Marginal, average and total revenue — AQA A-Level Economics

Total revenue (TR) is the total receipts from selling output, calculated as price multiplied by quantity, while average revenue (AR) equals price and represents the firm's demand curve. Marginal revenue (MR) measures the addition to total revenue from selling one extra unit, reaching zero when total revenue is maximised at unitary price elasticity.

Revenue analysis examines the income a firm generates from selling goods and services at various price levels. In AQA A-Level Economics, understanding Total Revenue (TR), Average Revenue (AR), and Marginal Revenue (MR) is fundamental to analysing market structures, firm objectives, and business conduct.

This topic forms the analytical bridge connecting consumer demand elasticity with the theory of the firm. Mastering the distinction between price takers in perfect competition and price makers in imperfect competition enables students to accurately evaluate profit-maximising (MC = MR), revenue-maximising (MR = 0), and sales-maximising (AR = AC) strategies.

• →Total Revenue (TR = P x Q): The aggregate gross earnings received by a firm from selling a specific volume of output.
• →Average Revenue (AR = TR / Q = P): The revenue earned per unit sold, which is mathematically identical to price and therefore defines the firm's demand curve.
• →Marginal Revenue (MR = ΔTR / ΔQ): The additional revenue generated from the sale of one extra unit of output.
• →Price Taker vs Price Maker: In perfect competition, the firm faces a horizontal demand curve where P = AR = MR. In imperfect competition, the firm faces a downward-sloping demand curve where MR lies below AR.
• →PED and Revenue Relationships: MR is positive when PED > 1 (elastic), zero when PED = 1 (unitary, TR maximised), and negative when PED < 1 (inelastic).

• Define Total Revenue (TR) as the total value of sales, calculated using the formula TR = P × Q.
• Define Average Revenue (AR) as revenue per unit, calculated as TR / Q, which is equal to the price of the product.
• Define Marginal Revenue (MR) as the addition to total revenue from selling one more unit, calculated as ΔTR / ΔQ.
• Explain the relationship between MR and TR: when MR is positive, TR is rising; when MR is zero, TR is maximised; when MR is negative, TR is falling.
• State that Average Revenue (AR) is calculated as Total Revenue divided by Quantity (TR / Q).
• Explain that since TR = P × Q, substituting this into the AR formula gives AR = (P × Q) / Q, which simplifies to AR = P.
• Define the demand curve as showing the relationship between the price of a good and the quantity demanded by consumers.
• Conclude that because the price on the demand curve is identical to the average revenue received by the firm, the AR curve is the firm's demand curve.
• Define average revenue as total revenue divided by quantity, representing the firm's demand curve.
• Define marginal revenue as the change in total revenue resulting from the sale of one additional unit.
• Explain that when average revenue is constant, such as in perfect competition, marginal revenue is equal to average revenue.
• Explain that when average revenue is downward sloping, such as in imperfect competition, marginal revenue falls at twice the rate of average revenue.
• State that marginal revenue is the addition to total revenue from the sale of one more unit.
• Explain that total revenue increases as long as marginal revenue is positive.
• Identify that total revenue is maximised at the exact output level where marginal revenue equals zero.
• Explain that total revenue decreases when marginal revenue becomes negative.
• Accurate calculation of Total Revenue using the formula TR = Price × Quantity.
• Accurate calculation of Average Revenue using the formula AR = TR / Quantity.
• Accurate calculation of Marginal Revenue using the formula MR = ΔTR / ΔQ.
• Correct identification of the relationship where Average Revenue is always equal to the price of the product.
• Accurate drawing of horizontal AR and MR curves for a perfectly competitive firm.
• Accurate drawing of downward-sloping AR and MR curves for a firm with market power, with MR falling twice as steeply as AR.
• Correct illustration of the TR curve as an inverted U-shape for a price-making firm, peaking exactly where MR = 0.
• Interpretation of the AR curve as the firm's demand curve.
• Linking the elasticity of the AR curve to the sign of MR, identifying that demand is elastic when MR > 0 and inelastic when MR < 0.

• 💡Always state the formulas for TR, AR, and MR when defining them in an essay to secure knowledge marks quickly.
• 💡Use a numerical table in your exam answer to demonstrate how TR, AR, and MR change as price falls and quantity increases.
• 💡When drawing revenue curves, ensure the MR curve falls twice as steeply as the AR curve for a downward-sloping demand curve.
• 💡When drawing market structure diagrams, always label the downward-sloping or horizontal curve as 'AR = D' to show you understand they are the same.
• 💡Use the mathematical proof (AR = TR / Q = P) in written explanations to secure analytical marks when discussing revenue curves.
• 💡Remember that factors shifting the demand curve (like changes in consumer income) will identically shift the firm's average revenue curve.
• 💡Always label the average revenue curve as the demand curve (D=AR) to demonstrate understanding of their equivalence.
• 💡When sketching imperfect market diagrams, ensure the marginal revenue curve crosses the x-axis exactly halfway between the origin and where the average revenue curve meets the x-axis.
• 💡Use numerical examples in essay questions to prove why marginal revenue falls faster than average revenue when prices are reduced.
• 💡When drawing stacked diagrams, use a ruler to draw a vertical dashed line from where marginal revenue crosses the x-axis up to the peak of the total revenue curve.
• 💡Use the marginal revenue and total revenue relationship to explain price elasticity of demand: MR>0 is elastic, MR=0 is unitary, and MR<0 is inelastic.
• 💡In quantitative questions, calculate marginal revenue by finding the difference in total revenue between consecutive output levels to pinpoint where total revenue is maximised.
• 💡When completing a revenue table, calculate Total Revenue first, as it forms the basis for finding Marginal Revenue.
• 💡Double-check your Marginal Revenue calculations if the quantity increases by increments other than one, ensuring you divide by the change in quantity.
• 💡Remember that the Average Revenue column will always be identical to the Price column in your data table.
• 💡Use a ruler to ensure the MR curve bisects the horizontal distance between the vertical axis and the AR curve for a price-making firm.
• 💡When asked to show revenue maximisation, explicitly mark the point where MR = 0 and draw a dashed line up to the peak of the TR curve.
• 💡Always state that the AR curve is the demand curve when interpreting revenue diagrams for imperfectly competitive markets.
• 💡In any microeconomics essay examining firm objectives, sketch the downward-sloping AR and MR diagram alongside an inverted-U TR curve to gain analysis marks.
• 💡When explaining price elasticity on a linear demand curve, highlight that elasticity varies along the curve: the upper portion is elastic (MR > 0), the midpoint is unitary (MR = 0), and the lower portion is inelastic (MR < 0).
• 💡Always state units when calculating AR, MR, or TR in Paper 1 and Paper 3 data response questions (e.g., '£ millions' or '£ per unit').

