Every business that has ever cut a price has been asking the same question: will enough extra customers arrive to make up for the money lost on each sale? Price elasticity of demand is the tool economists use to answer it. It measures how strongly buyers react when a price changes.
Price elasticity of demand
A measure of the responsiveness of quantity demanded to a change in price.
PED = % change in quantity demanded ÷ % change in priceFormulae are not supplied in the exam. You must recall this.
Calculating PED
A café raises the price of a coffee from 10 to 12 riyals. Weekly sales fall from 500 cups to 400. Calculate PED.
Ignore the minus sign when judging the strength of the response, and read only the size of the number. A coefficient between 0 and 1 means demand is inelastic: buyers barely react, so quantity changes proportionately less than price. A coefficient greater than 1 means demand is elastic: buyers react sharply, and quantity changes proportionately more than price.
The negative sign is not an error. Demand curves slope downward, so price and quantity always move in opposite directions and PED is almost always negative. Show the sign in your working, then discuss the magnitude. Candidates who claim the negative sign means demand is inelastic lose the interpretation mark every time.
A 10% fall in the price of a good causes quantity demanded to rise by 25%. What is the PED?
Whether demand is elastic or inelastic depends mainly on how easily buyers can escape the price rise. Close substitutes make demand elastic, because customers simply switch. Necessities tend to be inelastic, since people buy them regardless. Goods taking a large share of income are more elastic, because the price change is felt more keenly. Habit-forming goods are inelastic. Time matters too: demand becomes more elastic in the long run as buyers find alternatives.
Sketch two demand curves through the same point, one elastic and one inelastic, and show how the same price rise affects quantity differently on each.
A steeper curve indicates more inelastic demand over that range. Label both axes and mark the quantity change on each.
Two extreme cases complete the picture. Perfectly inelastic demand has a PED of 0: quantity does not change at all when price changes, and the demand curve is vertical. Perfectly elastic demand has an infinite PED: at one price buyers will take any quantity, but at any higher price they buy none, and the demand curve is horizontal. Unitary elasticity, a PED of exactly 1, means quantity changes by the same percentage as price.
PED, spending and revenue
The amount consumers spend on a good and the revenue firms earn from it are the same number: price multiplied by quantity. PED tells you what happens to it when price changes. If demand is elastic, a price rise loses so many sales that total spending and revenue fall, and a price cut raises them. If demand is inelastic, a price rise loses few sales, so spending and revenue rise, and a price cut lowers them. If demand is unitary, revenue stays the same.
Whether a price change raises revenue
A cinema cuts its ticket price from $8 to $6 and weekly attendance rises from 1,000 to 1,500. A bus company raises its fare from $2.00 to $2.50 and weekly passengers fall from 10,000 to 9,000. For each, calculate PED and the change in revenue.
Draw two demand curves, one steep (inelastic) and one flat (elastic). On each, show the same price rise and shade the revenue gained from the higher price on units still sold and the revenue lost from units no longer sold.
Revenue rises when the gained rectangle is bigger than the lost one. On the inelastic curve it is; on the elastic curve it is not. The two rectangles are the whole argument in one picture.
PED matters for decisions across the economy. Consumers facing a price rise on a good with inelastic demand, such as fuel, end up spending more of their income on it. Firms use PED to set prices: they raise prices where demand is inelastic and cut them where it is elastic. Workers are affected because a firm whose demand is elastic may lose many sales, and so jobs, if its costs and prices rise. Governments tax goods with inelastic demand, such as tobacco and petrol, because consumption falls only a little, so the tax raises a lot of revenue, though for the same reason it does less to cut consumption.