Question

In: Economics

Microeconomics

A firm sells each unit of its product for $400. The cost function which describes the total cost C as a function of the number of units produced and sold is x is:

C = 40x + 0.25x2 + 250

Determine the maximum profit and the corresponding total revenue and total cost.

Solutions

Expert Solution

Profit = Revenue - Total Cost

Profit = PQ - Total Cost

π = 400x - (40x + 0.25x2 + 250)

π = 400x - 40x - 0.25x2 -250

π = - 0.25x2 + 360x – 250

dπ/dx = -0.5x + 360

0.5x + 360 = 0

-0.5x = -360

x = 720

π = -0.25(7202) + 360(720) – 250

π = 129,350

Maximum profit = 129,350

Total revenue = PQ

Total revenue = 400 ×720

Total revenue = 288, 000

Total cost = 40x + 0.25x2 + 250

Total cost = 40(720) + 0.25(7202) + 250

Total cost = 158,650

The profit of a firm is given by the difference in total revenue and total cost. The firm achieves its maximum profit by operating at the point where the difference between the two is at its greatest.

Joes answered 3 years ago
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