In: Economics

# A firm produces output y using two factors of production (inputs), labour L and capital K....

A firm produces output y using two factors of production (inputs), labour L and capital K. The firm’s production function is ?(?,?)=√?+√?=?12+?12. The wage rate w = 6 and the rental price of capital r = 2 are taken as parameters (fixed) by the firm. a. Show whether this firm’s technology exhibits decreasing, constant, or increasing returns to scale. b. Solve the firm’s long run cost minimization problem (minimize long run costs subject to the output constraint) to derive this firm’s i. demand function for labour L = L(y) ii. demand function for capital K = K(y) iii. long run total cost function C = C(y). c. Suppose in the short run, capital is fixed at K = 100. Derive the firm’s short run total cost function C = C(y). d. Derive the AFC, AVC, AC, and MC curves for the firm and graph them on the same diagram – be sure to label them. (Recall: these are short run cost curves). e. Let p be the price of the output y. Derive this firm’s short run supply function y = y(p) assuming it is a competitive firm?

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