Please see the attached file for full problem description.
Epren manufactures engine parts for an automobile manufacturer. It operates 2 plants, which have the following production functions:
Plant A: Qa = 30Sa - 0.25 Sa2
Plant B: Qb = 40Sb - 0.50Sb2
where Qa is the unit output from plant A, Qb is the unit output from plant B and Sa and Sb are the units of the variable factor steel used, respectively at plant A and B.
a. Suppose the steel availability is 30 units. What is the optimal allocation between the two plants?
b. A sudden supplier problem reduces availability of steel to plant B by 10 units. How should Epren reallocate steel between the plants? Explain.
Explain how the following events will affect the average and marginal cost curves of the firm.
a. an increase in lease payments.
b. A decrease in utility cost.
c. Stricter environmental regulations requiring installation of scrubbers on smokestacks.
d. An increase in the corporate profit tax.
e. An increase in learning on the part of labor.
Please refer to the attachment.
<br>a. Suppose the steel availability is 30 units. What is the optimal allocation between the two plants?
<br>It will produce at a level where the marginal product in both plants are equal, then the cost is minimized.
<br>MCa = dQa / dSa = 30-0.5Sa
<br>MCb = dQb / dSb = 40-Sb
<br>Set MCa = MCb:
<br>30-0.5Sa = 40-Sb (1)
<br>s.t. Sa+Sb = 30 (2)
<br>solve the above two equations:
<br>(2)-(1): 1.5 Sa = 20
<br>then Sa = 20/1.5= 13.3
<br>Sb = 30-Sa = 16.7
<br>b. A ...
What will happen to the average and marginal cost curves of the firm?