Calculation of TR and AR

Microeconomic Decision‑Makers: Firms’ Costs, Revenue and Objectives (Cambridge IGCSE/A‑Level Economics 0455)

Learning Objectives

• Explain the basic economic problem (scarcity, choice and opportunity cost).
• Describe how markets allocate resources (demand, supply, equilibrium, elasticities).
• Identify the five key decision‑makers (households, firms, workers, government, money‑banking) and their main economic activities.
• Define and calculate the main revenue concepts – Total Revenue (TR) and Average Revenue (AR) – and relate them to price (P) and marginal revenue (MR).
• Define and calculate the main cost concepts – Fixed Cost (FC), Variable Cost (VC), Total Cost (TC) and the corresponding average costs (AFC, AVC, ATC) and marginal cost (MC).
• Determine profit or loss (π) and locate the break‑even point.
• Explain the typical objectives of firms (survival, profit‑maximisation, growth, social welfare).
• Compare perfect competition and monopoly – the market structures examined in the syllabus – and know which diagrams are required in exam answers.

1. The Basic Economic Problem

1.1 Scarcity & Choice

• Resources (land, labour, capital, entrepreneurship) are limited, but human wants are unlimited.
• Because of scarcity, societies must decide what to produce, how to produce it and for whom.

1.2 Factors of Production & Rewards

1.3 Opportunity Cost & the Production‑Possibility Curve (PPC)

• Opportunity cost = the value of the next best alternative foregone when a choice is made.
• The PPC shows the maximum combinations of two goods that can be produced with available resources and technology.
• Points on the curve: efficient production.
  

  Inside the curve: under‑utilisation (inefficiency).
  

  Outside the curve: unattainable with current resources.

2. Allocation of Resources (Markets)

2.1 Role of Markets

Markets bring buyers and sellers together, allowing the forces of demand and supply to determine the allocation of scarce resources.

2.2 Demand

• Definition: The quantity of a good that consumers are willing and able to buy at each possible price.
• Law of Demand: As price falls, quantity demanded rises (ceteris paribus).
• Determinants (shifters): consumer income, tastes, price of related goods, expectations, number of buyers.
• Movement along the curve = change in price; shift of the curve = change in any determinant.

2.3 Supply

• Definition: The quantity of a good that producers are willing and able to sell at each possible price.
• Law of Supply: As price rises, quantity supplied rises (ceteris paribus).
• Determinants (shifters): input prices, technology, expectations, number of sellers, taxes/subsidies.
• Movement along the curve = change in price; shift of the curve = change in any determinant.

2.4 Market Equilibrium

Equilibrium occurs where the quantity demanded equals the quantity supplied.

\$\text{Equilibrium price (}Pe\text{)}\;:\; QD = Q_S\$

• At \$P_e\$ there is no tendency for price to change.
• Diagram: downward‑sloping demand intersecting upward‑sloping supply.

2.5 Price Changes

• A change in price results in a movement along the demand or supply curve.
• A shift of either curve creates a new equilibrium price and quantity.

2.6 Elasticities

• Price Elasticity of Demand (PED) – responsiveness of quantity demanded to a change in price.
  

  \$\text{PED} = \frac{\%\Delta Q_D}{\%\Delta P}\$

  • Determinants: availability of substitutes, proportion of income spent, necessity vs luxury, time horizon.
  • Interpretation: \$|PED|>1\$ (elastic), \$|PED|<1\$ (inelastic), \$|PED|=1\$ (unitary).

• Price Elasticity of Supply (PES) – responsiveness of quantity supplied to a change in price.
  

  \$\text{PES} = \frac{\%\Delta Q_S}{\%\Delta P}\$

  • Determinants: spare capacity, time to adjust, mobility of factors, nature of the good.

2.7 Market Failure & Government Intervention (brief)

• Market failure occurs when the free market does not allocate resources efficiently (e.g., externalities, public goods, information asymmetry).
• Typical government tools: taxes, subsidies, price controls (ceilings & floors), regulation, provision of public services.

3. Micro‑economic Decision‑Makers

3.1 Money & Banking

• Functions of money: medium of exchange, unit of account, store of value, standard of deferred payment.
• Central bank (e.g., Bank of England): issues currency, controls interest rates, implements monetary policy.
• Commercial banks: accept deposits, provide loans, create money through the multiplier effect.

3.2 Households

• Decide how much to spend, save or borrow.
• Consumption decisions are influenced by income, interest rates, expectations and the price level.

