problem set 5

# problem set 5 - Middle East Technical University Department...

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Middle East Technical University Spring 2011 Department of Economics ECON 201 Erol Çakmak TA: Osman Değer PROBLEM SET 5 1. Suppose a firm s production function is given as Q(K,L)= 150K 2 L 2 K 3 L 3 Assume capital is fixed at K= 5 units. a. Derive the firm s total product of labor, marginal product of labor and average product of labor. b. Plot MPL and APL on the same graph. c. Find the amount of labor at which MPL is maximized. d. Find the amount of labor necessary for this production process for MPL=APL. e. What is the maximum number of output the firm can produce in the short run? 2. Calculate the degree of homogeneity associated with the following production functions and comment on their returns to scale. a. Q(K,L) = AK α L β b. Q(K,L) = α K + β L c. Q(K,L) = K 3 /(KL + L 2 ) d. Q(K,L) = (L 2 + 8KL) 1/2 e. Q(K,L,M) = (MK + KL M 2 )/ L 3/2 3. Briefly answer the following questions: a. Must perfect substitutes have isoquants that are parallel straight lines with a slope of

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## This note was uploaded on 03/22/2012 for the course ECON 201 taught by Professor Çakmak during the Fall '10 term at Middle East Technical University.

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problem set 5 - Middle East Technical University Department...

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