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eco204_HW_15 - University of Toronto Department of...

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Unformatted text preview: University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain ECO 204 2008‐2009 Ajaz Hussain HW 15 Question 1 (Based on Practice problems 16) Hee Haw (HH), a Canadian company, is the only manufacturer of specialized farm equipment. HH’s domestic demand curve is P = 3,000 ‐ Q, where P is the price in Canadian dollars and Q is output sold per month. HH’s fixed costs are $250,000 per month and its marginal cost is $1,000. You’re in charge of planning output and price each month. (a) Suppose you’re planning output and prices for April. What’s your decision? Show all calculations and steps clearly. (b) Suppose that a new market for HH’s products emerges in South America. HH has begun selling equipment in several test markets there and has found that demand to have a constant elasticity of demand, E = ‐3 (Review Lecture 4 on demand functions with constant elasticity 1 The cost of shipping to South America is $200/unit. One manager argues that the foreign price should be $200 above the domestic price in (a). Do you agree? Explanations must be brief. Question 2 A British Columbia resort offers year‐round activities: in winter, skiing and other cold weather activities and, in summer, golf, tennis, and hiking. The resort’s operating costs are essentially the same in winter and summer. Management charges higher rates in the winter ‐‐ resulting in average occupancy rates of 75% ‐‐ than in the summer ‐‐ when its average occupancy rate is 90%. Can this policy be consistent with profit maximization? Note what the question is asking: is it correct that management has 25% excess capacity in the 1 Remember that a linear demand function (P = a ‐ bQ) has a different price E at each point whereas a log‐linear demand function (Q = aP‐b or ln Q = ln a ‐ b ln P) has constant elasticity E = ‐b. 1 University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain winter compared to a 10% excess capacity in the summer? Should management drop prices in the winter to fill more rooms? Question 3 You’re advising a golf course “Expensive Ways to Play Marbles” on their fees for weekday and weekend golfers. Demand during the week is: P = 36 – Q/10 and demand during the weekend is: P = 50 – Q/12. The capacity of the course is 240 rounds per day. (a) Can the gold course charge different prices during the week and the weekend? If so, what are these prices and how many daily rounds of golf will there be on the weekdays and weekends? (b) Which market is more elastic—weekday or weekend? Hint: Use the point E formula: E = (dQ/dP)(P/Q). Question 4 General Motors produces light trucks in several Michigan factories, where its annual fixed costs are $180m and marginal cost per truck is approximately $20,000. Regional demand for trucks is given by: P = 30,000 – 0.1Q, P is in $ and Q is annual sales of trucks. (a) What is GM’s profit maximizing P and Q? What are light trucks profits? (b) GM is getting ready to export trucks to China. Based on marketing surveys, GM has found the elasticity of demand to be constant at E = ‐9. The additional cost of shipping is $800 per truck. A manager argues that the price in China should be at least $800 higher than the domestic price. Is this manager correct? (c) GM produces another version of the light truck at a marginal cost of $12,000 per truck. At the current price of $20,000, sales of the light truck have been disappointingly low with the result that GM has an inventory of 18,000 unsold trucks. The best estimate for the remaining trucks is: P = 30,000 – Q One manager recommends keeping price at $20,000. Another favors cutting prices to clear the entire inventory. In your opinion, what should GM do? 2 ...
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