Question

A monopoly produces widgets at a marginal cost of $10 per unit and zero fixed costs. It faces an inverse demand function given by P = 50 - Q. What are the profits of the monopoly in equilibrium
A. $300.B. $400.C. $500.D. $600.

Answer 1

Answer: B. $400

Explanation:

Profit is maximised at point where Marginal revenue equals marginal cost.

The Marginal revenue curve is below the demand curve for a monopolist and is double slopped compared to an inverse demand curve.

The expression for the Marginal Revenue is therefore;

MR = 50 - 2Q

MR = MC

50 - 2Q = 10

2Q = 50 - 10

2Q = 40

Q = 20

P = 50 - Q

=50 - 20

= $30

Total revenue = P * Q

= 30 * 20

= $600

Total cost.

= AC * Q

MC is given as a fixed number so can be considered as Average Cost

= 10 * 20

= $200

Profit = TR - TC

= 600 - 200

= $400

Answer 2

Based on the information given the profits of the monopoly in equilibrium

is: B. $400.

Given:

Marginal cost = $10 per unit

Fixed costs=0

P = 50 - Q

Hence:

MR = 50 - 2Q

MR = MC

50 - 2Q = 10

2Q = 50 - 10

2Q = 40

Q = 20

P = 50 - Q

P=50 - 20

P= $30

Total revenue = 30×20

Total revenue = $600

Total cost= 10 × 20

Total cost= $200

Profit = Total Revenue - Total Cost

Profit= 600 - 200

Profit= $400

Inconclusion the profits of the monopoly in equilibrium  is: B. $400.

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