Revenue and profit – Firm Behaviour (Senior 4 Economics) | Ganzaa

Firm Behaviour

Lessons

Senior 4 · Economics

Firm Behaviour

5 lessons

Lesson 5 of 5

Revenue and profit

30 min

Price times quantity

In the financial year 2024–25 Rwanda exported 37,693 tonnes of tea at an average of US$2.94 a kilogram, earning US$110.99 million (National Bank of Rwanda). A year earlier it had sold 38,483 tonnes at US$2.99 a kilogram, for US$114.96 million. Both price and quantity fell a little, so revenue fell by about 3%.

Revenue is the money a firm receives from sales; profit is what is left after costs. This lesson defines total, average and marginal revenue, shows how they behave in different markets, and puts them together with the cost curves of lesson 3 to find the output that maximises profit.

Definition

Total revenue (TR): all the money received from selling a given output: $TR = P \times Q$ .

Average revenue (AR): revenue per unit sold: $AR = \frac{TR}{Q} = \frac{P \times Q}{Q} = P$ . So the AR curve is the firm's demand curve.

Marginal revenue (MR): the change in total revenue from selling one more unit: $MR = \frac{\Delta TR}{\Delta Q}$ .

Example: $37{,}692{,}630 \text{ kg} \times 2.94 \approx 110.8$ million dollars, close to BNR's US$110.99 million (the unit value is rounded).

1. Revenue under perfect and imperfect competition

Perfect competition. A firm that is one of very many sellers of an identical product is a price taker: it can sell as much as it likes at the market price, and nothing at a higher price. Each extra unit adds exactly the price to revenue, so $A R = M R = P$ , a horizontal line, and TR is a straight line through the origin.

Imperfect competition (monopoly, oligopoly, monopolistic competition). A firm whose product is different, or which is large in its market, faces a downward-sloping demand curve: to sell more it must lower its price, on every unit. So MR is less than AR. For a straight-line demand curve $P = a - b Q$ :

TR = aQ - bQ^2, \qquad AR = a - bQ, \qquad MR = a - 2bQ

MR starts at the same point as AR and falls twice as steeply. TR is greatest where $M R = 0$ , which is also where demand is unit elastic (unit 3). Where MR is negative, demand is inelastic and selling more reduces revenue.

Q	P = AR = 123 − 6Q	TR	MR (per unit, from the table)
0	123	0	–
1	117	117	117
2	111	222	105
4	99	396	81
6	87	522	57
7	81	567	45
8	75	600	33
10	63	630	9
11	57	627	−3
12	51	612	−15

Reading the diagrams. In (a) every unit sells for 87, so revenue per unit and extra revenue are the same. In (b) the firm moves down its demand curve: at 7 units the price is 81, but the 7th unit adds only $567 - 522 = 45$ to revenue, because the price cut applies to the first 6 units too. The TR arch peaks at 10.25 units, exactly where MR crosses zero. (The MR values in the table are whole-unit steps; the curve is drawn from $M R = 123 - 12 Q$ .)

Definition

Profit = total revenue − total cost. In economics, total cost includes the opportunity cost of the owner's own resources, including normal profit: the minimum return that keeps the entrepreneur in the industry.

Normal profit: $T R = T C$ , or $A R = A T C$ . The firm covers all its costs, including the return its owner needs.
Supernormal (abnormal, economic) profit: $T R > T C$ , or $A R > A T C$ .
Subnormal profit (economic loss): $T R < T C$ , or $A R < A T C$ .

Example: a shop makes an accounting profit of Frw 1.8 million a year, but its owner could earn Frw 2.4 million as a manager elsewhere. Its economic profit is $1.8 - 2.4 = - 0.6$ million: a subnormal profit.

2. Profit maximisation

A firm maximises profit at the output where the gap between TR and TC is greatest. Equivalently, it keeps producing while each extra unit adds more to revenue than to cost:

\text{Profit is maximised where } MR = MC, \text{ with MC cutting MR from below.}

If $M R > M C$ , one more unit adds more to revenue than to cost, so output should rise. If $M R < M C$ , the last unit lost money, so output should fall. The second condition matters because MC can also equal MR on its falling part, where profit is at a minimum, not a maximum.

