eco204_HW_14_solution

eco204_HW_14_solution - University of Toronto, Department...

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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 14 Solutions ______________________________________________________________________________ In lecture 16, we discussed some “commerce” applications of the black box monopoly model. One of the applications was optimal (re) pricing under uncertainty where after producing the output the firm had to re‐optimize in light of new information. In this question, you’ll practice uncertainty for the black box model (where what a firm produces is sent to the market to be sold and MC is solely due to manufacturing costs). Question 1 (Based on ECO 204 2007‐2008 Test 3) Sweet Ajax ‐‐ a Canadian company ‐‐ manufactures Halal maple syrup, sold in Canada and USA. Sweet Ajax’s marketing group estimates demand for each month of 2009 to be: P = 3,000 ‐ Q Where P is in Canadian dollars and Q is units of output. Sweet Ajax’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 February 2009. What’s your decision? Show all calculations and steps clearly. Answer: To figure out how much to produce and sell, Sweet Ajax sets MR = MC. The interpretation of MR is additional revenue from producing and selling another unit while the interpretation of 1 University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain MC is additional cost of producing and selling another unit. If a company is maximizing profits, MR = MC. Now: MR = MC → 3000 – 2Q = 1000 → 2Q = 2000 → Q = 2000/2 = 1000 → P = 3000 – 1000 = $2000 This is what you’ll plan to produce. Unless there is new information before production begins you will give the order to produce 1000 units, priced at $2000 each. (b) Suppose that before production of the output in part (a) begins, your finance group informs you that the Canadian dollar has appreciated substantially against the US dollar (i.e., it takes more U.S dollars to buy a Canadian dollar). The marketing department estimates that the max WTP (“willingness to pay”) has fallen by $500 and recommends that prices in February should be $500 less than the price in part (a). Do you think they are right? Show all calculations and steps clearly. Answer: It’s important to note the timing of this new information‐‐ the new demand curve is given to you before production has begun. Thus, it is as if you’re starting the problem from scratch: you should set MR = MC. The new demand curve is: P = 2500 – Q. Setting MR = MC: 2500 – 2Q = 1000 → 2Q = 1500 → Q = 1500/2 = 750 → P = 2500 – 750 = $1750 Compared to part (a), the price should be lowered by $250 even though max WTP has fallen by 2 University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain $500! Note the marketing department is incorrect. (c) Now suppose that after production of the output in part (a) begins, your finance group informs you that the Canadian dollar has appreciated substantially against the US dollar (i.e., it takes more U.S dollars to buy a Canadian dollar). The marketing department estimates that the max WTP (“willingness to pay”) has fallen by $500 and recommends that prices in February should be $500 less than the price in part (a). Do you think they are right? Show all calculations and steps clearly. Answer: It’s important to note the timing of this new information‐‐ the new demand curve is given to you after production has been completed. Recalling that in this question all MCs are due to production (not selling) costs, the MC will be 0. With the new demand curve P = 2500 – Q and setting MR = MC: MR = 0 So that you’re maximizing revenues (i.e. when MC = 0 profit maximization is equivalent to revenue maximization). Thus: 2500 – 2Q = 0 → Q = 1250 That is, with the new demand and to maximize revenues, you should plan to sell 1,250 units. But you only have 1,000 units for sale. Hence, you will sell 1,000 units and the price will be: → P = 2500 – 1000 = $1500 Compared to part (a), the price should be lowered by $500 max WTP. So the marketing department is correct. (d) Return to the original question. Suppose MC decreases from $1,000 to $500 before production begins. What is the optimal price and output compared to part (a)? Answer: The timing of the information is crucial here. Observe that MC has changed before production begins. Hence, the company should optimize using MR = MC: 3 University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain 3000 ‐ 2Q = 500 → 2Q = 2500 → Q = 2500/2 → Q = 1250 Which is the same output in part (c) except that this time this is the output to be produced and sold. Thus, you will order 1250 units to be produced and sold. The price will be: P = 3000 ‐ Q → P = 3000 ‐ 1250 → P = $1750 Study Hint: Observe how when new information arrives before production we use MR = MC where the MC > 0. But when new information arrives after production we use MR = 0 as there is no longer a MC of production. 4 ...
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This note was uploaded on 05/02/2011 for the course ECO 204 taught by Professor Hussein during the Fall '08 term at University of Toronto.

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