Revenue in Perfect Competition: Videos & Practice Problems

In a perfectly competitive market, understanding revenue is crucial for firms as it directly impacts their financial performance. Revenue, defined as the total money received by a firm, can be calculated using the formula for total revenue (TR), which is the product of price (P) and quantity (Q): TR = P \times Q. This total revenue represents the benefits to the firm, and when analyzing how revenue changes with production, we consider both average revenue (AR) and marginal revenue (MR).

Average revenue is calculated by dividing total revenue by the quantity sold: AR = \frac{TR}{Q}. Substituting the total revenue formula into this equation, we find that AR = \frac{P \times Q}{Q} = P. This indicates that in perfect competition, average revenue equals the price of the product, which also corresponds to the demand curve faced by the firm. This relationship holds true across all market structures, not just in perfect competition.

Marginal revenue, on the other hand, measures the additional revenue generated from selling one more unit of a product. It is defined as the change in total revenue divided by the change in quantity: MR = \frac{\Delta TR}{\Delta Q}. In a perfectly competitive market, the price remains constant regardless of the quantity sold, meaning that if a firm sells one additional unit, it does so at the market price. Therefore, the change in total revenue from selling one more unit is equal to the price: MR = P.

This unique characteristic of perfect competition leads to the conclusion that average revenue, marginal revenue, and price are all equal: AR = MR = P. This equality is a defining feature of perfect competition and distinguishes it from other market structures, where marginal revenue typically decreases as more units are sold due to the downward-sloping demand curve.

Understanding these concepts is essential for firms operating in a perfectly competitive market, as they highlight how pricing and revenue generation are interlinked, allowing firms to make informed production and pricing decisions.

In a perfectly competitive market, the price remains constant regardless of the quantity sold. For instance, if the market price for wheat is set at $4 per bushel, this price will not fluctuate with changes in quantity. To understand the relationship between revenue, cost, and profit, we can analyze a simple numerical example.

Total revenue (TR) is calculated by multiplying the price (P) by the quantity (Q) sold. In this case, the total revenue for different quantities can be summarized as follows:

• 0 units: TR = 0 × 4 = $0
• 1 unit: TR = 1 × 4 = $4
• 2 units: TR = 2 × 4 = $8
• 3 units: TR = 3 × 4 = $12
• 4 units: TR = 4 × 4 = $16
• 5 units: TR = 5 × 4 = $20
• 6 units: TR = 6 × 4 = $24

Profit is determined by subtracting total costs (TC) from total revenue (TR). For example, if fixed costs are $2.50, the profit calculations for each quantity sold would be:

• 0 units: Profit = 0 - 2.50 = -$2.50
• 1 unit: Profit = 4 - 4.50 = -$0.50
• 2 units: Profit = 8 - 7 = $1
• 3 units: Profit = 12 - 10 = $2
• 4 units: Profit = 16 - 13.50 = $2.50
• 5 units: Profit = 20 - 18 = $2
• 6 units: Profit = 24 - 24 = $0

Marginal revenue (MR) is the additional revenue generated from selling one more unit. In a perfectly competitive market, MR remains constant and equals the price. Thus, for each additional unit sold, the marginal revenue is consistently $4:

• From 0 to 1 unit: MR = 4
• From 1 to 2 units: MR = 4
• From 2 to 3 units: MR = 4
• From 3 to 4 units: MR = 4
• From 4 to 5 units: MR = 4
• From 5 to 6 units: MR = 4

On the other hand, marginal cost (MC) reflects the change in total cost when production is increased by one unit. The marginal cost can vary and is typically increasing due to diminishing returns. For example:

• From 0 to 1 unit: MC = 4.50 - 2.50 = $2
• From 1 to 2 units: MC = 7 - 4.50 = $2.50
• From 2 to 3 units: MC = 10 - 7 = $3
• From 3 to 4 units: MC = 13.50 - 10 = $3.50
• From 4 to 5 units: MC = 18 - 13.50 = $4.50
• From 5 to 6 units: MC = 24 - 18 = $6

The change in profit can be calculated by comparing the profit at each level of output or by subtracting marginal cost from marginal revenue. The goal is to maximize profit, which occurs where the profit is highest. In this example, the maximum profit of $2.50 occurs when producing 4 units.

In summary, in a perfectly competitive market, marginal revenue remains constant and equals the price, while marginal cost typically increases with production. Understanding these concepts is crucial for determining the optimal level of output to maximize profit.