Reading the diagram. Combine the bakery's cost curves from lesson 3 with a downward-sloping demand $P = 123 - 6 Q$ . MR = MC at 7 hundred loaves. The firm charges the highest price buyers will pay for that quantity, read off the AR curve: 81. Average cost there is about 61.6, so profit per unit is about 19.4 and total supernormal profit is the green rectangle, about Frw 136 thousand a day.

When to stop producing. In the short run a firm making a loss should still produce if price covers average variable cost, because its fixed costs must be paid anyway; it shuts down if $P < A V C$ . In the long run it must cover all costs, $P \ge ATC$ , or leave the industry.

Worked example 1: a price taker maximises profit

The bakery of lesson 3 sells in a perfectly competitive market at $P = 87$ (Frw thousand per hundred loaves).

Step 1: MR = MC. $M R = P = 87$ . $MC = 60 - 24Q + 3Q^2 = 87 \Rightarrow 3Q^2 - 24Q - 27 = 0 \Rightarrow Q^2 - 8Q - 9 = 0 \Rightarrow (Q - 9)(Q + 1) = 0$ , so $Q = 9$ .

Step 2: profit. $TR = 87 \times 9 = 783$ ; $T C = 256 + 297 = 553$ ; profit $= 783 - 553 = 230$ thousand francs a day.

Step 3: check neighbours. At $Q = 8$ : $696 - 480 = 216$ . At $Q = 10$ : $870 - 656 = 214$ . Both are lower. ✔

Step 4: kind of profit. $ATC = \frac{553}{9} \approx 61.4 < 87$ , so the bakery earns supernormal profit, which in a competitive market would attract new firms.

Worked example 2: a firm with a downward-sloping demand curve

Same costs, but demand is $P = 123 - 6 Q$ , so $M R = 123 - 12 Q$ .

Step 1: MR = MC. $123 - 12Q = 60 - 24Q + 3Q^2 \Rightarrow 3Q^2 - 12Q - 63 = 0 \Rightarrow Q^2 - 4Q - 21 = 0 \Rightarrow (Q - 7)(Q + 3) = 0$ , so $Q = 7$ .

Step 2: price and profit. $P = 123 - 42 = 81$ ; $T R = 567$ ; $T C = 431$ ; profit $= 136$ thousand francs a day.

Step 3: compare with revenue maximisation. A sales-revenue maximiser would produce where $M R = 0$ : $Q = 10.25$ , $P = 61.5$ , $TR \approx 630.4$ , but $TC(10.25) \approx 687.1$ , a loss of about 57. This is why lesson 1's revenue-maximiser needs a profit floor.

3. What determines profit, and why profit matters

Determinants of profit. (1) Demand and the price the product commands. (2) The costs of production: input prices, wages, rent, interest and energy. (3) The efficiency of the firm and its technology. (4) The scale of production and economies of scale. (5) The market structure: the less competition, the easier it is to keep supernormal profit. (6) Government policy: taxes, subsidies and regulation. (7) The quality of management and entrepreneurship. (8) General economic conditions, such as booms and recessions.

The role of profit.

Reward for risk and enterprise: profit pays the entrepreneur for bearing uncertainty.
Signal: supernormal profit in an industry attracts new firms and resources; losses push resources out. Profit guides resources to where consumers want them (unit 4).
Source of investment: retained profit is the main source of funds for internal growth.
Incentive: the chance of profit encourages efficiency and innovation.
Measure of performance for owners, lenders and investors.
Source of tax revenue: governments tax company profits to fund public services.

Warning

Profit is maximised where MR = MC, not where profit per unit is highest, and not where TR is highest. At the lowest point of ATC (Q = 8 in lesson 3) cost per unit is smallest, but the profit-maximising output here is 7. And "normal profit" is a cost to economists: a firm earning only normal profit is doing well enough to stay.

