only. The two companies have identical cost functions and the marginal cost of distribution. For this question assume both companies have ample (unlimited) capacity. In this question, denote D & H’s output by and CM’s output by . Calculate and give all answers up to two decimal places. You can hold D & H’s NYC and Toronto prices and outputs constant. (a) [10 points] Suppose D & H and CM compete as Cournot rivals. Calculate the optimal outputs and price in April 2010. Show all calculations and state any assumptions. Answer: Page 20 of 28 (b) [10 points] Suppose D & H and CM compete as Stackelberg rivals with D & H as the leader. Calculate the optimal outputs and price in April 2010. Show all calculations and state any assumptions. Answer: Page 21 of 28 (c) [10 points] Suppose D & H and CM secretly collude and act as a cartel. Calculate the optimal outputs and price in April 2010. Show all calculations and state any assumptions. Hints: Do not assume that the firms in the cartel will produce the monopoly profit maximizing output (instead, solve the cartel’s optimization problem). Answer: Page 22 of 28 (d) [15 points] Suppose D & H (player 1) and CM (player 2) play a one‐shot simultaneous game in April 2010 where each firm can produce the cartel output, Cournot output, or the profit maximizing monopoly output. Fill the tables below and compute the pure strategy Nash equilibrium. Hint: Exploit the fact that the two firms are symmetrical, so that to calculate the entries below you need to do 6 calculations, not 9. Answer Price of Jackets in the Boston Market Cartel Output = Cournot Output = Monopoly Output = Cartel Output = Cournot Output = Monopoly Output = Show all calculations below. Page 23 of 28 Revenues Cartel Output = Cournot Output = Monopoly Output = Cartel Output = Cournot Output = Monopoly Output = Show all calculations below. Page 24 of 28 Total Variable Cost Cartel Output = Cournot Output = Monopoly Output = Cartel Output = Cournot Output = Monopoly Output = Show all calculations below. Page 25 of 28 Payoffs (Total Gross Profits) Cartel Output = Cournot Output = Monopoly Output = Cartel Output = Cournot Output = Monopoly Output = Show the pure strategy Nash equilibrium above. Indicate if this is a prisoner’s dilemma game. (e) [10 points] True or false: “A cartel of D & H and CM will eventually break down because each party has an incentive to cheat”? Show all calculations and state any assumptions. Answer: Page 26 of 28 Question 5 [30 points] [For this question, use information from question 1 only] Recall that D &H has a contract to sell Harry Boor‐ son 20 jackets per month at a price of $100 per jacket. Harry Boor‐son is famous for its markdown policy: over time the store drops the price of unsold items. On April 1st 2010, Harry Boor‐son has priced D & H jackets 25% markup over cost. Consider a customer who wants to buy one D & H jacket: he is willing to pay $120 for the jacket. He can buy the jacket today (week 1) or wait until week 2 when the jacket may be available with 2/3 probability and marked down to $75. The customer can buy the jacket in week 2 or wait until week 3 when the jacket may be available with 1/2 probability and marked down to $60. The customer can buy the jacket in week 3 or wait until week 4 when the jacket may be available with 1/4 probability and marked down to $50. If the jacket is not sold in week 4 it is removed from the shelf and given to Harry Boor‐son’s cousin Da Ali Gee. For your convenience, the following table summarizes Harry Boor‐son’s policy: Week 5 + Week 1 Week 2 Week 3 Week 4 Probability Jacket is available Price 1 2/3 1/2 1/4 0 25% markup over cost $75 $60 $50 Not for Sale Assuming the customer is risk neutral and decides on the basis of consumer surplus, what is the customer’s optimal strategy? What is Harry Boor‐son’s expected revenues and when does it expect to sell the jacket? Show all calculations. Hint: Draw a decision tree. Answer: Page 27 of 28 Page 28 of 28 ...
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This note was uploaded on 12/07/2011 for the course ECON 204 taught by Professor Ajazhussain during the Spring '09 term at University of Toronto- Toronto.

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