eco204_HW_11 - 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 11 Question 1 Ajax Microchips produces graphic chips 3G phones. Ajax has a patent on the chip and is therefore a monopolist. Using ECO 220 and ECO 204 tools, it has estimated the demand equation to be Q = 5 ‐ 0.05P and the cost equation to be C(Q) = 100 + 20Q where Q is in ‘000s and P is in $. Ajax has a capacity of 3,000 units. (a) What is Ajax’s MR? (b) What is Ajax’s MC? (c) Ajax’s objective is to maximize profits. Suppose Ajax’s decision variable is Q: using MR = MC, solve for the profit maximizing output. What is the optimal price? (d) At the profit maximizing output, what must be true of Marginal ∏ (“M∏”)? Confirm your answer using the result from part (c). (e) Ajax’s objective is to maximize profits. Suppose Ajax’s decision variable is P: using MR = MC, solve for the profit maximizing price. What is the optimal output? Hint: think carefully about what MR = MC means. (f) Your answer in part (c) is below Ajax’ capacity: that is, it is optimal to “waste” capacity. Your boss, who has an MBA from University of Worst Odors (UWO), feels that there is something wrong with wasting capacity. Convince him that he is wrong. (g) Now suppose Ajax’s objective is to maximize revenues. Suppose Ajax’s decision variable is Q. Solve for the revenue maximizing output. What is the optimal price? 1 University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain (h) Compare the profit and revenue maximizing output and price: what is the intuition for your result? (i) From the Fall semester, what is the price elasticity when a firm maximizes revenues? Confirm your answer using the result in part (g). (j) In class, we saw that: R(Q) = P(Q) Q → dR(Q)/dQ = P(Q) + {dP(Q)/dQ} Q Use this formula to prove that a firm with a linear demand will maximize revenues when price elasticity is ‐1. (k) Given your answer in part (h) what must be true about the price elasticity at the revenue maximizing price and output? We’ll return to this result next week. 2 ...
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