Question

Consider a monopolist that faces an inverse demand for its product given by p=600-4Q The firm...

Consider a monopolist that faces an inverse demand for its product given by

p=600-4Q

The firm has a cost function C(Q)=9Q2+400

What is the profit-maximizing price for this monopolist? Provide your answer to the nearest cent (0.01)

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Answer #1

The inverse demand function is given as:

P = 600 - 4Q

The total revenue function is:

TR = PQ = 600Q - 4Q²

The marginal revenue function is:

MR = d(TR)/dQ = 600 - 8Q

The total cost function is:

TC = 9Q² + 400

The marginal cost function is calculated below:

MC = d(TC)/dQ = 18Q

The monopolist maximizes the profit when marginal revenue is equal to the marginal cost. So,

600 - 8Q = 18Q

26Q = 600

Q = 600/26 = 23.077

Putting Q = 23.077 in the demand function:

P = 600 - 4(23.077)

P = 600 - 92.308

P = 507.692

So, the profit-maximizing price is 507.69.

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