Theme 3: Business Behaviour and the Labour Market
Section 3.3: Revenues, Costs and Profits — 3.3.1 Revenue
Welcome to your study notes on Revenue! Whether you are aiming for an \(A^*\) or trying to get your head around the basics, this guide breaks down everything you need for Pearson Edexcel A Level Economics A (9EC0). Revenue appears across Paper 1 (Markets and Business Behaviour) and synoptically in Paper 3 (Microeconomics and Macroeconomics). Let’s master these core principles step by step.
---1. The Core Building Blocks: Definitions and Formulae
Before a business can calculate its profit, it must know how much money is coming through the till. That money is called revenue.
A. Total Revenue (\(\text{TR}\))
• Definition: The total amount of income received by a firm from the sale of any given quantity of output.
• Formula: \(\text{TR} = P \times Q\)
• Variables: \(P = \text{Price per unit}\), \(Q = \text{Quantity sold}\).
• Units: Measured in monetary terms (e.g. \(£\)).
• Analogy: If you run a coffee stall and sell \(50\) cups of coffee at \(£3\) each, your Total Revenue is \(£3 \times 50 = £150\).
B. Average Revenue (\(\text{AR}\))
• Definition: The average amount of money received per unit of output sold.
• Formula: \(\text{AR} = \frac{\text{TR}}{Q} = \frac{P \times Q}{Q} = P\)
• Crucial Exam Identity: Because \(\text{AR} = P\), the Average Revenue curve is identical to the firm's Demand curve (\(D = \text{AR} = P\)).
• Units: Measured in monetary amount per unit (e.g. \(£\text{ per unit}\)).
C. Marginal Revenue (\(\text{MR}\))
• Definition: The addition to total revenue resulting from the sale of one extra unit of output.
• Formula: \(\text{MR} = \frac{\Delta \text{TR}}{\Delta Q}\) (or for a single extra unit: \(\text{MR}_n = \text{TR}_n - \text{TR}_{n-1}\)).
• Units: Measured in monetary amount per unit (e.g. \(£\text{ per unit}\)).
• Analogy: If selling \(10\) concert tickets brings in \(£100\), and selling \(11\) tickets brings in \(£108\), the Marginal Revenue of that \(11^{\text{th}}\) ticket is \(£108 - £100 = £8\).
Quick Key Takeaway:
• \(\text{TR}\) is the entire cash pile: \(P \times Q\).
• \(\text{AR}\) is the price tag: \(P\).
• \(\text{MR}\) is the extra cash from the next unit sold: \(\Delta \text{TR} / \Delta Q\).
2. Calculating Revenue: Standard Examiner Schedule
In the exam, you may be given an incomplete table and asked to fill in missing values. Don't worry if this seems tricky at first—just follow the formulae step-by-step!
\(\begin{array}{|c|c|c|c|} \hline \textbf{Output } (Q) & \textbf{Price / AR } (£) & \textbf{Total Revenue } (TR = P \times Q) \; [£] & \textbf{Marginal Revenue } (MR = \Delta TR / \Delta Q) \; [£] \ \hline 0 & 10 & 0 & - \ 1 & 9 & 9 & 9 \ 2 & 8 & 16 & 7 \ 3 & 7 & 21 & 5 \ 4 & 6 & 24 & 3 \ 5 & 5 & 25 \; (\textbf{Maximum } TR) & 1 \ 6 & 4 & 24 & -1 \ \hline \end{array}\)
Step-by-Step Calculation Walkthrough:
1. At \(Q = 1\): \(\text{TR} = 9 \times 1 = £9\). The extra revenue compared to \(Q = 0\) is \(£9 - £0 = £9\). So, \(\text{MR} = £9\).
2. At \(Q = 2\): Price drops to \(£8\). \(\text{TR} = 8 \times 2 = £16\). \(\text{MR} = £16 - £9 = £7\).
3. At \(Q = 5\): Price is \(£5\). \(\text{TR} = 5 \times 5 = £25\). \(\text{MR} = £25 - £24 = £1\). \(\text{TR}\) is at its peak!
4. At \(Q = 6\): Price drops to \(£4\). \(\text{TR} = 4 \times 6 = £24\). \(\text{MR} = £24 - £25 = -£1\). Notice that \(\text{MR}\) is now negative because the price cut needed to sell the \(6^{\text{th}}\) unit reduced overall revenue.
3. Revenue Curves by Market Structure
The shape of a firm's revenue curves depends entirely on whether the firm has market power to set its own price.
A. Price Takers (e.g. Perfect Competition)
• Market Condition: The individual firm is tiny relative to the market and must accept the equilibrium price determined by market supply and demand.
• \(\text{AR}\) and \(\text{MR}\) Curves: Because the price never changes regardless of how much output the firm sells, price is constant: \(\text{Price} = \text{AR} = \text{MR} = D\). This is drawn as a horizontal, perfectly elastic straight line at the market price.
• \(\text{Total Revenue (TR)}\) Curve: Rises at a constant rate as output expands. Graphically, it is a straight, upward-sloping ray starting from the origin with a constant slope equal to \(P\).
B. Price Makers (e.g. Monopoly, Oligopoly, Monopolistic Competition)
• Market Condition: The firm faces a downward-sloping demand curve. To sell more units, the firm must lower its price.
• The \(\text{AR}\) and \(\text{MR}\) Relationship:
— \(\text{AR}\) slopes downwards (this is the demand curve, \(D = \text{AR}\)).
— Unless the firm price discriminates, lowering the price to sell an extra unit means cutting the price on all previous units sold as well.
— Therefore, \(\text{MR}\) falls at twice the rate of \(\text{AR}\) and lies strictly below the \(\text{AR}\) curve.
