Revenue

Total, Average and Marginal RevenueRelationship between TR, AR and MRRevenue Curves: Perfect vs Imperfect Competition

Total, Average and Marginal Revenue

Just as a firm has costs of production, it also earns revenue from selling its output. Revenue is the money a firm receives from selling its goods. There are three measures, parallel to the cost measures:

  • Total Revenue (TR) — the total money received from selling a given quantity of output: TR = Price × Quantity (P × Q).
  • Average Revenue (AR) — revenue per unit sold: AR = TR ÷ Q. Since TR = P × Q, dividing by Q gives AR = P. So average revenue is the same as the price of the good. This is why the AR curve is also the firm's demand curve.
  • Marginal Revenue (MR) — the addition to total revenue from selling one more unit: MR = change in TR (TRₙ − TRₙ₋₁).

For example, if a firm sells 10 units at ₹5 each, its TR = 5 × 10 = ₹50, and its AR = 50 ÷ 10 = ₹5 (= the price). If selling the 11th unit raises TR from ₹50 to ₹54, the MR of that unit = 54 − 50 = ₹4. These three revenue concepts, together with the cost concepts, are what a producer compares to decide how much to produce.

1
Worked Example
Example 1: Write the formulas for total, average and marginal revenue.
Solution

One total, one per-unit, one extra.

  • TR = Price × Quantity.
  • AR = TR ÷ Q (= price); MR = change in TR.
2
Worked Example
Example 2: A firm sells 8 units at ₹12 each. Find TR and AR.
Solution

Use the formulas.

  • TR = 12 × 8 = 96.
  • AR = 96 ÷ 8 = 12 (= price).
3
Worked Example
Example 3: Why is average revenue equal to the price of the good?
Solution

Start from TR = P × Q.

  • AR = TR ÷ Q = (P × Q) ÷ Q = P.

Key Points

    • TR = P × Q; AR = TR ÷ Q = Price (so the AR curve is the demand curve); MR = change in TR.
    • A firm compares revenue with cost to decide its output.
✎ Quick Check — 2 questions0 / 2
Q1.Total revenue is calculated as:
Explanation: TR = Price × Quantity.
Q2.Average revenue is always equal to the:
Explanation: AR = TR ÷ Q = P, so AR equals the price.

Relationship between TR, AR and MR

The three revenue measures are linked, and their relationship depends on whether the price stays the same as more is sold.

When price is constant (the firm can sell any quantity at the same price — as under perfect competition):

  • AR = MR = Price (all equal and constant).
  • TR rises in a straight line as output rises.

When price falls as more is sold (the firm must lower price to sell more — as under monopoly/imperfect competition):

  • AR falls as output rises (the AR/demand curve slopes downward).
  • MR falls faster and lies below AR.
  • TR rises, reaches a maximum (where MR = 0), and then falls.

The general links: TR = AR × Q; AR = TR ÷ Q; and MR is the change in TR. A useful rule connects MR to TR: when MR is positive, TR is rising; when MR = 0, TR is maximum; when MR is negative, TR is falling. This relationship (especially MR = 0 at maximum TR) is important later when we find the producer's profit-maximising output, where the firm balances marginal revenue against marginal cost.

1
Worked Example
Example 1: When the price is constant, what is the relationship between AR and MR?
Solution

They are equal and constant.

  • AR = MR = Price.
2
Worked Example
Example 2: When a firm must lower price to sell more, how do AR and MR behave?
Solution

Both fall, MR faster.

  • AR (the demand curve) slopes downward.
  • MR falls faster and lies below AR.
3
Worked Example
Example 3: Total revenue is maximum when marginal revenue is:
Solution

Recall the TR–MR link.

  • TR is maximum when MR = 0.
  • Beyond that, MR is negative and TR falls.

Key Points

    • Constant price (perfect competition): AR = MR = Price; TR a straight rising line.
    • Falling price (imperfect competition): AR falls (downward curve), MR below AR and falls faster.
    • TR & MR link: MR > 0 → TR rising; MR = 0 → TR maximum; MR < 0 → TR falling.
✎ Quick Check — 2 questions0 / 2
Q1.When price is constant, AR and MR are:
Explanation: With constant price, AR = MR = price.
Q2.Total revenue is maximum when marginal revenue is:
Explanation: TR is maximum at the output where MR = 0.

Revenue Curves: Perfect vs Imperfect Competition

The shape of a firm's revenue curves depends on the market in which it sells.

Under perfect competition, a single firm is so small that it cannot influence the market price — it is a price taker and can sell any quantity at the ruling price. So its price is constant, which means AR = MR = Price, and the AR (and MR) curve is a horizontal straight line parallel to the X-axis at the level of the price.

Under imperfect competition (monopoly, monopolistic competition), a firm has some control over price and must lower its price to sell more. So its AR (demand) curve slopes downward, and its MR curve also slopes downward but lies below the AR curve. The diagrams below show the contrast:

Figure — Revenue Curves: Perfect vs Imperfect Competition
Perfect competitionAR = MR = PImperfect competitionARMR
1
Worked Example
Example 1: Why are AR and MR equal and horizontal under perfect competition?
Solution

The firm is a price taker.

  • It can sell any quantity at the same ruling price.
  • So price is constant, AR = MR = price, and the curve is horizontal.
2
Worked Example
Example 2: Under imperfect competition, how do the AR and MR curves look?
Solution

The firm lowers price to sell more.

  • AR (demand) slopes downward.
  • MR also slopes downward but lies below AR.
3
Worked Example
Example 3: What does 'price taker' mean?
Solution

The firm accepts the market price.

  • A firm too small to affect the market price; it sells at the price set by the market.

Key Points

    • Perfect competition: firm is a price taker; AR = MR = Price; revenue curve is a horizontal line.
    • Imperfect competition: firm lowers price to sell more; AR slopes downward and MR lies below AR.
✎ Quick Check — 2 questions0 / 2
Q1.Under perfect competition, a firm's AR curve is:
Explanation: A price-taking firm has a horizontal AR = MR = price line.
Q2.Under imperfect competition, the MR curve lies:
Explanation: When price must fall to sell more, MR lies below the downward AR curve.