1 Competitive Markets and the Profit-Maximizing Firm

Competition and price taking

A perfectly competitive market has many buyers and sellers, identical products, broad access to relevant market information, and free entry and exit. Since each firm is small relative to the whole market, no individual firm can meaningfully change the market price. Market supply and demand determine that price.

Each firm is a price taker: it accepts the market price rather than setting its own. If it asks more for an identical product, buyers can purchase from other sellers. From the perspective of an individual firm, demand is horizontal at the market price, so its main decision is how much to produce.

Revenue for a competitive firm

For a firm selling quantity $Q$ at price $P$, total revenue is its sales receipts, given by $TR=P\times Q$. Average revenue is revenue per unit, $AR=TR/Q$; for a competitive firm, $AR=P$.

Marginal revenue is the extra revenue from selling one more unit, expressed as $MR=\Delta TR/\Delta Q$. A price-taking firm can sell each additional unit at the same market price, so $MR=P$. Consequently, for a competitive firm:

Costs and cost per unit

Costs describe the resources used to produce output. Fixed costs do not change with output over the period being considered, such as rent on a facility already leased. Variable costs change as output changes, such as materials used for each unit.

Total cost is fixed cost plus variable cost:

Average total cost is cost per unit, $ATC=TC/Q$. Average variable cost is variable cost per unit, and average fixed cost is fixed cost per unit. Marginal cost is the additional cost of producing more output, $MC=\Delta TC/\Delta Q$. Since fixed cost does not change with output, marginal cost reflects the change in variable cost.

Economic profit

A firm's economic profit is total revenue minus total economic cost. Economic cost includes opportunity costs—the value of the next-best use of the firm's resources—not only direct cash expenses.

Profit is calculated as:

Choosing output to maximize profit

The firm compares the additional revenue from one more unit with the additional cost of producing it. If marginal revenue exceeds marginal cost, producing another unit adds more to revenue than to cost, so profit rises. If marginal revenue is less than marginal cost, that unit costs more than it adds to revenue, so profit falls.

The profit-maximizing output is where marginal revenue equals marginal cost, using the point where marginal cost is rising. For a perfectly competitive firm, marginal revenue equals price, so the rule is:

Applying the rule

Suppose the market price is $\$8$ per unit and successive units have marginal costs of $\$2$, $\$4$, $\$6$, $\$8$, and $\$10$. The first three units each add more to revenue than to cost. The fourth adds $\$8$ in revenue and costs $\$8$, while the fifth costs $\$10$ but adds only $\$8$. The firm should produce four units; producing more would reduce profit.

The rule identifies the best output, but does not by itself guarantee positive profit. Whether the firm earns a profit also depends on its total costs at that output.