# Suppose a monopolist produces according to the following demand curve: P=200-4Q. Assume that the...

## Question:

Suppose a monopolist produces according to the following demand curve: P = 200 - 4Q.

Assume that the firm faces a constant marginal cost and constant average total cost of $56 per unit produced.

a) Write down the equation for the marginal revenue curve.

b) Graph this, including the demand curve, the MR curve, and the AC/MC line.

c) What quantity should this firm produce?

d) What price should it charge per unit?

e) What profit will it make, taking into account your answers in parts b and c?

## Monopoly Market:

In a monopoly, there's a single firm that charges a price that's above the marginal cost (MC) by producing less output in such a manner that the profit is at its maximum where the marginal revenue (MR) is equal to the marginal cost. It shows that the monopoly has the market power to charge a higher price, making the firm the price maker.

## Answer and Explanation: 1

**a)** As we know:

- {eq}P=200-4Q {/eq}

- {eq}TR=P\times Q {/eq}

- {eq}TR=(200-4Q)Q {/eq}

- {eq}TR=200Q-4Q^{2} {/eq}

The equation for the marginal revenue (MR) curve is:

{eq}MR=200-8Q {/eq}.

**b)** The marginal revenue curve can be graphed as follows:

**c)** At equilibrium:

{eq}MR=MC {/eq}

{eq}200-8Q=56 {/eq}

{eq}8Q=144 {/eq}

{eq}Q=18 {/eq}

**d)** The quantity this firm should produce can be calculated as:

{eq}P=200-4Q {/eq}

{eq}P=200-4(18) {/eq}

{eq}P=200-72 {/eq}

{eq}P=128 {/eq}

**e)** Taking into account the answers for parts b and c, the firm's profit will be:

{eq}Profit(\pi)=TR-TC {/eq}

{eq}=200Q-4Q^{2}-56Q {/eq}

{eq}=144Q-4Q^{2} {/eq}

{eq}=144(18)-4(18)^{2} {/eq}

{eq}=2592-1296 {/eq}

{eq}\pi=1296 {/eq}

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Chapter 3 / Lesson 13Explore natural monopolies. Learn the definition of natural monopoly and understand how it functions. See characteristics of natural monopolies with examples.

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