For a price taker, price equals marginal revenue

Every additional unit sells at the unchanged market price.

Because the firm can sell its chosen quantity without changing price, P=AR=MR. The firm’s demand curve is perfectly elastic at market price. Market demand still slopes downward. Confusing the two graphs creates the false claim that consumers will buy unlimited industry output at one price.

Average revenue is TR/q. Because TR=Pq and price is fixed for the firm, AR=P. Marginal revenue is the change in total revenue from one more unit. Each unit adds the same market price, so MR=P. The three equalities arise from price taking, not from a universal revenue identity.

If price is $18, total revenue at 10 units is $180 and at 11 units is $198. MR of the eleventh is $18. The firm can choose output but not price. Charging $18.01 loses buyers to identical rivals. Charging less gives away revenue without increasing the price-taker’s feasible sales assumption.

The firm chooses q where P=MC on the rising portion of MC, provided P≥ AVC. The rising-MC qualification excludes an unstable crossing where expanding output could still improve profit.

Before the crossing, price exceeds marginal cost and units add profit. After it, marginal cost exceeds price and units subtract. If quantities are discrete, produce the last unit with P≥ MC. The same rule is MR=MC. Perfect competition simply makes MR equal the given price.

Price taker schedule

At a market price of $25, a firm’s MC for successive units is $12, $18, $23, $27. The first three units add more revenue than cost. The fourth does not. The firm produces three, provided price covers AVC. It does not choose the unit where MC is lowest or where ATC is minimized.

The phrase “perfectly elastic firm demand” means the firm can sell its small feasible output at market price in the model. It does not claim total market demand is infinite. If every firm tried to expand, market supply would change and price could fall. One firm’s curve holds the market outcome fixed.

A fixed-cost increase leaves the chosen output unchanged because MC is unchanged, though profit falls. A per-unit tax raises MC and reduces output at a given price. The marginal rule identifies which cost changes matter for quantity.

If market price falls, the firm does not shift its MC curve. The horizontal revenue line moves down and selects a smaller quantity. If it falls below minimum AVC, supply becomes zero. This is movement along the firm’s short-run supply relationship.

Perfectly elastic firm demand is conditional on the market price. A market demand or supply shift can change that price, after which the firm faces another horizontal line. “Perfectly elastic” does not mean the line can never move vertically. It means one small firm cannot alter the given price through its own output choice.