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WELLESLEY COLLEGE DEPARTMENT OF ECONOMICS ECONOMICS 201-03 JOHNSON Problem Set #5 (due IN LECTURE Friday, October 24 th ) 1. You are given the following production function for watches: q = KL - .8K 2 - .2L 2 Where q represents total watches produced, K represents units of capital input, and L represents units of labor input. a. Suppose that K = 10. Graph the total product of labor curve and the average product of labor curve. Can these be on the same graph? Why or why not? What value of L maximizes the average product of labor? How many watches are produced at that point? b. Stay with K = 10. Graph the MP L curve. At what point does the MP L = 0? Put the AP L from (a) and the MP L on the same graph. [Why can they be on the same graph?]. Where do they intersect and why? c. Suppose K jumps to 20. How would your answers to (a) and (b) change? d. Does watch production exhibit CRS, IRS, or DRS? Explain. 2. Economists use a concept called the elasticity of substitution to describe how quickly the MRTS changes (if at all) as we move around a given isoquant (thus as we change the capital/labor ratio in producing the given amount of output on the isoquant). That elasticity is given by the following expression: σ = % ( K / L ) / % MRTS Or, equivalently: σ = ∂ ln ( K / L ) / ∂ ln MRTS Calculate this elasticity of substitution for the following production functions. Comment on whether the value of this elasticity implies that K and L are easily
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