eco204_HW_18 - University of Toronto, Department of...

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Unformatted text preview: University of Toronto, Department of Economics, ECO 204 20082009 S. Ajaz Hussain ECO 204 20082009 Ajaz Hussain HW 18 Question 1 In this question, you will practice 3rd degree price discrimination. Suppose you are pricing manager of parking Toronto's Pearson airport. You've identified two market segments: "short" and "long" term parkers. The demands for each segment are: Short term: Ps = 3 Qs/200 Long term: PL = 2 QL/200 P is hourly rate and Q is number of cars. There is a single garage with 600 spaces and you have to allocate spaces between the two segments. Let the MC of parking be negligible. (a) What is the garage owner's objective? (b) Suppose the garage charges a single price for both segments. What is the optimal price? Hint: the short and long term parkers are being "aggregated". (c) Suppose the garage charges each segment a different price what are each segment's optimal prices? Hint: first try the problem as if there is no constraint and then if necessary as if there is a constraint (you did the same thing for the single output case with capacity in Lecture 13). What is the price elasticity in each segment? (d) Repeat question (c) with a capacity of 400 instead of 600. Question 2 (20072008 Final Exam Question) PooJoe is a French car maker. It manufactures cars in France at MC = $100. Demand for cars in France is given by the equation PF = 3,000 5QF. PooJoe also exports cars to Japan where 1 University of Toronto, Department of Economics, ECO 204 20082009 S. Ajaz Hussain demand is given by the equation PJ = 1,500 6QJ. Suppose transportation cost between countries is $200 per car. (a) How many cars should be manufactured for the French and Japanese markets? Assume that French Customs doesn't allow cars bound for Japan to be "reimported" back into France. Calculate the French and Japanese prices. Show all calculations clearly. Hint: That cars cannot be reimported means there can be on no arbitrage between France and Japan. Moreover, think carefully what the MC in France and Japan are. (b) Now suppose French Customs allows cars exported to Japan to be reimported back to Japan. What should be the French and Japanese prices and number of cars? Show all calculations clearly. Hint: Look at Lecture 20 discussion on the price gap needed to prevent arbitrage. Question 3 (20072008 Test 3 Question) Alma Construction Company (ACC) has a manufacturing plant in London, Ontario with cost function: C(Q) = 500 + 5Q2 and demand function Q = 120 0.2P. Suppose ACC builds an identical manufacturing plant adjacent to the first manufacturing plant. Argue that ACC should divide output equally between the two plants. Show all calculations and steps clearly. Hint: Use marginal analysis technique in Lecture 20. Question 4 Ajax produces output from two factories located in Buffalo, NY and Toronto, ON. The Buffalo factory has cost equation: C = 20QBuffalo + QBuffalo2 and the Toronto factory has cost equation: C = 10QToronto + (5/2)QToronto2. If Ajax is currently minimizing cost its costs and produces 5 units of output in Buffalo how many units is it producing in Toronto? 2 ...
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