Consider a firm that employs capital (K) and labour (L) and uses the production technology Q = 3K + 4L. Let factor prices be r = $40 for capital and w = $20 for labour.

a) What is the firm's minimization problem?

b) Plot the isoquant for Q =100. What is the Marginal Rate of Technical Substitution (MRTS)?

c) For any output Q, what is the optimal combination of K and L given the input prices? Hint set MRTS = r/w and solve for L)

d) What is the cost function? Confirm C(Q=100) = 500

e) Given the above, what must the supply curve look like in long-run equilibrium?