Question

All-Leather is a tanning company in Chicago. Its total cost function is C(QA) = 125 + 8QA + 5QA2, where QA is leather production per week in thousands of pounds.

a) What is the formula for All-Leather’s marginal cost function?

b) If leather sells for $408 per thousand pounds, how much leather will All-Leather produce?

c) How much profit will All-Leather make?

Answer 1

A) Given that, Total cost = C(QA) = 125+8QA + 5QA²

Therefore, MC = d(TC)/d(QA) = d[C(QA)]/d(QA) = 0 + 8 + 10QA = 8 + 10QA

B) If price = $408 per thousands of pounds, the company will produce at the point where price = MC to maximize profit.

Therefore, setting Price = MC,

8 + 10QA = 408

Or, 10QA = 400

Or, QA = 40

Therefore, the leather company will produce 40 thousands of pounds leather.

C) Total revenue = price * quantity = $(408 * 40 ) = $16,320

And, TC = 125 + (8*40) + (5*40²) = 125+320+8000 = $8445

Profit = TR - TC = $(16,320 - 8445) = $ 7875