A firm faces a production function given by q = √kl where q is the output, k is the firm’s amount of capital equipment and ? is the amount of labour-time employed. (a) In the short run, the amount of capital equipment is fixed at k = 100. The rental rate for k is v = $1, and the wage rate for l is w = $2. Calculate the firm’s short-run average cost (SAC) and short-run marginal cost (SMC) functions. Graph the SAC and the SMC curves for the firm. (b) Where does the SMC curve intersect the SAC curve? Explain why the SMC curve will always intersect the SAC curve at its lowest point. (c) Calculate the long-run total cost of production. For w = $2, v = $1, graph the long-run total cost curve. Show that this is an envelope for the short-run curves computed in part (a).
A firm faces a production function given by
q = √kl
where q is the output, k is the firm’s amount of capital equipment and ? is the
amount of labour-time employed.
(a) In the short run, the amount of capital equipment is fixed at k = 100.
The rental rate for k is v = $1, and the wage rate for l is w = $2.
Calculate the firm’s short-run average cost (SAC) and short-run
marginal cost (SMC) functions. Graph the SAC and the SMC curves for
the firm.
(b) Where does the SMC curve intersect the SAC curve? Explain why the
SMC curve will always intersect the SAC curve at its lowest point.
(c) Calculate the long-run total cost of production. For w = $2, v = $1,
graph the long-run total cost curve. Show that this is an envelope for
the short-run curves computed in part (a).
Step by step
Solved in 7 steps with 2 images
