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.
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