# A monopoly has total cost and marginal cost given by: TC = Q^{2} + 5Q + 100 MC = 2Q + 5 The...

## Question:

A monopoly has total cost and marginal cost given by:

{eq}TC = Q^{2} + 5Q + 100 {/eq}

{eq}MC = 2Q + 5 {/eq}

The market demand curve is given by:

P = 65 - 2Q

A. Use the twice-as-steep rule to find the equation of the marginal revenue curve corresponding to the market demand curve.

B. Find the profit-maximizing quantity of output for the monopoly and the price the monopolist will set.

C. Calculate the monopolist's profits. Calculate the value of the Lerner Index.

D. Calculate the consumer surplus under monopoly.

E. What quantity of output would be produced if the monopolist acted like a perfect competitor and set MC equal to P?

F. Calculate profits and consumer surplus corresponding to the competitive equilibrium.

G. Find the deadweight loss due to the monopoly.

## Lerner Index:

The Lerner Index is a measure of market power. It ranges from 0 to 1, where 1 is a monopoly.

## Answer and Explanation:

Marginal Revenue is the twice the slope of the inverse demand, therefore MR = 65 - 4Q. The monopolist will sell when MC = MR. In this case when 2Q +...

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