A firm has a production function f (k; l) = pkl. Suppose that in the short run the quantity of capital that the firm has to use is fixed at the level of 9 (and so k = 9), but when producing zero the firm can fully recover the cost of capital (the cost of the fixed level of capital is fully nonsunk).
Suppose that the prices of capital and labor are r = 3 and w = 2, respectively. Find a short run total cost curve of the firm.