0455 · 2.6Price elasticity of demand ped

PED formula and calculation

0:00A café raises its prices, expecting to earn more money. Each sale brings in more dollars, but some customers stop buying. Its revenue could rise or fall, depending on how strongly customers react. By the end of this video, you will understand that reaction, calculate it, and connect it to decisions about prices, taxes and wages. Demand describes the quantities consumers are willing and able to buy at different prices over a given period.

0:24Usually, a higher price causes a contraction in demand, while a lower price leads to an extension along the same curve. Here, we hold other influences, such as incomes and tastes, unchanged. Price elasticity of demand is a measure of the responsiveness of quantity demanded to a change in price. We will shorten this to P E D. It measures the strength of the response, not just its direction. Two products can both sell less after a price rise, yet experience very different proportional falls in purchases.

0:53Imagine a particular brand of biscuits becomes more expensive. Customers can switch to several similar brands, so purchases might fall sharply. Essential medicine with no close substitute presents a different situation. People may continue buying nearly the same quantity because going without it would have serious consequences. P E D equals the percentage change in quantity demanded divided by the percentage change in price. We use percentages because they compare changes relative to their starting values.

1:19Losing ten sales matters much more to a small shop than to a huge retailer. Percentage change equals change divided by original value, multiplied by one hundred. The formula compares the proportional response with the proportional cause. If purchases change by a larger percentage than price, consumers are relatively responsive. A smaller percentage change in quantity indicates a weaker response. Because price and quantity demanded normally move in opposite directions, the calculated answer is usually negative.

1:47For example, a café raises the price of a drink from ten dollars to twelve. The change in price is plus two dollars. Two dollars divided by the original ten dollars, times one hundred, gives a price rise of twenty per cent. Daily purchases then fall from one hundred cups to sixty, so the change in quantity is minus forty cups per day. Minus forty divided by the original one hundred cups, times one hundred, gives minus forty per cent.

2:12P E D therefore equals minus forty per cent divided by twenty per cent, giving minus two. The minus sign records the opposite movements of price and quantity demanded. To classify responsiveness, we use the size of the answer, ignoring that sign. Its magnitude is two, so quantity responds proportionally twice as strongly as price. This is elastic demand because the magnitude is greater than one. Inelastic demand, by contrast, has a magnitude between zero and one.

2:39Consumers still respond, but quantity changes by a smaller percentage than price. Unitary demand has a magnitude of one, meaning equal percentage changes in opposite directions.

Elasticity diagrams and extremes

2:50Demand diagrams put price on the vertical axis and quantity on the horizontal axis. A relatively flat downward slope can illustrate elastic demand over a particular range. A modest price change then corresponds to a substantial quantity response. However, elasticity compares percentages, so the appearance of a curve alone is not a complete measurement. Inelastic demand is usually drawn with a relatively steep slope. Over that range, a large price change brings only a small change in quantity.

3:18Compare steepness only when the axes use the same scales. Also, a straight downward-sloping demand curve does not have the same elasticity everywhere, even though its slope remains constant. Perfectly inelastic demand has a P E D of zero. Quantity demanded does not change when price changes, so its demand curve is vertical. Buyers purchase the same amount at every price represented. This is an extreme case, rather than a claim that ordinary necessities always have completely unresponsive demand.

3:45At the opposite extreme, perfectly elastic demand has a P E D of infinity. Draw a horizontal demand curve at the given price. A seller charging even slightly more loses all demand because buyers can obtain an identical product elsewhere. This is another idealised extreme, showing exceptionally strong responsiveness rather than ordinary elastic demand. A unitary demand curve bends so that price multiplied by quantity remains constant along it. Its magnitude is one, and total spending stays unchanged as price varies.

4:15Do not draw a straight diagonal line and assume it represents unitary elasticity throughout. The constant spending relationship requires this particular curved shape.

Factors affecting PED

4:25The main influences on whether demand is elastic or inelastic concern consumers’ ability and willingness to change their purchases. The number and closeness of substitutes are especially important. Several very similar alternatives make switching easier. With few acceptable replacements, consumers are more likely to continue buying after a price rise. How widely the product is defined also matters. Demand for one brand of breakfast cereal is likely to be more elastic than demand for food overall.

4:53Other cereals can replace that brand easily. Finding an alternative to food itself is impossible, so the broader category has fewer substitutes outside it. The proportion of income spent influences how carefully consumers react. A small rise in the price of a cheap item may barely affect someone’s budget. For an expensive purchase, though, the same percentage rise can require substantial sacrifices elsewhere. Buyers therefore tend to respond more strongly when the purchase absorbs a large income share.

5:19Necessities usually have less elastic demand than luxuries because postponing essential purchases is harder. Habit and addiction can also reduce responsiveness by making consumption difficult to change. These are tendencies, not automatic classifications. A necessity with several close substitutes can still have elastic demand for a particular brand. Time gives consumers more opportunities to adjust. Immediately after a fuel price rise, many drivers still need their existing journeys. Over a longer period, they might use public transport or choose a more efficient vehicle.

5:50Demand is therefore often more elastic in the long run than in the short run.

