Suppose a firm’s production function is given by Q = L 1/2 , K 1/2.
a) Suppose the firm has a fixed cost FC=6, the price of labor is w = 64 and the price of capital is r = 4. Derive the firm’s total cost function, TC(Q).
b) What is the firm’s marginal cost?
c) Graph the firm’s isoquant for Q = 20 units of output. On the same graph, sketch the firm’s isocost line associated with the total cost of producing Q = 20 units of output. To get this total cost, you must use the total cost function from part a). For the isocost line, clearly identify the vertical and horizontal intercepts. For the isoquant, clearly identify 4 combinations of labor and capital that will produce Q = 20.... include the bundle that minimizes the firm’s cost of production.
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