The firm has a factory that produces widgets using a production function of q=2kl, where k is fixed capital of 100 and l is labor. The rental rate of capital is $1 and wage is $4. The document asks to calculate the short run total cost, average cost, and marginal cost curves for this factory. It then states that the firm acquired a second plant with capital of 25 and asks how output should be allocated to minimize total cost and to calculate the aggregate cost curves if output is optimally allocated.

1. A firm has a factory where it produces widgets. The production function of this firm is q=2kl. In
the short run, the firms amount of capital equipment is fixed at k = 100. The rental rate for k is v
= $1 and the wage rate is w = $4. You are asked to calculate the firms:
a. short run total cost curve (SC) (2 points)
b. short run average cost curve (SAC) (2 points)
c. short run marginal cost function (SMC) (2 point)
Assume now that this firm acquires a second plant and that the capital equipment in this second
plant is k_2=25. The capital equipment of the first plant remains k_1=100 as specified above.
The rental rate and the wage remain unchanged.
d. If the firm wishes to minimize short run total costs of widget production, how should output
be allocated between the two factories? (2 points)
e. Given that output is optimally allocated between the two factories, calculate the short run total,
average, and marginal cost curves (in terms of aggregate output q). (2 points)