# A monopolist faces a demand curve given by P = 220 - 3Q, where P is the price of the good and Q...

## Question:

A monopolist faces a demand curve given by P = 220 - 3Q, where P is the price of the good and Q is the quantity demanded. The marginal cost of production is constant and is equal to $40. There are no fixed costs of production.

a. What quantity should the monopolist produce in order to maximize profit?

b. What price should the monopolist charge in order to maximize profit?

c. How much profit will the monopolist make?

d. What is the deadweight loss created by this monopoly?

e. If the market were perfectly competitive, what quantity would be produced?

## Monopoly:

A monopoly is a market form which sells the good which has no close substitute available in the market. This market has some sort of market power which helps to discriminate the prices in the market for the same good. Also, there is no entry and exit of the firms in such a market.

## Answer and Explanation: 1

**a)** The total revenue and marginal revenue functions are:

{eq}\begin{align*} TR &= PQ\\ &= 220Q - 3{Q^2}\\ MR &= \dfrac{{\partial TR}}{{\partial Q}}\\ &= 220 - 6Q \end{align*} {/eq}

In order to maximize the profits, the monopolist should produce the number of units where the marginal revenue and marginal cost are equal.

{eq}\begin{align*} MR &= MC\\ 220 - 6Q &= 40\\ Q &= 30\,{\rm{units}} \end{align*} {/eq}

**b)** The price charged by the monopolist to maximize the profits is calculated below:

{eq}\begin{align*} P &= 220 - 3Q\\ &= 220 - 3\left( {30} \right)\\ &= \$ 130 \end{align*} {/eq}

**c)** The amount of profit earned by the monopolist is:

{eq}\begin{align*} \pi &= TR - TC\\ &= \left( {\$ 130 \times 30} \right) - \left( {\$ 40 \times 30} \right)\\ &= \$ 3,900 - \$ 1,200\\ &= \$ 2,700 \end{align*} {/eq}

**d)** The equilibrium quantity and price under perfect competition is calculated below:

{eq}\begin{align*} P &= MC\\ 220 - 3Q &= 40\\ Q &= 60\,{\rm{units}}\\ P &= \$ 40 \end{align*} {/eq}

The deadweight loss created by the monopoly is:

{eq}\begin{align*} DWL &= 0.5 \times \left( {130 - 40} \right) \times \left( {60 - 30} \right)\\ &= \$ 1,350 \end{align*} {/eq}

**e)** If the market was perfectly competitive, then the quantity produced by the firm will be 60 units.

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Chapter 7 / Lesson 2Understand the meaning of a monopoly in economics and what it does. Also, know the characteristics of a monopoly and the different types of monopolies.

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