Assume that a firm faces the following production function-
q(L,K) = L^(1/4) * K^(3/4)
a) Derive the Iso-quant curve for this firm.
b) Derive the Expansion path for the firm if w=1 and r=3.
c) Derive the short term cost function for a give level of k = 3.
d) Derive the long run cost function if w=1 and r=3
e) What is the optimal capital and labor if you want to produce 500 units of output?