— For a linear demand curve, the \(\text{MR}\) curve is twice as steep and cuts the horizontal axis exactly halfway between the origin and the quantity where \(\text{AR} = 0\).
— \(\text{MR}\) becomes negative when the price reduction across existing units outweighs the gain from the additional unit sold.
• \(\text{Total Revenue (TR)}\) Curve: Has an inverted U-shape (quadratic). It rises, reaches a maximum point where \(\text{MR} = 0\), and then declines as \(\text{MR}\) turns negative.
Quick Key Takeaway:
• Price Taker: \(\text{AR} = \text{MR} = P\) (Horizontal Line), \(\text{TR}\) is a straight diagonal line.
• Price Maker: \(\text{MR}\) drops twice as fast as \(\text{AR}\), \(\text{TR}\) is an inverted U-shape.
4. The Relationship Between Revenue and Price Elasticity of Demand (\(\text{PED}\))
A classic Edexcel exam question links revenue directly to the Price Elasticity of Demand (\(\text{PED}\)) along a linear, downward-sloping demand curve.
Did you know? Even though a straight-line demand curve has a constant gradient, its elasticity changes continuously from top to bottom!
\(\begin{array}{|c|c|c|c|c|} \hline \textbf{Segment on Demand Curve} & \textbf{Value of PED } (|\text{PED}|) & \textbf{Marginal Revenue } (\text{MR}) & \textbf{Effect of a Price Cut} & \textbf{Effect of a Price Rise} \ \hline \textbf{Upper Half (High } P\textbf{, Low } Q\textbf{)} & \text{Elastic } (|\text{PED}| > 1) & \text{Positive } (\text{MR} > 0) & \text{TR Increases} & \text{TR Decreases} \ \hline \textbf{Mid-point} & \text{Unitary } (|\text{PED}| = 1) & \text{Zero } (\text{MR} = 0) & \textbf{TR is Maximised} & \textbf{TR is Maximised} \ \hline \textbf{Lower Half (Low } P\textbf{, High } Q\textbf{)} & \text{Inelastic } (|\text{PED}| < 1) & \text{Negative } (\text{MR} < 0) & \text{TR Decreases} & \text{TR Increases} \ \hline \end{array}\)
Understanding the Three Zones:
1. Elastic Region (\(|\text{PED}| > 1\)): Consumers are very responsive to price changes. A percentage cut in price leads to an even bigger percentage increase in quantity sold, meaning total revenue rises. Because \(\text{TR}\) is rising, \(\text{MR}\) is positive (\(\text{MR} > 0\)).
2. Unitary Elastic Midpoint (\(|\text{PED}| = 1\)): The percentage change in quantity matches the percentage change in price. This is the exact output where \(\text{TR}\) is at its maximum, and \(\text{MR} = 0\).
3. Inelastic Region (\(|\text{PED}| < 1\)): Consumers are unresponsive. A percentage cut in price results in a smaller percentage increase in quantity sold, so total revenue falls. Because \(\text{TR}\) is falling, \(\text{MR}\) is negative (\(\text{MR} < 0\)).
The Rule for Revenue Maximisation:
A firm maximises total revenue at the quantity where:
\(\text{MR} = 0\) (and \(|\text{PED}| = 1\)).
5. Common Pitfalls and Examiner Warnings
Be sure to avoid these frequent errors highlighted in Pearson Edexcel examiner reports:
• Pitfall 1: Confusing Revenue with Profit!
Correction: Revenue is gross income (\(\text{TR} = P \times Q\)), whereas Profit is net gain after costs (\(\text{Profit} = \text{TR} - \text{TC}\)). A firm that maximises revenue (\(\text{MR} = 0\)) is not usually maximising profit (which happens at \(\text{MC} = \text{MR}\)).
• Pitfall 2: Confusing Revenue Maximisation with Sales Volume Maximisation!
Correction: Revenue maximisation occurs where \(\text{MR} = 0\). Sales volume maximisation means selling as many physical units as possible without making a loss, which occurs where \(\text{AR} = \text{AC}\).
• Pitfall 3: Misaligning Revenue Diagrams!
Correction: When drawing two diagrams stacked vertically (TR on top, AR/MR below), the peak of the \(\text{TR}\) curve must align perfectly with the quantity where \(\text{MR} = 0\) and the midpoint of the \(\text{AR}\) curve.
• Pitfall 4: Assuming PED is Constant on a Straight-Line Demand Curve!
Correction: A linear demand curve does not have constant elasticity. It is elastic at the top, unitary in the middle, and inelastic at the bottom.
• Pitfall 5: Drawing Marginal Revenue Incorrectly!
Correction: Never draw \(\text{MR}\) parallel to \(\text{AR}\). For a linear demand curve, \(\text{MR}\) must be drawn twice as steep as \(\text{AR}\) and must extend below the horizontal axis into negative values.
Quick Revision Checklist
Can you answer these key test questions without looking?
1. What is the formula for Marginal Revenue? (\(\Delta \text{TR} / \Delta Q\))
2. Why is the \(\text{AR}\) curve identical to the firm's demand curve? (\(\text{AR} = \text{TR}/Q = (P \times Q)/Q = P\))
3. What is the value of \(\text{MR}\) when Total Revenue is at its maximum? (\(\text{MR} = 0\))
4. What is the value of \(\text{PED}\) at the revenue-maximising level of output? (\(|\text{PED}| = 1\))
5. If a firm with downward-sloping demand cuts price in an inelastic region, what happens to \(\text{TR}\)? (\(\text{TR}\) falls because \(\text{MR} < 0\))