A firm has a factory where it produces widgets. The production function of this firm is q=2kl. In the short run, the firm's 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 firm's:

a. short run marginal cost function (SMC)

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.

b. If the firm wishes to minimize short run total costs of widget production, how should output be allocated between the two factories?

c. 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).