Tip

The three-step drill for any profit diagram: (1) find Q where MR = MC; (2) go up to AR for the price; (3) compare AR with ATC at that Q: the rectangle between them is the profit (or loss).

Important

Discuss. Some people say high profits show that a firm is exploiting its customers; others say they reward efficiency and fund investment. Using the role of profit, discuss when supernormal profit is a good sign and when it should worry a government.

tutor2u, "Total, Average and Marginal Revenue I A Level and IB Economics". Watch how the presenter derives AR and MR from a downward-sloping demand curve and links MR = 0 to the top of the TR curve, as in diagrams (b) and the TR arch above.

✦

Practice

Define total, average and marginal revenue, and show that average revenue equals price.
A firm faces demand $P = 100 - 5 Q$ . Calculate TR, AR and MR for $Q = 1$ to $10$ . At what output is TR greatest?
Explain why AR = MR for a firm in perfect competition but MR < AR for a firm in imperfect competition.
Distinguish between normal, supernormal and subnormal profit, and between accounting and economic profit.
The bakery of lesson 3 sells at $P = 120$ in a competitive market. Find its profit-maximising output and its profit.
Explain the rule $M R = M C$ and why MC must cut MR from below.
State five determinants of a firm's profit.
"Profit serves no useful purpose for society." Evaluate this statement.

Show answersHide answers

TR = P × Q; AR = TR ÷ Q = (P × Q) ÷ Q = P; MR = ΔTR ÷ ΔQ.
TR = 100Q − 5Q²: 95, 180, 255, 320, 375, 420, 455, 480, 495, 500. AR = 95, 90, …, 50. MR (whole steps) = 95, 85, 75, 65, 55, 45, 35, 25, 15, 5. TR is greatest at Q = 10 (500), where MR = 100 − 10Q = 0.
A price taker sells every unit at the same price, so each extra unit adds exactly P. A firm facing downward-sloping demand must cut its price on all units to sell one more, so the extra revenue is less than the price.
Normal profit: TR = TC (AR = ATC), the minimum to keep the firm in the industry. Supernormal: TR > TC. Subnormal: TR < TC. Accounting profit subtracts explicit costs only; economic profit also subtracts implicit (opportunity) costs.
$60 - 24Q + 3Q^2 = 120 \Rightarrow Q^2 - 8Q - 20 = 0 \Rightarrow (Q - 10)(Q + 2) = 0$ , so $Q = 10$ . Profit $= 1,200 - 656 = 544$ thousand francs.
If MR > MC, producing more adds to profit; if MR < MC, producing less adds to profit; so profit is greatest where they are equal. Where MC cuts MR from above (MC falling), profit is at a minimum, so MC must be rising through MR.
Any five: demand and price; input costs; efficiency and technology; scale; market structure; government policy; management; economic conditions.
Against the statement: profit rewards risk-taking, signals where resources are wanted, funds investment, encourages efficiency and innovation, and is taxed to fund public services. For it: supernormal profit protected by barriers to entry can mean high prices and poor service. Conclude that profit is useful in competitive markets but needs regulation where competition is weak.

Quick check

Key points

$TR = P \times Q$ ; $A R = P$ (the demand curve); $MR = \frac{\Delta TR}{\Delta Q}$ .
In perfect competition AR = MR = P; in imperfect competition MR lies below AR, and TR is greatest where MR = 0.
Normal profit (AR = ATC) is a cost; supernormal profit means AR > ATC; subnormal profit means AR < ATC.
Profit is maximised where MR = MC with MC rising; profit rewards risk, signals where resources are wanted and funds investment.

1Price times quantity

21. Revenue under perfect and imperfect competition

32. Profit maximisation

43. What determines profit, and why profit matters

Price times quantity

1. Revenue under perfect and imperfect competition

2. Profit maximisation

3. What determines profit, and why profit matters