The cost per unit of producing a product is dollars, where x represents the number of units produced per week. If the equilibrium price determined by a competitive market is $200, how many units should the firm produce and sell each week to maximize its profit?
A)32
B)16
C)256
D)none
E)as many as possible

Question

The cost per unit of producing a product is  dollars, where x represents the number of units produced per week. If the equilibrium price determined by a competitive market is $200, how many units should the firm produce and sell each week to maximize its profit? ​
A)32 
B)16 
C)256 
D)none 
E)as many as possible

Quizplus · Accepted Answer

The profit-maximizing level of output occurs where marginal cost (MC) equals marginal revenue (MR), which is also where the price (P) equals MC. In this case, the cost per unit is given by $11x. The equilibrium price is given as $200, so the profit-maximizing output level occurs where:
P = MC
$200 = $11x
x = $200/$11 = 18.18 (rounded to the nearest unit)
Thus, the firm should produce and sell about 18 units per week to maximize its profit. However, since we can only choose from the given answer choices, the closest option is B, which is 16. By producing 16 units, the firm's total cost would be:
Total Cost = TC = 16*$11 = $176
Therefore, the firm's profit would be:
Profit = Total Revenue - Total Cost
Profit = 16*$200 - $176
Profit = $3,024
Since this is the highest profit achievable from the given answer choices, B is the best option.

The Cost Per Unit of Producing a Product Is