The influence of sales on revenue

Micro‑economic Decision‑Makers – Firms’ Costs, Revenue and Objectives

1. Objectives of a Firm (Cambridge syllabus 3.6)

• Survival – covering all costs in the short run.
• Profit maximisation – producing the output where MR = MC and profit (TR – TC) is highest.
• Growth / market‑share expansion – may involve temporary losses to increase sales.
• Social or environmental goals – e.g., corporate‑social‑responsibility, which can modify the profit‑maximising rule.

In exam answers, state the hierarchy (survival → profit → growth) and, where relevant, explain why a firm might temporarily sacrifice profit.

2. Costs of Production

2.1 Key Definitions

• Fixed Cost (FC): does not vary with output (e.g., rent, salaried staff).
• Variable Cost (VC): varies directly with output (e.g., raw materials, hourly wages).
• Total Cost (TC): TC = FC + VC.
• Average Fixed Cost (AFC): AFC = FC ÷ Q.
• Average Variable Cost (AVC): AVC = VC ÷ Q.
• Average Total Cost (ATC): ATC = TC ÷ Q = AFC + AVC.
• Marginal Cost (MC): extra cost of producing one more unit.
  

  MC = ΔTC ÷ ΔQ.

• Marginal Revenue (MR): extra revenue from selling one more unit.
  

  MR = ΔTR ÷ ΔQ.

2.2 Short‑run vs Long‑run Costs

• Short‑run: at least one factor (e.g., plant size) is fixed → FC > 0.
• Long‑run: all factors are variable → FC can be altered; firms can achieve the lowest possible ATC (minimum efficient scale).
• In the short run the ATC curve is U‑shaped because of diminishing marginal returns; in the long run the LRATC curve shows economies of scale (downward slope) followed by diseconomies of scale (upward slope).

2.3 Illustrative Cost Table

2.4 Sketching Cost Curves (exam expectations)

• Draw a typical U‑shaped ATC curve that falls, reaches a minimum, then rises.
• Plot the MC curve intersecting ATC at its lowest point (the efficient scale).
• Show AFC (downward‑sloping) and AVC (U‑shaped) – MC cuts AVC at its minimum.
• Label axes: Quantity (Q) – horizontal, Cost per unit – vertical.
• Explain that when MC is below ATC, ATC is falling; when MC is above ATC, ATC is rising.

2.5 Break‑even Analysis (TR = TC)

Use the cost table above and a price of $9 per unit (as in the revenue example).

The break‑even output is 50 units (where TR = TC). On the exam, draw the TR line and the TC curve on the same graph and mark the intersection.

2.6 Economies & Diseconomies of Scale

• Economies of scale: ATC falls as Q rises (e.g., spreading fixed cost, bulk buying).
• Diseconomies of scale: ATC rises after a certain output (e.g., management inefficiencies, over‑crowding).
• In the long‑run diagram, the LRATC curve first slopes down (economies) then up (diseconomies). The minimum point is the minimum efficient scale.

3. Revenue

3.1 Definitions

• Total Revenue (TR): income from all sales.
  

  TR = P × Q

• Average Revenue (AR): revenue per unit sold.
  

  AR = TR ÷ Q = P (for a price‑taking firm).

• Marginal Revenue (MR): extra revenue from selling one more unit.
  

  MR = ΔTR ÷ ΔQ.

3.2 Worked Example – Calculating Revenue

Suppose a firm sells 120 units at $15 each.

• TR = 15 × 120 = $1,800
• AR = TR ÷ Q = 1,800 ÷ 120 = $15
• If output rises to 130 units and the price falls to $14:
  

  TR = 14 × 130 = \$1,820, AR = \$14.

3.3 Price Elasticity of Demand (recap)

• Elastic demand (|ε| > 1): quantity changes proportionally more than price.
• Unit‑elastic demand (|ε| = 1): percentage change in quantity equals percentage change in price.
• Inelastic demand (|ε| < 1): quantity changes proportionally less than price.

3.4 Revenue Behaviour by Elasticity (corrected)

3.5 Numerical Illustration

In this example TR rises as price falls from \$10 to \$6, indicating that demand is elastic over that range. After the peak (around $6), further price cuts produce smaller percentage increases in Q, so TR growth slows – the region becomes increasingly inelastic.

3.6 Suggested Diagrams (exam practice)

• Demand curve – label three zones: elastic (upper‑left), unit‑elastic (mid‑point), inelastic (lower‑right).
• Total‑Revenue curve – plotted against price (or quantity). It rises, peaks at the unit‑elastic point, then falls.
• Mark the point where MR = 0; this corresponds to the maximum of the TR curve (unit‑elastic demand).

