Slick Shades has a constant marginal cost of production equal to $40 and the distributors have a constant marginal cost of distribution equal to $20. If Slick Shades is producing the profit- maximizing number of sunglasses (in hundreds)and charging the profit- maximizing wholesale price, what is the retail price?
A)$150
B)$120
C)$140
D)$160

Question

Quizplus · Accepted Answer

To find the profit-maximizing quantity, we need to set the marginal revenue equal to the marginal cost of production. Since there is no information given about the demand curve, we can assume that the marginal revenue is equal to the wholesale price.

Therefore, $Wholesale \; Price - $40 = 0

$Wholesale \; Price = $40

To find the retail price, we need to add the distributor's marginal cost to the wholesale price.

Retail Price = $40 + $20 = $60

However, this is not the profit-maximizing retail price. To find the profit-maximizing retail price, we need to use the following formula:

Profit = (Retail Price - $40 - $20) x (Quantity in Hundreds)

Setting the derivative of this formula with respect to the retail price equal to zero, we get:

(Quantity in Hundreds) - (Retail Price - $40 - $20)/$2 = 0

Quantity in Hundreds = (Retail Price - $60)/$2

Substituting this expression into the profit formula, we get:

Profit = (Retail Price - $40 - $20) x [(Retail Price - $60)/$2]

Simplifying this formula, we get:

Profit = ($20/$2) x (Retail Price - $60)^2

This is a quadratic equation with a positive coefficient for the squared term, which means that the profit is maximized at the vertex.

The vertex of this quadratic equation is at:

(Retail Price - $60) = 0

Retail Price = $60

Therefore, the profit-maximizing retail price is $60 + $20 = $80.

However, this is not one of the answer choices. The closest answer choice is C, which is $140. This is not the profit-maximizing retail price, but it is the closest answer choice to the calculated profit-maximizing retail price.

Therefore, the best choice is:

Answer: C

The profit-maximizing retail price is $80, but the closest answer choice to this value is $140.

Slick Shades Has a Constant Marginal Cost of Production Equal