8.2 How Perfectly Competitive Firms Make Output Decisions

Profit Maximization and Output Decisions in Perfect Competition

Calculation of firm profits

Profit is the difference between what a firm earns and what it spends. The formula is straightforward:

$Profit = TR - TC$

Total revenue (TR) is the money coming in: price times quantity sold.

$TR = P \times Q$

For example, if the market price is $10 and the firm sells 100 units, $TR = \$10 \times 100 = \$1{,}000$.

Total cost (TC) includes both explicit costs and implicit costs. Explicit costs are direct payments for inputs like wages, raw materials, and utilities. Implicit costs are the opportunity costs of using resources you already own. If you run your business out of a building you own, the rental income you're giving up counts as an implicit cost. This distinction matters because economic profit accounts for both types, while accounting profit only captures explicit costs.

Profit analysis with cost curves

You can quickly assess a firm's profit situation by comparing price to average total cost (ATC):

• Price > ATC → the firm earns economic profit, calculated as $(P - ATC) \times Q$
  • Example: Price is $15, ATC is $12, quantity is 1,000 units → profit = $(\$15 - \$12) \times 1{,}000 = \$3{,}000$
• Price < ATC → the firm incurs an economic loss, calculated as $(ATC - P) \times Q$
  • Example: Price is $8, ATC is $10, quantity is 500 units → loss = $(\$10 - \$8) \times 500 = \$1{,}000$
• Price = ATC → the firm breaks even with zero economic profit

Zero economic profit doesn't mean the firm earns nothing. It means the firm covers all its costs, including the opportunity cost of the owner's time and capital. The firm is doing exactly as well as its next-best alternative.

Shutdown point implications

The shutdown point is the minimum price at which a firm will keep producing in the short run. It occurs where price equals average variable cost (AVC).

Why AVC and not ATC? Because fixed costs (rent, insurance, equipment leases) must be paid whether the firm produces or not. As long as revenue covers variable costs, producing is better than shutting down, since the firm at least chips away at its fixed costs. Once price drops below AVC, every unit produced actually adds to the firm's losses beyond what it would lose by simply closing the doors.

• If $P \geq AVC$, the firm should continue producing in the short run.
• If $P < AVC$, the firm should shut down. Its losses then equal its total fixed costs.
• At $P = AVC$, the firm is indifferent between producing and shutting down.

Example: If AVC is $6 and the market price is $8, the firm should keep producing. If the price drops to $4, the firm should shut down.

In the long run, the relevant threshold is ATC, not AVC, because there are no fixed costs in the long run (all costs become variable). If price stays below ATC, the firm will exit the market entirely.

Output optimization in competition

The profit-maximizing rule for any firm is to produce where marginal revenue (MR) equals marginal cost (MC):

$MR = MC$

In perfect competition, each firm is a price taker, meaning it can sell as many units as it wants at the market price without affecting that price. This makes marginal revenue equal to price:

$MR = P$

So the rule simplifies to:

$P = MC$

Here's the intuition behind this rule:

1. If $P > MC$ for the next unit, producing it adds more to revenue than to cost. The firm should increase output.
2. If $MC > P$ for the last unit, that unit costs more to make than it brings in. The firm should reduce output.
3. Profit is maximized at the quantity where $P = MC$, because there's no remaining unit that could improve the firm's position.

Example: The market price is $18. If the MC of the 200th unit is $18, then 200 units is the profit-maximizing quantity. Producing a 201st unit (with MC of, say, $19) would reduce profit.

One more detail: the firm's short-run supply curve is the portion of its MC curve that lies above AVC. Below AVC, the firm shuts down and supplies nothing.

Market Equilibrium and Efficiency

In the short run, market equilibrium occurs where the market supply and demand curves intersect. Individual firms may earn economic profits or suffer losses depending on where price sits relative to their ATC.

In the long run, profits and losses trigger entry and exit:

• Economic profits attract new firms into the market, increasing supply and driving the price down.
• Economic losses cause firms to exit, decreasing supply and pushing the price up.

This process continues until price settles at the minimum ATC, and every remaining firm earns zero economic profit. At this long-run equilibrium, two types of efficiency are achieved:

• Allocative efficiency ($P = MC$): Resources go where consumers value them most. The price consumers pay reflects the true cost of producing the last unit.
• Productive efficiency ($P = \text{minimum ATC}$): Firms produce at the lowest possible cost per unit, so no resources are wasted.