Reference no: EM132421799
Problem: Consider the following production technology: Y = K + KαL β + L, where Y is output, K is capital, L is labor, and denote the wage by W, rental rate on capital by R and the price of output by P; α and β are positive parameters.
Required:
Question 1: For what values of α and β does this production technology exhibit diminishing marginal products of capital and labor?
Question 2: For what values of α and β does the production technology have constant, increasing, or decreasing returns to scale? In the remaining parts assume that the production function has Constant Returns to Scale (you should use the parameter restrictions you found in part (b)).
Question 3: Show that if the production function has constant returns to scale, then π(λK, λL) = λπ(K, L) for any λ > 0. (we showed in class that this is true in general, but here you only have to prove it for the given production function).
Question 4: Explain why part (c) implies that if we tried to solve the profit maximization problem, we would not be able to find a unique solution for K∗ and L ∗.