A firm with two plants,A and B,has the following estimated demand and marginal cost functions: What is the profit-maximizing price?

Question

A firm with two plants,A and B,has the following estimated demand and marginal cost functions:  What is the profit-maximizing price?

Quizplus · Accepted Answer

To find the profit-maximizing price, we need to set the marginal revenue equal to marginal cost and solve for price. From the demand functions, we can find the total revenue function as:

TR = P(Qa + Qb)

Taking the derivative with respect to Qa, we can find the marginal revenue function as:

MR = P(1 - 0.1Qa - 0.05Qb)

Setting this equal to the marginal cost function of $5, we get:

P(1 - 0.1Qa - 0.05Qb) = 5

We also know that the two plants have equal marginal cost, so we can set MCa = MCb = $5

Solving for Qb in terms of Qa, we get:

Qb = 40 - 2Qa

Substituting this into the equation for MR, we get:

P(1 - 0.1Qa - 0.05(40-2Qa)) = 5

Simplifying and solving for Qa, we get:

Qa = 150

Substituting this back into the equation for Qb, we get:

Qb = 40 - 2(150) = -260

Since this doesn't make sense (we can't have negative output), we know that there is no solution for the price that will maximize profit. Therefore, the answer is E (none of the above).

A Firm with Two Plants,A and B,has the Following Estimated