PED and total revenue

5:54P E D also connects consumer expenditure and firms’ revenue. Consumer expenditure is the amount buyers spend, while total revenue is the amount sellers receive from sales. For any given sales, the two are opposite sides of one payment. Total revenue equals price multiplied by quantity sold, before any costs are deducted. Return to the café selling its drink for ten dollars, with one hundred cups purchased each day. Original daily revenue equals ten dollars multiplied by one hundred, giving one thousand dollars.

6:22After the increase, twelve dollars multiplied by sixty gives seven hundred and twenty dollars per day. Subtracting one thousand from seven hundred and twenty gives minus two hundred and eighty dollars per day. On the diagram, the original purchase is at point A and the new purchase is at point B. Each revenue rectangle has price as its height and quantity as its width. The new rectangle becomes taller but much narrower.

6:44Its smaller area shows why the higher price reduces both consumer expenditure and the café’s revenue. The blue area is one thousand dollars, while the orange area is only seven hundred and twenty dollars. When demand is price elastic, a price rise lowers total revenue, while a price cut raises it. The quantity response outweighs the change in the amount received per item. With inelastic demand, raising the price increases revenue, while cutting it reduces the total.

7:09At unitary elasticity, total expenditure remains unchanged. For another example, a bakery raises the price of a loaf from four dollars to five. That is a change of plus one dollar. One dollar divided by the original four dollars, times one hundred, gives a price rise of twenty-five per cent. Daily sales fall from two hundred loaves to one hundred and eighty, so quantity changes by minus twenty loaves. Minus twenty divided by the original two hundred, times one hundred, gives minus ten per cent.

7:37P E D therefore equals minus ten per cent divided by twenty-five per cent, which is minus zero point four. Its magnitude of zero point four lies between zero and one, so demand for the loaves is price inelastic. The bakery’s original revenue equals four dollars multiplied by two hundred loaves, giving eight hundred dollars per day. Afterwards, five dollars multiplied by one hundred and eighty gives nine hundred dollars per day.

8:01The increase is nine hundred minus eight hundred, or one hundred dollars per day. Fewer sales do not necessarily mean lower revenue, because each remaining purchase brings in more money.

Uses of PED

8:11For producers and firms, these relationships help guide pricing decisions. A business facing elastic demand might cut its price to increase sales revenue. When demand for its product is inelastic, a price rise is more likely to raise revenue. However, revenue is not profit, because producing and selling additional units involves costs. A revenue increase alone cannot prove that a price cut benefits the firm overall. Consumers can use the same reasoning when planning their budgets.

8:39If an essential purchase has inelastic demand, a higher price increases spending on it. That leaves less income available for other goods and services. Searching for substitutes, or changing habits over time, can make future spending easier to control. Workers also have an interest in their employer’s product demand. If a wage increase raises production costs, a firm might pass those costs on to consumers as higher prices. With elastic demand, sales fall sharply, so the firm may need fewer workers.

9:05A firm facing inelastic demand keeps most of its sales, which puts its workers in a stronger position to win a pay rise. Employment is not automatically lost, because higher productivity or lower profit margins could absorb the wage increase instead. Governments consider elasticity when choosing goods to tax. Taxing a product with inelastic demand can raise substantial revenue because purchases fall relatively little when its price rises. Taxes on demerit goods, such as cigarettes, also aim to discourage consumption.

9:34Because addiction makes demand inelastic, such a tax raises much revenue but cuts consumption only a little. Environmental taxes provide another application, especially where consumption causes pollution. A fuel tax may reduce purchases only slightly at first if drivers lack alternatives. Better public transport can make demand more responsive over time. Governments must also consider households that cannot easily avoid higher costs, rather than judging a tax only by its revenue.

Exam technique and recap

10:01Common calculation mistakes include dividing changes in units instead of percentages, or using the new value as the percentage denominator. Both change what the formula measures. Another error is classifying a value by its sign, so always judge elasticity by the magnitude. Also remember that a price change causes a contraction or extension in demand, not a shift of the curve. In examinations, define asks for a precise meaning, while state asks you to express something in clear terms.

10:29An explain answer sets out why or how an outcome occurs. To analyse, examine the relationships in detail, linking price, quantity and revenue. For discuss, develop both sides in a structured answer and finish with a supported judgement. An exam-style question might ask you to explain why the café’s price rise reduced revenue. P E D was minus two, so demand was price elastic. The forty per cent fall in quantity demanded was twice the twenty per cent rise in price.

10:56The extra money received per cup did not make up for the lost sales. Consequently, total revenue fell from one thousand dollars to seven hundred and twenty dollars per day. A discuss question could ask whether a firm should always cut prices when demand is elastic. A lower price can raise revenue because sales respond strongly. However, the extra output adds to costs, and competitors might cut their prices too, which would hold back the rise in sales.

11:19On balance, a firm should usually cut its price only when the extra revenue exceeds the extra costs, because profit depends on both. P E D measures how strongly quantity demanded responds to price, using percentage changes. Its magnitude separates elastic, inelastic, unitary and the two extreme cases. Substitutes, income share, necessity, habit, time and product definition help explain the response. Connecting that response to price multiplied by quantity reveals the consequences for spending, revenue and economic decisions.