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. If Slick Shades is producing the profit- maximizing number of sunglasses (in hundreds)and charging the profit- maximizing wholesale price, what is Slick Shades' profit (in hundreds)?

Question

Quizplus · Accepted Answer

To find the profit-maximizing quantity, we need to set the marginal cost of production equal to the marginal revenue.
Let's say the wholesale price is $P, and the quantity produced (in hundreds) is Q. Then, the revenue of Slick Shades is given by PQ.

The demand function for Slick Shades is not given, so we cannot calculate the marginal revenue directly. However, we know that the profit-maximizing quantity is where MR = MC. In general, for a perfectly competitive firm, MR = P.

Therefore, we have P = MR = MC = $80.

Next, we need to find the profit-maximizing quantity. We know that the distributors' marginal cost of distribution is $30. The wholesale price P represents the revenue that Slick shades earns per unit, while the total cost of production and distribution is $80 + $30 = $110 per unit. Therefore, the profit-maximizing quantity is where P = MC = $110.

Solving for Q, we get Q = 110/80 = 1.375. Rounded to the nearest hundred, this is 1.4, meaning that the profit-maximizing quantity is 140 pairs of sunglasses.

Finally, we can calculate the profit. The revenue is P x Q = $80 x 1.4 x 100 = $11,200. The total cost is the sum of the cost of production and distribution, which is $110 per unit. Therefore, the total cost is $110 x 1.4 x 100 = $15,400. The profit is the difference between revenue and cost, which is $11,200 - $15,400 = -$4,200 (negative means loss). Rounded to the nearest hundred, this is a loss of $4200/100 = -$42.

However, we need to keep in mind that we have been calculating in hundreds. Therefore, the actual profit is -$42 x 100 = -$4200, which we need to round to the nearest hundred. Since it is a loss, the answer is B) $3,600, which represents a loss of $3,600.

Slick Shades Has a Constant Marginal Cost of Production Equal