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
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 ...
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.