4. Linking Costs and Revenue – Decision‑Making

4.1 Profit Formula

Profit (π) = Total Revenue – Total Cost = TR – TC

4.2 Profit‑Maximising Condition

• Produce up to the output where MR = MC.
• If MR > MC the firm can increase profit by producing more.
• If MR < MC the firm should cut output.
• At the profit‑maximising output, compare price (AR) with ATC to see whether the firm makes a profit, breaks even, or incurs a loss.

4.3 Example – Using the Demand Schedule (Section 3.5) and Cost Data

Fixed cost = \$200; Variable cost = \$4 × Q. Calculate MC, TR, TC, profit and MR for each price‑quantity pair.

Maximum profit occurs at Q = 120 (price \$10) where MR (\$6) > MC (\$4) but begins to fall thereafter. The firm is operating in the elastic region at this output because a price cut from \$12 to $10 raised TR.

4.4 Decision‑Making Checklist (exam style)

1. Calculate TR, TC and profit for each output level.
2. Derive MR from the demand schedule and MC from the cost data.
3. Identify the output where MR = MC (or where MR just exceeds MC and the next unit would make MR < MC).
4. Check whether AR (price) is above ATC at that output – if yes, the firm makes a profit; if AR = ATC, it breaks even; if AR < ATC, it incurs a loss.

5. Types of Markets (Cambridge syllabus 3.7)

5.1 Comparative Box

5.2 Sketch for Monopoly (exam tip)

• Draw a downward‑sloping demand curve (D).
• Draw the MR curve with twice the slope of D (starts at the same price‑intercept, cuts the horizontal axis at half the quantity).
• Show MC (usually upward‑sloping) intersecting MR at the profit‑maximising output.
• From that output draw a vertical line up to the demand curve – the price charged is above MC.

6. Link‑in to the Other Decision‑Maker Sections (Money & Banking, Households, Workers)

The analysis of a firm’s costs, revenue and objectives is one part of the broader “Micro‑economic decision‑makers” unit (Cambridge 0455). Teachers should remind students that:

• Households make consumption choices based on income (derived from wages, interest, profits) and prices – the same demand curves we have used for firms.
• Workers decide how much labour to supply, influenced by wage rates, which are part of a firm’s variable cost.
• The banking system supplies the finance that firms may need for investment; interest rates affect both firms’ cost of borrowing and households’ saving decisions.
• Linking these sections helps students see the circular flow of income and understand why a change in one market (e.g., a rise in interest rates) can shift both cost curves and demand curves for firms.

7. Key Points to Remember

• TC = FC + VC; ATC = TC ÷ Q; MC = ΔTC ÷ ΔQ.
• TR = P × Q; AR = P (price‑taking); MR = ΔTR ÷ ΔQ.
• Revenue response to a price change:

  • Elastic demand – price cut → TR rises.
  • Unit‑elastic – price cut → TR unchanged.
  • Inelastic – price cut → TR falls.

• Profit‑maximising output is where MR = MC. Compare price (AR) with ATC to determine profit, break‑even or loss.
• Short‑run: at least one fixed factor; long‑run: all factors variable, allowing firms to achieve the lowest possible ATC.
• Market type matters: in perfect competition P = MR = MC at equilibrium; in monopoly P > MC because MR < D.
• Four common firm objectives: survival → profit maximisation → growth → social/ethical goals.

8. Practice Questions

8.1 Revenue & Elasticity

A firm sells 500 units at \$12 each (TR = \$6,000). After reducing the price to $10, sales rise to 650 units.

1. Calculate the new total revenue.
2. State whether revenue has increased or decreased.
3. Based on the change, indicate whether the firm is operating on the elastic, unit‑elastic or inelastic portion of its demand curve.

8.2 Cost Calculations (using the table in 2.3)

1. What is the average total cost when Q = 150?
2. If the firm sells 150 units at the price $9, calculate profit (or loss).
3. Is the firm covering its average total cost at this output level?

8.3 Combined Decision‑Making (profit‑maximisation)

Demand schedule:

Fixed cost = \$200; variable cost = \$4 × Q.

• For each price‑quantity pair, compute TR, TC, profit (TR – TC).
• Calculate MR between each successive pair and compare with MC ($4).
• Identify the output that gives the highest profit and state the elasticity condition (elastic, unit‑elastic, inelastic) at that point.

8.4 MC & MR Calculation (short‑run)

Using the cost table in 2.3, find MC for each increase in output and show how MR can be derived from the revenue example in 3.2. Explain why the profit‑maximising output is where MR = MC.