Quantitative Intermediate Microeconomics Problem Set #3 1) Suppose that the production function is given by q=L α K β where α >0, β >0, and α + β <1. Show that (a) the production function is characterized by diminishing marginal product of labor (that is, calculate the marginal product of labor and show that it declines with higher quantities of labor), (b) the marginal rate of technical substitution depends only on the ratio K/L and not on the level of output, and (c) the production function is characterized by decreasing returns by scale. 2) The production function for the local electric utility company in Medford is given by: q=L M where L is labor and M is materials. Suppose that the city requires 100 units of electricity per month, that the cost of labor per unit equals 2 and that the cost of materials per unit equals 2. Calculate total costs of producing the 100 units at the Medford electric utility company. (Assume that Medford wants to provide the 100 units in the least cost way.)
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