# Marginal revenue equation

Please help with the following problem. Provide step by step calculations for each.

The following information about a monopoly is given:

Demand: Q = 40-2P(Q) Average cost: AC(Q) = Q

Marginal Cost: MC(Q) = 2(Q)

(a) Derive the marginal revenue equation

(b) Find the quantity at which profits are maximal. given that quantity, find the price charged and the monopolist's profits. (solve for answers using the equations)

(c) What is the efficient output?

For a monopolistic producer facing two markets, given the price and output in one of two markets, how would you determine the profit-maximizing output and price in the other market under price discrimination?

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#### Solution Preview

(a) Derive the marginal revenue equation

Total Revenue (TR)=P*Q

Write Demand: Q = 40-2P(Q) as P(Q) = (40-Q)/2

TR= (20 - Q/2)*Q = 20 Q-Q^2/2

MR=dTR/dQ = 20-Q

(b) ...

#### Solution Summary

This solution helps with problems about monopolies. Concepts discussed include marginal revenue equation, profits and efficient output. Step by step calculations are given for each.