If Slick Shades has a constant marginal cost of production equal to $80 and the distributors have a constant marginal cost of distribution equal to $30, what is the profit- maximizing number of sunglasses (in hundreds)for Slick Shades to produce?
A)55
B)80
C)40
D)60

Question

Quizplus · Accepted Answer

To find the profit-maximizing quantity of sunglasses to produce, we need to determine where marginal revenue (MR) equals marginal cost (MC). However, we are not given a specific demand function or price, so we cannot directly calculate MR. Instead, we can use the fact that the profit-maximizing quantity occurs where marginal cost equals average revenue (AR), which is also equal to price (P) under standard assumptions.

Assuming that Slick Shades sells all of its output, the profit-maximizing quantity occurs where MC = AR = P. We know that MC = $80, and we can calculate AR by dividing total revenue (TR) by the quantity sold (Q). Since the revenue from selling q hundred units of sunglasses would be Pq, we have:

AR = TR/Q = Pq/Q = P

Therefore, we can set MC = P and solve for Q:

$80 = P
P = MR = AR
AR = TR/Q = Pq/Q
$80 = Pq/Q
Q = $80/($P/100) = 100*$80/$P

Since we do not know the price, we cannot calculate Q exactly, but we can see that Q is inversely proportional to price. In other words, as price goes down, quantity goes up, and vice versa. Since the demand curve slopes downwards under standard assumptions, we know that a lower price would lead to a higher quantity sold, so the profit-maximizing quantity must be greater than 50 (since 50 is the quantity that would be produced if MC = $30).

Therefore, the only answer option greater than 50 is D) 60, so that is the best choice.

If Slick Shades Has a Constant Marginal Cost of Production