Problem 1: Suppose f(L; K) = K2 + LK + L1/2K1/2: Does this production function exhibit increasing, decreasing or constant returns to scale? Show your work.
Problem 2: Suppose f(L;K) = KL9 w = 1;r = 2: MPL = 9L8K;MPK = L9: How much labor and capital should the firm hire if it wants to produce 10 units of output while minimizing its cost of production? Show your work.
Problem 3: Suppose f(L; K) = min{2K; 5L}: w = 1; r = 2500: Derive the cost function. Show your work
Problem 4: Suppose we have a perfectly competitive market with price p. A typical firm, in the short run, hasVC(q)=q+aq2 andF (Fixed cost). MC(q)=1+2aq:a is a constant such that a > 0:
a) Derive expressions for AVC and AC
b) What is the range of prices for which the firm would shut down, in the short run? Explain.
c) What is the short-run supply function for the firm?
d) Suppose p = 3: Calculate firm's profits as a function of a: Show your work.
e) How do profits calculated in part d change with a? Explain.
Problem 5: Suppose there are n identical firms each having a supply function p = aq2. What is the market supply function? Show your work.