An entrepreneur bought two shoe factories. Shoes produced in each of the factories are identical, and the production function is given by Q=(Ki Li)⁰.⁵, where i denotes the factory, that is, i=1,2. The two factories differ in their capital endowment: K1=25, K2=100. Prices of K and L are identical, r=w=$1.
a. The entrepreneur wishes to minimize the total costs of production in the short run. How should he divide the production between factories 1 and 2 ?
b. Determine the short run total, marginal and average costs, assuming that the production is optimally split between the factories.
c. What would be the allocation of production between the two factories in the long run?
d. What would the answer to c. be if the identical production functions in the two factories were characterized by decreasing returns to scale, ceteris paribus?