Douglas A. Ruby
Revised: 01/17/2003

Production Relationships

A Producer Optimum

Cost Relationships

Market Structure

Microeconomic Theory
Profit Maximization

In describing a producer optimum, we have defined the profit maximization condition with respect the variable factor input (labor) as:
MPL = w/P.
or
P = w/MPL = MC.
For the competitive firm (a price taker), we can write:
Revenue (TR) = P x Q
and
Marginal Revenue (MR) = dTR/dQ = P!
Thus an alternative expression for profit maximization for a competitive firm is:
P = MC.
Figure 1, Profit Maximization: A Competitive Firm

described as where the revenue from selling one more unit of output (P, MR) is exactly equal to the cost of producing that last unit of output (MC).

If P (MR)  >  MC then additions to revenue exceed the additions to cost (via the production and sale of one more unit of output) and the firm will be able to increase profits by selling that additional unit.

If the opposite is true, P (MR)  <  MC then additions to costs exceed the additions to revenue (via the production and sale of one more unit of output) and the firm will be able to increase profits by reducing output by one additional unit.

 * Tutorial: Profit Maximization *

Imperfectly Competitive Firms
In the case of a firm with market (monopoly) power -- a price maker, the market demand curve is also the demand curve for that firm's output. Assuming that the demand curve is linear we find:
P = a - bQ -- the inverse demand curve
and
TR = PxQ = aQ - bQ2 -- Total Revenue -- a quadratic equation!
and
Marginal Revenue (MR) = dTR/dQ = a - 2bQ
The equation for Marginal Revenue has the same intercept 'a' and is twice as steep as the slope of inverse demand. The condition for profit maximization still holds:
MR = MC.
Figure 2, An Imperfectly Competitive Firm

 * Profit Maximization: Imperfectly Competitive Firms *

Concepts for Review:
• Costs (of Production)
• Demand
• Inverse Demand
• Marginal Costs (MC)
• Marginal Revenue (MR)
• [An] Imperfectly Competitive Firm
• Monopoly
• [A] Perfectly Competitive Firm
• [A] Price-maker
• [A] Price-taker
• [A] Producer Optimum
• (Sales) Revenue
• Total Revenue (TR)