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ajaz_eco_204_2012_2013_chapter_13_Short_Run_CMP_PP

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University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. 1 ECO 204 Chapter 13: Practice Problems & Solutions for The Short Run Cost Minimization Problem in ECO 204 (this version 2012-2013) Department of Economics (STG), ECO 204, Sayed Ajaz Hussain _________________________________________________________________________________________________ P RACTICE P ROBLEMS W ITH S OLUTIONS TO C HAPTER 13: T HE S HORT R UN C OST M INIMIZATION P ROBLEM 1 Updated: 3/11/2013 (13.1) True, False: Short run cost of production to produce a target output is smaller than its long run cost of production. Explain your answer and give a graphical analysis to prove your point. You can assume Cobb-Douglas production function. (13.2) State the optimal labor rule and explain under what condition it hold. (13.3) Given the following production function, state under what conditions it is increase, decreasing and constant returns. Where is quantity is fixed capital, are labour, material input 1, and material input 2. (13.4) Consider a company with two divisions: division 1 and division 2. Suppose the price of each division’s output are independent of output (i.e. constants). However, the are functions of output (i.e. are not constants): for example, perhaps ( ) and ( ) where are constants . Derive the breakeven quantity of division 1 (use the cost functions provided). (13.5) In this question you will examine the properties of the cost, average cost, average variable, average fixed and marginal cost functions for the short Cobb-Douglas production function: are parameters and may be positive, zero or negative. (a) When does this production function exhibit increasing, constant or decreasing returns to labor? What is the connection between returns and returns to scale? (b) What is the percentage change in output due to a 1% increase in labor? Interpret the elasticity in light of the answer in part (a). 1 Thanks to Akber Nafeh for preparing these PPs from past HWs, tests, and finals. For feedback and comments please e-mail [email protected]
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University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. 2 ECO 204 Chapter 13: Practice Problems & Solutions for The Short Run Cost Minimization Problem in ECO 204 (this version 2012-2013) (c) Derive the optimal (short term) demand for labor. Why doesn’t optimal labor depend on wages? (d) Derive the short run total cost function. Examine the functional form when there are increasing, constant and decreasing returns. (e) Derive the short run average variable cost and average cost functions. Examine the functional form when there are increasing, constant and decreasing returns. In particular where does the U shaped short run AC come from? (13.6) Ajax Corporation has production function and has target output q. Currently, and (a) Under what conditions will Ajax have constant returns? Interpret constant returns. (b) For a given value of α, what is Ajax’s short run demand for labor?
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