What is the 1. Consider a firm with the Cobb - Douglas production function f (K, L) = 4K 1/2 L 1/3, where K denotes units of capital and L represents units of labor. Assume that the firm faces input prices of r = $10 per unit of capital, and w = $7 per unit of labor.18 (a) Solve the firm's cost - minimization problem, to obtain the combination of inputs (la bor and capital) that minimizes the firm's cost of producing a given amount of output, q. (b) Use your results from part (a) to find the firm's cost function. This is its long-run total cost, as all inputs can be altered. (c) Find the firm's marginal cost function and its average cost function. Interpret. (d) Assume now that the amount of capital is held fixed af K = 3 units. Solve the firm's cost minimization problem again to find the amount of labor that minimizes the firm's cost. (e) Use your results from part (c) to find the firm's short-run cost function (because in the short run, the firm can alter the amount of labor, but without changing the units of capital)1. Consider a firm with the Cobb - Douglas production function f (K, L) = 4K 1/2 L 1/3, where K denotes units of capital and L represents units of labor. Assume that the firm faces input prices of r = $10 per unit of capital, and w = $7 per unit of labor.18 (a) Solve the firm's cost - minimization problem, to obtain the combination of inputs (la bor and capital) that minimizes the firm's cost of producing a given amount of output, q. (b) Use your results from part (a) to find the firm's cost function. This is its long - run total cost, as all inputs can be altered. (c) Find the firm's marginal cost function and its average cost function. Interpret. (d) Assume now that the amount of capital is held fixed af K = 3 units. Solve the firm's cost minimization problem again to find the amount of labor that minimizes the firm's cost. (e) Use your results from part (c) to find the firm's short - run cost function (because in the short run, the firm can alter the amount of labor, but without changing the units of capital)