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Exercises · Q7

Q.Why is a firm's Average Revenue (AR) curve the same as the demand curve it faces? Explain with reference to the formula for AR.

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✓ Free question

By definition, Total Revenue is price multiplied by quantity sold: TR=P×QTR=P\times Q. Average Revenue is defined as revenue per unit sold:

AR=TRQ=P×QQ=PAR=\dfrac{TR}{Q}=\dfrac{P\times Q}{Q}=P

So AR, at any given output, is ALGEBRAICALLY IDENTICAL to the price at which that output is sold — dividing total revenue by the number of units sold can only ever give back the per-unit price.

A demand curve (or demand schedule) shows exactly the same relationship from the buyers' side: at each quantity that buyers are willing to purchase, it shows the price at which they will purchase it. Since AR at a given quantity IS the price at which the firm sells that quantity, and the demand curve at that same quantity shows the same price, the two curves must be one and the same line — plotting AR against output is mathematically identical to plotting the firm's demand curve.

✓Final answer

Because AR=TR/Q=(P×Q)/Q=PAR=TR/Q=(P\times Q)/Q=P, AR at every output level equals the price — exactly what the demand curve shows — so a firm's AR curve and its demand curve are the same curve.

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