Part I The cost function c(w1,w2,y) of a firm gives the cost of producing y units of output when the wage of factor 1 is w1 and the wage of factor 2 is w2. Find the cost functions for the following firms:

a) A firm with production function f(x1,x2) = min{ax1,bx2}

b). A firm with production function f(x1,x2) = ax1+bx2

3 c). A firm with production function f(x1,x2) = max{ax1,bx2}

d). A firm with production function f(x1,x2)=(243+(x1âˆ'9)3)x2

Part II For each of the cost functions found in part I, find the marginal cost, the average cost function and the average variable cost function.

Part III Assume that x2 is fixed in the short run to x2 = 10. Find the short run supply function

Part IV Find the long run supply function