Suppose the following equations are true:
Production Function: Q = K^(1/3)L^(2/3),
which means MPK = 1/3K^(-2/3)L^(2/3),
MPL = 2/3K^(1/3)L^(-1/3)
MRTS = 2(K/L)
Total Cost = rK + wL
r = .2
w = $5
A) Currently, K = 100. What is the cost of producing 10 units in the short run? Hint: first determine how much labor is needed.
B) Given these prices, what is the optimal ratio of K to L to minimize cost in the long run?
C) Given the optimal ratio, what are the optimal quantities of K and L to produce 10 units in the long run?
D) What is the total cost of producing 10 units in the long run?