eco204_summer_2009_HW_7 - University of Toronto, Department...

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Unformatted text preview: University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain ECO 204 Summer 2009 S. Ajaz Hussain HW 7 Please help improve the course by sending me an email about typos or suggestions for improvements Question 1 A 1984 study on cigarette demand estimated the equation: log(Q) = 2.55 0.29 log(P) 0.09 log(Y) + 0.08 log(A) 0.1 W where Q = annual consumption, P = price of cigarettes, A = annual expenditure on advertising, Y = per capita income and W = 1 for years after 1953, when the American Cancer Society first linked smoking to cancer. The "logs" are natural logs. (a) Write the model in the "constant elasticity" demand function form. (b) What is the price elasticity? (b)What is the income elasticity? Are cigarettes a normal good? (c) What is the advertising elasticity? (d) Interpret the coefficient on W. Ceteris paribus what was the impact of the cancer report on cigarette sales? Question 2 In this question you will do a competitive firm's profit maximization in two ways. In the first, you will set up the problem where the firm chooses optimal output and labor subject to the constraint that output produced equals the target output. In the second, you will set up the problem where the firm chooses optimal output given the cost function (i.e. the CMP has already been done). 1 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain Suppose a competitive firm has a CobbDouglas technology Q = L1/2 k1/2 (note how capital is fixed since K = k) and PL = $10, PK = $10, k = 100 and P = $20. (a) Calculate numerically and algebraically the firm's profit maximizing output and labor subject to the constraint that output produced equals the target output. (b) From your answer in part (a), calculate the actual dollar cost and derive the optimal short run cost function. Hint: a cost function gives the cost of producing target output using optimal labor and fixed capital. As such, it should be expressed in terms of q only. Use the algebraic answer from above. (c) Now solve the profit maximizing problem the way most textbooks do: instead of being given wages and lease rates, suppose the firm only has the cost function from part (b). Using M = 0 and MR = MC calculate the profit maximizing output. For MR = MC check whether you have the conditions allowing MR to equal MC. Obviously, you should get the same answer for output as in part (a). (d) Which of these will have the biggest impact on a competitive firm's profits: an increase in output price, or an equal decrease in wages or equal decrease in the cost of leasing capital? (e) Now suppose the company does not know its technology or its input prices. Will the firm's profits be impacted more by an increase in output price or a decrease in fixed costs? Question 3 (20082009 Final Exam Question) Jenn Inc. is a perfectly competitive firm with a capacity of 100 units. She uses labor (L) and capital (K) as variable inputs to produce output (q). Jenn's production function is given by: q = K1/2 L1/2 Suppose the price of labor is $160/worker and the price of capital is $10/machine. Denote the price of output by P. Assume both K and L are variable inputs. (a) Does Jenn's technology have increasing, constant, or decreasing returns to scale? Prove your answer. (b) Derive Jenn's long run cost function and show that it exhibits the returns to scale from your answer in part (a). Show your calculations. (c) If Jenn is a "rational" producer, what is the equation of her supply curve? Show all calculations and graph the supply curve below. Notice in this question, since all inputs are variable, you're actually deriving the long run supply curve 2 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain (d) Ettore Inc. is a "rational" producer and has the same technology as Jenn (i.e. q = K1/2 L1/2). E ttore proposes a merger with Jenn arguing that the merger will benefit from economies of scope. Is Ettore correct? (e) [This part can be answered without answering parts (a) (c)]. Assume Jenn is an "irrational" producer. Graph her supply curve below and briefly explain your reasoning. Question 4 Masued Inc. uses labor (L) and capital (K) to produce output (q). In the short run, K is fixed and L is variable. Masued's cost function is: C(q) = 50 + 4q + 2q2. Masued operates in a competitive market. Currently the market price is $16. (a) Does Masued have increasing, constant, or decreasing returns with respect to labor? (b) Derive Masued's supply curve equation. (c) At the current price, how much will Masued produce? (d) At the current price, is Masued profitable? (e) Suppose market demand is given by the equation Qd = 200 5P. Assuming the industry consists of identical firms, how many firms are currently operating? (f) What is the market supply curve? (g) Use your answer in parts (e) and (f) to verify the current price is $16. (h) Given your answer in part (d), predict what will happen in the long run. Be specific, quantifying your answers. Hint: Predict long run price, firm output, market supply curve etc. 3 ...
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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- Toronto.

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