Problem 1: Suppose f(L; K) = K² + LK + L^1/2K^1/2: 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.