# 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.

Determining Optimal Output Level

Please refer attached file for graph.

A hypothetical monopoly firm is characterized by the following diagram.

a. Assuming that the above firm is a profit maximizer operating in the short run, determine its optimal price?

b. Determine the firm's profit per unit.

c. What is the ATC in dollars?

d. If the above monopolist were to behave like a perfectly competitive firm (operating in the long run), determine its price