Maximizing Profit: The MR = MC Rule

Maximizing Profit: The MR = MC Rule
The standard economic model assumes that a firm maximizes profit. How does it do this? The optimal production volume is determined by the MR = MC rule—one of the fundamental rules in microeconomics.

Revenue: Total, Average, Marginal
Total Revenue (TR): total revenue = P × Q
Average Revenue (AR): AR = TR / Q = P (price per unit)
Marginal Revenue (MR): MR = ΔTR / ΔQ—additional revenue from selling one more unit

For a price taker: MR = P
The firm can sell any quantity at the market price—each additional unit brings P.

For a price maker: MR

Profit Maximization Condition
Profit = TR − TC
Profit is maximized when the derivative with respect to Q equals zero:
dProfit/dQ = dTR/dQ − dTC/dQ = MR − MC = 0

First-order condition: MR = MC
Second-order condition: MC must be increasing at the intersection point (otherwise, it’s a profit minimum).

Intuition Behind the MR = MC Rule
If MR > MC:

• The additional unit brings more than it costs
• Profit increases as output rises
• One should produce more

If MR < MC:

• The additional unit costs more than it brings
• Profit decreases as output rises
• One should produce less

If MR = MC:

• The last unit adds exactly as much as it costs
• Further change will not improve profit
• Optimum

Graphical Analysis
Curves:

• MC — U-shaped, then increasing
• MR — depends on market structure
  Their intersection determines Q*

Profit:
Profit per unit = AR − ATC = P − ATC
Total Profit = (P − ATC) × Q
Graphically—rectangle between P and ATC at Q*

Universality of the MR = MC Rule
MR = MC works for all market structures:

• Perfect competition: MR = P (price is given) → P = MC
• Monopoly: MR < P
• Monopolistic competition: similar to monopoly
• Oligopoly: more complicated due to interdependence, but the principle is the same

Short-run Decision: To Produce or to Shut Down?
In the short run, a firm may incur losses. Should it continue?

Shutdown rule: shut down if P < AVC
Logic:
If P > AVC: revenue covers variable costs and a part of fixed costs. Better to operate than pay all FC.
If P < AVC: revenue fails to cover variable costs. Loss exceeds fixed costs. Better to stop.

Shutdown point: minimum AVC—the price below which the firm does not produce.

Long-run Decision: Exit the Industry
In the long run, all costs are variable.

Exit rule: exit the industry if P < ATC
Logic:
If P < ATC: all costs are not covered.
Resources are better used elsewhere
Exit releases resources for more valuable uses

For the Investor
Margin analysis:
How does MC change as volume changes?
Is there potential to grow without significant MC increase?

Operating leverage:
High FC, low VC → high operating leverage
Profit is sensitive to revenue changes

Breakeven analysis:
Breakeven point: TR = TC, or Q = FC / (P − AVC)
The closer to breakeven—the higher the risk

Pricing power:
Ability to raise price (shift MR upward)—competitive advantage
Lowering MC (efficiency)—also a path to profit growth