eco204_summer_2009_practice_problem_15

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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 15 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 In this question you will practice shocks to a competitive industry. Suppose all existing firms in a competitive industry have CobbDouglas technologies: Q = L1/2 k1/2 Note how capital is fixed since K = k. Suppose PL = $10, PK = $10, k = 10 and P = $20. (a) Calculate numerically and algebraically each 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) If the industry is in the long run, then confirm that the output price of $20 is the long run equilibrium price. (d) Suppose the market demand curve is P = 100 0.04Q. How many firms are in this industry? (e) Derive the long run supply equation. 1 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain (f) Confirm your answer in part (e) by solving for market equilibrium price and output. (g) Suppose market demand experiences a positive shock where the new demand equation is: P = 200 0.04Q Suppose this is an increasing cost industry assume the expansion of this industry raises the price of capital to $40. Further assume that all potential entrants have the same technology as the incumbent firms. What is the equilibrium price, the optimal number of workers and the number of new (if any) firms? Assume existing firms continue to hold capital at k =10. You may want to think about why this question tells you that the new firms have the same technology as incumbent firms. 2 ...
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