3.3 Workers (Labour Market)

• Supply labour based on wages, working conditions, education, and expectations.
• Demand for labour derived from the marginal product of labour and the price of the output.
• Wage determination can be illustrated with a labour‑market diagram (intersection of labour supply and demand).

3.4 Firms

3.4.1 Revenue Concepts

• Total Revenue (TR): money received from selling output.
  

  \$TR = P \times Q\$

• Average Revenue (AR): revenue per unit of output.
  

  \$AR = \frac{TR}{Q}=P\$

• Marginal Revenue (MR): change in total revenue from selling one additional unit.
  

  \$MR = \frac{\Delta TR}{\Delta Q}\$

3.4.1.1 Calculation – Perfect Competition (price taker)

1. Read the market price \$P\$ – it is the same for every unit sold.
2. Identify the intended output \$Q\$.
3. Calculate \$TR = P \times Q\$.
4. Calculate \$AR = TR/Q\$ (or note \$AR = P\$).
5. Because \$P\$ is constant, \$AR\$ is a horizontal line; \$MR\$ = \$AR\$ = \$P\$.

3.4.1.2 Worked Example – Perfect Competition

3.4.1.3 Calculation – Monopoly (price maker)

1. Use the demand schedule to find the price that corresponds to each output level.
2. Calculate \$TR = P \times Q\$ for each row.
3. Find \$AR = TR/Q\$ (which will equal the price from the demand schedule).
4. Calculate \$MR\$ as the change in \$TR\$ between successive output levels.

3.4.1.4 Worked Example – Monopoly

3.4.2 Cost Concepts

3.4.2.1 Worked Example – Cost Calculations

A bakery has fixed costs of £120 per week. Variable cost = £2 per loaf.

3.4.3 Profit, Loss and Break‑Even

• Profit (π): difference between total revenue and total cost.
  

  \$\pi = TR - TC\$

• If \$\pi\$ is negative, the firm incurs a loss.
• Break‑even point: output where \$TR = TC\$ (profit = 0). It can be found algebraically or graphically.

3.4.3.1 Worked Example – Profit & Break‑Even

Using the bakery data above, selling price = £5 per loaf.

Break‑even: solve \$5Q = 120 + 2Q \;\Rightarrow\; 3Q = 120 \;\Rightarrow\; Q = 40\$ loaves. At \$Q=40\$, \$TR = £200\$ and \$TC = £200\$, so profit = £0.

3.4.4 Objectives of Firms

• Survival: cover variable costs in the short run.
• Profit maximisation: produce where \$MC = MR\$.
• Growth: expand output, market share or product range after profit maximisation.
• Social‑welfare / non‑profit objectives: public utilities, charities, co‑operatives aim to provide services at the lowest feasible price.

3.4.5 Market Structures Covered in the Syllabus

3.5 Government (as a decision‑maker)

• Imposes taxes (reduce demand or supply), provides subsidies (increase supply or demand), regulates markets, and may directly provide goods and services.
• Fiscal policy (government spending & taxation) interacts with monetary policy to influence aggregate demand.

4. Examination Tips (AO1 & AO2)

• Write the relevant formula before substituting numbers – this gains marks for method.
• Label all tables and diagrams clearly, include units (£, $) and headings.
• If a price is not given, derive it from a demand schedule or a price‑output table first.
• For profit questions: calculate TR and TC separately, then subtract.
• Break‑even: set \$TR = TC\$ and solve algebraically; a short step earns marks.
• Remember: in perfect competition \$AR = P = MR\$; in monopoly \$AR = MR\$ but both are downward‑sloping.
• Link calculations to the firm’s objective – e.g., “the firm will increase output until \$MC = MR\$ because it wants to maximise profit.”
• When drawing diagrams, use a clean, labelled axis, indicate the relevant curves, and shade the area representing profit or loss.

5. Suggested Revision Diagrams

• TR and AR curves: horizontal AR (perfect competition) or downward AR (monopoly); TR rises linearly.
• Cost curves: AFC (downward), AVC (U‑shaped), ATC (U‑shaped), MC (U‑shaped, intersecting ATC at its minimum).
• Profit/Loss diagram: show TR, TC and the vertical distance (π) at a chosen output.
• Break‑even diagram: intersection of TR and TC curves.
• Demand & Supply diagram: equilibrium, shifts, and price‑change movements.
• Elasticity diagram: steep vs flat demand curves to illustrate elastic and inelastic demand.
• Market‑type comparison: overlay AR/MR for perfect competition (horizontal) and monopoly (downward).