# A monopolist faces the following demand: P = 1,418 - 15Q The monopolist's cost function is: C...

## Question:

A monopolist faces the following demand:

{eq}P = 1,418 - 15Q {/eq}

The monopolist's cost function is:

{eq}C = 10Q2 + 667Q + 326 {/eq}

Find the equilibrium price, P, if this market was perfectly competitive. Round your answer to one decimal.

## Perfectly Competitive Market:

A perfectly competitive market is a market that has many buyers and many sellers in the market. The sellers sell goods that are homogeneous and sell at the same market price. Each firm in the market faces a perfectly elastic demand curve, which means that firms in a competitive market are price takers.

## Answer and Explanation: 1

Firms in a perfectly competitive market maximize their profits at the point where the market price is equal to their marginal cost of production. That is:

{eq}P = MC {/eq}

The firm has an inverse demand curve given by:

{eq}P = 1,418 - 15Q {/eq}

And the total cost curve given as:

{eq}C = 10Q2 + 667Q + 326 {/eq}

The marginal cost function for this firm is:

{eq}MC = \frac{\Delta C}{\Delta Q}= 20Q + 667 {/eq}

Equating the marginal cost to the inverse demand curve and solving for *Q*:

{eq}1,418 - 15Q= 20Q + 667 {/eq}

{eq}35Q= 751 {/eq}

Solving for *Q*:

{eq}Q^*= \frac{751}{35} = 21.5 {/eq} units.

To get the price charged by the firm, we will substitute the profit maximizing level of output into the inverse demand curve.

{eq}P = 1,418 - 15Q {/eq}

{eq}P^* = 1,418 - 15(21.5) = $1,095.5 {/eq}

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