18. Consider a firm that is using two plants, A and B, with these MC functions:

and

a. Find the inverse marginal cost functions.

b. Set MCA MCT and MCB MCT, and find the algebraic sum QA QB QT.

c. Take the inverse of the horizontal sum in part b to get the total marginal cost (MCT)

expressed as a function of total output (QT).

d. Beyond what level of output will the firm use both plants in production? (Hint: Find the output level where MCT kinks.)

e. If the manager of this firm wished to produce 1,400 units at the least possible total cost, should 700 units be produced in each plant? Why or why not? If not, what should the allocation be?

f. Draw a graph of MCA, MCB, and MCT. Check your algebraic derivation of total marginal cost with your graph. Check your answer to part e.