# Suppose a profit-maximizing monopolist can engage in perfect price discrimination and faces a...

## Question:

Suppose a profit-maximizing monopolist can engage in perfect price discrimination and faces a demand curve for its products given Q = 20 - 5P. This monopolist has a cost function of TC = 24 + 4Q. How much will monopolists profits be?

## Monopoly

The monopolist places strong barriers to entry into the industry. The monopoly firm does not have a supply curve due to its discriminatory price behavior. No close substitute for the good produced exists in the market.

## Answer and Explanation: 1

**There will be a loss of $24.**

The monopolist can distinguish among customers and sell the same quantity of goods at different prices to customers. In this way, all the consumer surplus can be obtained till P = MC.

The MC function is {eq}MC = \frac{{dTC}}{{dQ}} = 4. {/eq}

So, P = MC = 4.

Thus, the quantity produced by the monopoly firm is:

{eq}\begin{align*} Q &= 20 - 5\left( 4 \right)\\ Q &= 20 - 20\\ Q &= 0 \end{align*} {/eq}

The amount of profits are:

{eq}\begin{align*} \pi &= TR - TC\\ &= \left( {P \times Q} \right) - \left( {24 + 4Q} \right)\\ &= \left( {4 \times 0} \right) - 24 - \left( {4 \times 0} \right)\\ &= - 24 \end{align*} {/eq}

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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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