eco204_summer_2009_practice_problem_9

eco204_summer_2009_practice_problem_9 - University of...

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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 Practice Problems 9 Please help improve the course by sending me an email about typos or suggestions for improvements Note: Please don't memorize these solutions in the expectation that similar questions will appear on tests and exams. Instead, try to understand how to derive the answer as you'll be tested on techniques and applications, not on memorization. Moreover, tests and exams will cover topics and techniques that may not be in these practice problems. You are urged to go over all lectures, class notes and HWs thoroughly. Question 1 Suppose a company has the production function: q = L k and has constant returns (not the same as constant returns to scale) (a) What is the short run production function? (b) What is the elasticity of output with respect to labor? Does your answer make sense give the company has constant returns? (c) Suppose the company doubles labor. Without using the equation for C(q) what is the impact on total variable cost? Average variable cost? Average cost? Question 2 In this question you will examine the properties of the short run cost, average cost, average variable, average fixed and marginal cost functions for the short run CobbDouglas production function: Q = L k. Note that capital is fixed at a level k. (a) When does this production function exhibit constant returns to labor? (b) Derive the short run demand for labor. 1 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain (c) Derive the short run total cost functions and examine the functional form when there are increasing, constant and decreasing returns. (d) Examine the functional form of the average fixed cost function. (e) Examine the functional form of the average variable cost function. (f) Examine the functional form of the average cost function. (g) Give a returns to scale explanation for the long run Ushaped AC curve and contrast this with a returns explanation for the short run Ushaped AC curve. Restrict the discussion to the Cobb Douglas production function. (h) Examine the functional form of the marginal cost function. In particular, when is the MC curve above the AVC curve? When is the MC curve coincidental with the AVC curve? When is the MC curve below the AVC curve? Hint: derive MC and express it terms of AVC. Question 3 Ajax Inc. produces cranberry juice and has the short run cost function C(q) = 5 + Qc. Don Damiano Inc. produces grape juice and has the short run cost function C(q) = 5 + Qg. If Ajax and Don Daminao merge, the short run cost function for both cranberry and grape juice is: C(q) = 5 + Qc + Qg. Are there economies of scope from a Ajax and Don Damiano merger? Question 4 (Summer 2008 Test Question) The faculty club bar at the University of Toronto employs labor L (labor hours) to serve customers Q. The production function is: Q = 60L L2. Currently, PL = $16, P = $2 and L = 1. The club hires L and sells Q in competitive markets. (a) Currently, at L = 1, what is the MPL = dQ/dL? Show all calculations clearly and interpret your answer. (b) Does the faculty club have decreasing, increasing or constant marginal returns? Show all calculations clearly. (c) What is the profit maximizing number of customers and labor? Show all calculations clearly. Hint: this is not the typical producer CMP. Maybe you want to maximize profits. (d) What is the impact on the club's profits from, ceteris paribus, an increase in the price of output and wages? 2 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Question 5 (Summer 2008 Test question) Jen Burgers (JB) uses labor L and capital K to "produce" burgers. Her production function is: q = K 1/3L2/3. (a) Does JB have increasing, decreasing or constant returns to scale? Show all calculations. (b) Suppose JB always produces a fixed target output q. Show that if JB uses the optimal amount of capital and labor, then 2/3 of her cost will be due to labor costs. (c) Now suppose capital is a fixed input (say k = 1). Does JB have a concave, convex, or linear short run production function? Show all calculations and graph the production function below. (d) Based on the answer in part (c), derive JB's TVC(q) equation. Please plot this equation below and indicate whether it is concave, convex, or linear. 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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