Question

Компания производит продукцию в условиях чистой монополии. Функция спроса на данный товар: P = 100 – 4 Q, а функция средних затрат: АС = (20 : Q) + Q. При каком объеме выпуска будет максимальна прибыль компании?

Answer 1

Ответ:

To find the maximum profit, we need to find the level of output where marginal revenue equals marginal cost.

First, calculate the marginal revenue (MR):

MR = ΔP/ΔQ = 100 - 8Q

Next, calculate the marginal cost (MC):

MC = ΔAC/ΔQ = 20/Q + 1

Equalizing MR and MC, we get:

100 - 8Q = 20/Q + 1

Solving for Q:

8Q^2 - 80Q + 79 = 0

Using the quadratic formula:

Q = (80 ± √(80^2 - 4 * 8 * 79)) / (2 * 8)

Q = (80 ± √(6400 - 632)) / 16

Q = (80 ± √5768) / 16

Q = (80 ± 76) / 16

Since output cannot be negative, we only consider the positive solution:

Q = (80 + 76) / 16 = 156 / 16 = 9.75

Thus, the maximum profit for the company occurs when they produce 9.75 units of the product.