Question

You are given the following information for a firm.

Demand: P = 300 - 1.5Q

Cost: TC = 3.5Q² + 100Q + 1000

Find the quantity the firm produces to maximize their profit.

Find the price that the firm will charge to maximize their profit.

Answer 1

Demand function is as follows -

P = 300 - 1.5Q

Calculate the Total Revenue -

Total revenue = P * Q = (300 - 1.5Q) * Q = 300Q - 1.5Q²

Calculate the Marginal Revenue -

Marginal Revenue = dTR/dQ = d(300Q - 1.5Q²)/dQ = 300 - 3Q

Total cost function is as follows -

TC = 3.5Q² + 100Q + 1,000

Calculate the marginal cost -

MC = dTC/dQ = d(3.5Q² + 100Q + 1,000)/dQ = 7Q + 100

A firm maximizes profit when it produce that level of output corresponding to which marginal revenue equals the marginal cost.

MR = MC

300 - 3Q = 7Q + 100

10Q = 200

Q = 20

Thus,

The quantity the firm produces to maximize their profit is 20 units.

P = 300 - 1.5Q = 300 - (1.5 * 20) = 300 - 30 = 270

Thus,

The price that the firm will charge to maximize their profit is $270 per unit.