# Steps for a monopolist determine level of output

A single firm operating as a monopolist wishes to determine the level of output to produce that will maximize sales revenue.

a Provide first order conditions for revenue maximization

b show graphically and provide an economic explanation for the equilibrium position.

c How does the profit maximizing equilibrium position differ from that for revenue maximization? Show graphically and mathematically

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#### Solution Preview

Suppose that we have a market with an ordinary demand function P = a - bQ, for some constants a and b.

Also assume that the monopoly has a cost function c(Q).

We know that revenue = price X quantity = P X Q = (a - bQ)Q = aQ - bQ^2.

Then to maximize revenue, we take the derivative of the revenue function and set it to 0

d(rev)/dQ = a - 2bQ = 0 (First order condition for revenue max.) => Q = a/2b.

However, this is not the equilibrium position because the firm may be making money or lossing money, depending on what the cost function is like.

We have to consider a different ...

#### Solution Summary

The steps for a monopolist determine level of output are determined. The expert determines how the profit maximizing equilibrium position differs from that for revenue maximizations.