• Confusing marginal revenue with average revenue; correction: MR is the revenue from the last unit sold, whereas AR is the revenue spread across all units sold.
• Assuming total revenue always increases when output increases; correction: TR will fall if the firm must lower prices significantly to sell more units, causing MR to become negative.
• Calculating MR simply as TR divided by Q; correction: MR must be calculated as the change in TR divided by the change in Q (ΔTR / ΔQ).
• Stating that the marginal revenue curve is the demand curve; correction: the average revenue curve is the demand curve because it shows the price per unit, not the revenue from the extra unit.
• Assuming the AR curve is only the demand curve in perfect competition; correction: the AR curve is the firm's demand curve in all market structures, whether it is horizontal or downward-sloping.
• Failing to mathematically prove why AR equals price; correction: always show the steps TR = P × Q and AR = TR / Q to demonstrate that AR = P.
• Error: Assuming marginal revenue and average revenue are always the same curve. Correction: Marginal revenue only equals average revenue in perfect competition; in imperfect markets, marginal revenue is below average revenue.
• Error: Drawing the marginal revenue curve with the same gradient as the average revenue curve in a monopoly diagram. Correction: Draw the marginal revenue curve so it falls twice as steeply, bisecting the horizontal axis halfway between the origin and the average revenue curve.
• Error: Stating that marginal revenue is the average price of the last unit sold. Correction: State that marginal revenue is the addition to total revenue from selling one more unit, which accounts for the price reduction on all previous units.
• Error: Confusing profit maximisation (MC=MR) with revenue maximisation (MR=0). Correction: Clearly distinguish that MR=0 maximises total revenue, whereas MC=MR maximises total profit.
• Error: Stating that total revenue falls as soon as marginal revenue starts falling. Correction: Clarify that total revenue continues to rise even when marginal revenue is falling, provided marginal revenue remains above zero.
• Error: Drawing the peak of the total revenue curve misaligned with the MR=0 point on a diagram. Correction: Ensure the maximum point of the total revenue curve is vertically aligned with the exact point where the marginal revenue curve crosses the horizontal axis.
• Calculating MR as the difference in price rather than the difference in total revenue; always calculate MR using ΔTR / ΔQ.
• Assuming MR is always positive; MR can be negative if the price reduction required to sell an additional unit outweighs the revenue gained from that extra unit.
• Failing to divide by the change in quantity when calculating MR from data where quantity jumps by more than one unit; always divide ΔTR by ΔQ.
• Drawing the MR curve for a price-maker with the same gradient as the AR curve; the MR curve must be drawn twice as steep as the AR curve.
• Placing the peak of the TR curve arbitrarily; the peak of the TR curve must align vertically with the point where the MR curve crosses the horizontal axis.
• Labelling the axes incorrectly; always label the vertical axis as Revenue or Price and the horizontal axis as Quantity or Output.
• Believing that Average Revenue can differ from Price: Because AR is defined as TR/Q and TR is P x Q, AR identically equals P (assuming a uniform pricing model without price discrimination).
• Assuming Marginal Revenue is always positive: Students frequently overlook that MR can become negative if the price reduction required to sell an extra unit outweighs the gain in sales volume.
• Confusing revenue maximisation with profit maximisation: Revenue is maximised where MR = 0, whereas profit is maximised where MC = MR. These points only coincide if marginal costs are zero.

1. 1Day 1: Master core definitions and formulas for TR, AR, and MR; practice calculating them across both flat and downward-sloping schedules.
2. 2Day 2: Practice diagrammatic drawing of AR, MR, and TR for price takers versus price makers, paying attention to the twice-as-steep rule for MR.
3. 3Day 3: Link MR and TR directly to PED; write short chain-of-reasoning paragraphs explaining why TR falls when price cuts occur in the inelastic region.
4. 4Day 4: Apply revenue concepts to firm objectives (profit maximisation, revenue maximisation, sales volume maximisation) using past AQA exam questions.

• 📋Calculation and Data Response (Paper 3 / Paper 1 Context): Extracting price and quantity data from a table to calculate TR, AR, or MR and deduce elasticity.
• 📋9-mark Analysis Question (Paper 1): Explaining the relationship between price elasticity of demand and total revenue when a monopolist alters price.
• 📋25-mark Essay (Paper 1): Evaluating the economic effects of a firm pursuing revenue maximisation (MR = 0) instead of profit maximisation (MC = MR).