# A natural monopolist faces the following demand: P = 715 - 7Q The monopolist has the following...

## Question:

A natural monopolist faces the following demand:

{eq}P = 715 - 7Q {/eq}

The monopolist has the following cost function:

{eq}C = 319Q + 736 {/eq}

How much output will this firm produce to maximize profit? Round our answer to one decimal place.

## Monopoly's Profit Maximization:

A monopoly is a firm that is the sole seller of a certain product in the market. The product produced by a monopoly is unique and has no close substitutes. This means that the monopoly does not face any competition from other firms. Therefore, monopolies have the ability to set a price for its product and also have the exclusive control of the quantity supplied in the market.

## Answer and Explanation: 1

Monopoly firms maximize profits at the point where the marginal revenue is equal to their marginal cost of production. That is:

{eq}MR = MC {/eq}

The total revenues are calculated as:

{eq}TR = P*Q {/eq}

Where *P* is the inverse demand function.

The monopoly has an inverse demand curve given as:

{eq}P = 715 - 7Q {/eq}

Therefore, the total revenue function is:

{eq}TR = (715 - 7Q)Q = 715Q - 7Q^2 {/eq}

The marginal revenue curve is:

{eq}MR = \frac{\Delta TR}{\Delta Q} = 715 - 14Q {/eq}

The monopolist has the cost function:

{eq}C = 319Q + 736 {/eq}

Therefore, the marginal cost for the monopoly is:

{eq}MC = \frac{\Delta C}{\Delta Q} = 319 {/eq}

Equating the marginal revenue to the marginal cost and solving for *Q*:

{eq}715 - 14Q = 319 {/eq}

{eq}14Q = 396 {/eq}

{eq}Q_m = \frac{396}{14} = 28.2 {/eq} units

This is the monopoly's profit maximizing level of output.

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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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