Which of the following statements is/are true? A - In perfect competition, average revenue is equal to market price. B - In perfect competition, marginal revenue is equal to market price.
Both A and B are true
Understanding Revenue in Perfect Competition
Perfect competition is a market structure characterized by a large number of buyers and sellers, homogeneous products, perfect information, free entry and exit, and the absence of externalities. In this market structure, individual firms are price takers, meaning they have no control over the market price and must accept the price determined by the market supply and demand.
Statement A: Average Revenue (AR) is equal to Market Price in Perfect Competition
Average Revenue (AR) is calculated by dividing the Total Revenue (TR) by the quantity of output sold (Q). Total Revenue is simply the price (P) multiplied by the quantity (Q).
The formula for Total Revenue is:
\(TR = P \times Q\)
The formula for Average Revenue is:
\(AR = \frac{TR}{Q}\)
Substituting the formula for TR into the formula for AR:
\(AR = \frac{P \times Q}{Q}\)
Assuming Q > 0, we can cancel Q from the numerator and denominator:
\(AR = P\)
So, in perfect competition (or any market structure), Average Revenue is always equal to the price per unit of output. Since firms in perfect competition sell their output at the prevailing market price, Average Revenue for a perfectly competitive firm is equal to the market price.
Therefore, statement A is true.
Statement B: Marginal Revenue (MR) is equal to Market Price in Perfect Competition
Marginal Revenue (MR) is the additional revenue a firm earns from selling one more unit of output. It is calculated as the change in total revenue divided by the change in quantity sold.
The formula for Marginal Revenue is:
\(MR = \frac{\Delta TR}{\Delta Q}\)
In perfect competition, a firm can sell any quantity it wishes at the market price (P). This means that for every additional unit sold, the total revenue increases by exactly the market price (P), assuming the price does not change as the firm changes its output (which is true for a price taker).
Let's consider an example:
| Quantity (Q) | Price (P) | Total Revenue (TR = P x Q) | Marginal Revenue (MR = ΔTR / ΔQ) |
|---|---|---|---|
| 0 | $10 | $0 | - |
| 1 | $10 | $10 | $(10-0)/(1-0) = $10 |
| 2 | $10 | $20 | $(20-10)/(2-1) = $10 |
| 3 | $10 | $30 | $(30-20)/(3-2) = $10 |
As shown in the table, when the price is constant (as in perfect competition), the Marginal Revenue is equal to the price ($10 in this example). Selling an additional unit adds exactly the market price to the total revenue.
Therefore, statement B is true.
Conclusion on Perfect Competition Statements
Based on the analysis of both statements:
- Statement A: In perfect competition, average revenue is equal to market price. (True)
- Statement B: In perfect competition, marginal revenue is equal to market price. (True)
Both statements are true regarding the relationship between average revenue, marginal revenue, and market price in a perfectly competitive market.
Revision Table: Key Revenue Concepts in Perfect Competition
| Concept | Definition | Relationship in Perfect Competition | Formula |
|---|---|---|---|
| Total Revenue (TR) | Total earnings from selling a quantity of output. | Increases by Price for each additional unit. | \(TR = P \times Q\) |
| Average Revenue (AR) | Revenue per unit of output sold. | Equal to the market price. | \(AR = \frac{TR}{Q} = P\) |
| Marginal Revenue (MR) | Additional revenue from selling one more unit. | Equal to the market price. | \(MR = \frac{\Delta TR}{\Delta Q} = P\) |
Additional Information: Demand Curve in Perfect Competition
For a perfectly competitive firm, the demand curve it faces is perfectly elastic (a horizontal line) at the market price. This is because the firm is a price taker and can sell any quantity at the market price. This horizontal demand curve is also the firm's Average Revenue (AR) curve and Marginal Revenue (MR) curve. Therefore, in perfect competition, the demand curve, AR curve, and MR curve are all the same horizontal line at the market price.
Key characteristics of perfect competition that lead to this relationship:
- Large number of buyers and sellers
- Homogeneous products
- Firms are price takers
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