For a price taking firm in a perfectly competitive market, average revenue is equal to what in relation to the market price?

Introduction / Context:
Perfect competition is an important benchmark model in microeconomics. One of its key features is that individual firms are price takers and face a perfectly elastic demand curve at the market price. This has a direct implication for the relationship between average revenue, marginal revenue, and the market price. Examinations often test whether students know this equality.

Given Data / Assumptions:

• The firm is a price taker in a perfectly competitive market.
• The market price is determined by overall demand and supply.
• The firm can sell any quantity at the given market price.
• Average revenue is defined as total revenue divided by quantity sold.

Concept / Approach:
In perfect competition, the firm sells each unit of output at the same market price. Total revenue is therefore equal to price multiplied by quantity. Average revenue is total revenue divided by quantity, which simplifies directly to the price. Marginal revenue, the revenue from selling one more unit, is also equal to the price. Thus, for a price taking firm, average revenue and marginal revenue are both exactly equal to the market price at all levels of output.

Step-by-Step Solution:
1. Let P be the market price and Q be the quantity sold.2. Total revenue TR equals P * Q because each unit sells at price P.3. Average revenue AR is defined as TR divided by Q.4. Substituting TR, we get AR = (P * Q) / Q, which simplifies to AR = P.5. Therefore, average revenue for a price taking firm is equal to the market price at every output level.

Verification / Alternative check:
Take a numerical example. Suppose the market price is 10 units of currency and the firm sells 5 units. Total revenue is 10 * 5 = 50. Average revenue is 50 divided by 5, which equals 10. If the firm sells 8 units, total revenue is 80, and average revenue is 80 divided by 8, again 10. In each case, average revenue equals the market price. This simple calculation confirms the theoretical result.

Why Other Options Are Wrong:
Option A: Half of the market price would imply AR equals P/2, which contradicts the definition of revenue for a price taking firm.
Option C: Double the market price would imply AR equals 2P, which is also inconsistent with the revenue formula.
Option D: Less than the market price cannot be correct because total revenue divided by quantity when all units sell at price P is always exactly P, not less.
Option E: Greater than the market price at low outputs is not correct; AR is equal to price at all positive outputs in perfect competition.

Common Pitfalls:
Students sometimes confuse the case of a price taking firm with that of a monopolist. For a monopolist, average revenue falls as output increases because price must be reduced to sell more units, and marginal revenue is less than price. For a perfectly competitive firm, average revenue and marginal revenue are constant and equal to the market price. Keeping these two contrasting cases clearly separated is important in exam preparation.

Final Answer:
For a price taking firm, average revenue is equal to the market price.