Q.What is the relation between market price and marginal revenue of a price-taking firm?

A price-taking firm is one that operates under perfect competition, where it has no influence over the market price. The firm accepts the prevailing market price as given and can sell any quantity at that price.

For such a firm, the market price and marginal revenue are identical. When the firm sells one additional unit, it receives exactly the market price for it — there is no need to lower the price on previous units (as would happen under imperfect competition). Since total revenue increases by the market price with each extra unit sold, marginal revenue equals the market price at every level of output.

Mathematically, if the market price is $P$, then total revenue is $TR = P \times Q$. The marginal revenue is

because $P$ is constant for a price-taking firm. …

A price-taking firm is one that operates in a perfectly competitive market. The defining feature of such a market is that the individual firm is so small relative to the total market that its production decisions have no impact on the market price. The firm faces a horizontal demand curve at the market price—it can sell one unit, ten units, or a thousand units, all at exactly the same price per unit.

This seemingly simple observation has a powerful implication for marginal revenue. Marginal revenue is the additional revenue earned from selling one more unit of output. For most firms, selling more requires lowering the price, so marginal revenue falls below price. But a price-taking firm never has to lower its price to sell more. When it sells an additional unit, it receives exactly the market price for that unit, with no effect on the revenue from previous units.

Consider the arithmetic. If the market price is $P$, then:

• Total revenue from selling $q$ units: $TR = P \times q$
• Total revenue from selling $q+1$ units: $TR' = P \times (q+1)$
• Marginal revenue: $MR = TR' - TR = P \times (q+1) - P \times q = P$

The marginal revenue is simply the market price, regardless of the output level.

This equality holds at every level of output for a price-taking firm. The firm's marginal revenue curve coincides with its demand curve, both horizontal at the market price. This is fundamentally different from a monopolist or any firm with market power, where $MR < P$ because selling more requires a price cut that applies to all units sold. …