A firm is faced with a production technology that uses capital and labor: q = price of labor is w, and the price of capital is r. f (k, 1) = 11/3k1/3, the (a) Write down the cost minimization problem and determine the contingent input demand functions: 1°(w, r, q) and k“(w, r, q). Also, derive the cost function C(w, r, q). (b) The firm operates in a perfectly-competitive market and faces a market price of p. Write down the firm's profit function. Solve the maximization problem to determine (1) input demand, that is, the demand for labor and capital as a function of w, r, and p (2) the output supply function, q as a function of w, r, and p.

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