Elasticity of Demand

Ed = 1.5. Demand for these mangoes is elastic: a one per cent fall in price brings a one and a half per cent rise in quantity.

The five degrees of elasticity

An examiner asks for these by name, with the numerical value and the shape of the curve.

The two extreme cases are limiting cases used for teaching. Real goods lie between them, and most everyday goods sit somewhere between 0.2 and 3.

The four methods of measuring elasticity

MU can ask for these, and a complete answer names all four.

1. The percentage or proportionate method. The formula above. It is the standard method and the one to use unless a question specifies otherwise.

2. The total outlay or total expenditure method. Marshall's own method, and the most useful one to remember because it needs no arithmetic. Total outlay is price multiplied by quantity, which is also the seller's total revenue. Compare total outlay before and after the price change.

When price RISES the table reverses: outlay falling means elastic demand, outlay rising means inelastic demand.

Check it against the mango example. Before: 50 multiplied by 1,000 is 50,000 rupees. After: 40 multiplied by 1,300 is 52,000 rupees. Price fell and outlay rose, so demand is elastic. This agrees with the Ed of 1.5 calculated above, which is the point of running both methods on the same numbers.

3. The point method, also called the geometrical method. Elasticity at a single point on a straight line demand curve is measured by dividing the lower segment of the curve, below the point, by the upper segment, above the point. It follows that on a single straight line demand curve, elasticity is different at every point: greater than one on the upper half, exactly one at the midpoint, and less than one on the lower half. That is worth stating in an answer because it destroys the common belief that a straight demand curve has one elasticity.

4. The arc method. Between two points that are far apart, the percentage method gives a different answer depending on which point you start from. The arc method removes the ambiguity by using the averages of the two prices and the two quantities as the base:

Ed = (change in Q divided by the sum of the two quantities) divided by (change in P divided by the sum of the two prices), the factors of two cancelling.

Worked on the mangoes. Change in quantity 300, sum of quantities 2,300. Change in price 10, sum of prices 90. So 300/2300 is 0.1304 and 10/90 is 0.1111, giving Ed of 1.17. Note that this differs from the 1.5 found by the percentage method, and neither is wrong: the percentage method measures at a point and the arc method over a range.

What determines whether a good is elastic

Six determinants. An examiner asks for them and each carries an example.

1. The availability of close substitutes. The most important single determinant. The more and the closer the substitutes, the more elastic the demand, because buyers can switch. Demand for one brand of tea is elastic; demand for tea in general is much less so; demand for salt, which has no substitute, is nearly inelastic.

2. The nature of the good. Necessities have inelastic demand, because they must be bought whatever the price. Comforts are moderately elastic and luxuries are highly elastic.

3. The share of income spent on it. A good taking a tiny share of the budget, such as matchboxes or newspapers, has inelastic demand, because a doubling of its price is barely noticed. A good taking a large share, such as housing or a vehicle, has elastic demand.

4. The number of uses. A good with many uses, such as electricity or steel, has more elastic demand, because as its price falls it is put to further uses and as its price rises the least important uses are given up first.

5. Time. Demand is more elastic the longer the period allowed. A rise in the price of diesel changes little in a month and a great deal in five years, once vehicles and routes have been changed. Always add this if a question asks for determinants, because it is the one most often left out.

6. Habit and postponability. Goods of addiction or habit, such as tobacco, have inelastic demand. A purchase that can be postponed, such as repainting a house, has elastic demand.

A seventh point sometimes asked for is the existence of complementary goods: petrol's demand is tied to the stock of vehicles, which does not change quickly, and that ties down its elasticity in the short run.

A worked example: the tax that collects and the tax that reforms

The situation. The State of Maharashtra is considering two new levies of equal size: one on cigarettes and one on restaurant meals in a city where there are many restaurants.

Cigarettes. Demand is inelastic: habit, no close substitute, and a small share of most budgets. Suppose Ed is 0.4. A twenty per cent rise in price reduces quantity by eight per cent. The State collects a great deal of revenue and does relatively little to reduce smoking in the short run.

Restaurant meals. Demand is elastic: many substitutes including eating at home, the expenditure is postponable, and it takes a noticeable share of income. Suppose Ed is 2. A twenty per cent rise in price reduces quantity by forty per cent. The State collects much less than it hoped and the restaurants bear a large part of the burden through lost trade.

The two lessons a student should draw.

1. A revenue tax should be laid on inelastic goods; a discouraging tax works on elastic ones. Governments tax petrol, liquor and tobacco heavily for exactly this reason, and the fact that these are also goods policy wishes to discourage is a happy coincidence rather than the main motive.
2. Who actually bears a tax depends on elasticity. The more inelastic the demand relative to supply, the more of the tax the buyer pays; the more elastic the demand, the more the seller absorbs. This is called the incidence of a tax and it is taken up again in [The Sources of Public Revenue].

What beginners get wrong

"A steep curve is inelastic and a flat one elastic, always." Only when the two curves are drawn on the same axes and the same scale. Elasticity is not the slope; it is the slope multiplied by the ratio of price to quantity, which is why elasticity changes along a straight line.

"Elasticity is a property of the good." It is a property of the good at a price, in a market, over a period. Petrol is inelastic in a week and much more elastic over a decade.

"An elastic good is one people buy a lot of." No. It is one whose quantity responds sharply to price.

"Elasticity is negative, so the answer is minus 1.5." The ratio is negative and the convention is to quote the absolute value. Say once that the sign is dropped.

Limits and criticism

It assumes everything else is held constant, and inherits every assumption of the law of demand.

It is measured after the event. Elasticities are estimated from past data and can change when tastes, technology or the range of substitutes changes.

It varies along the curve, so a single number describes a range only approximately, which is why the arc method exists.

It says nothing about why. Two goods with the same elasticity can behave quite differently when a substitute appears.

Quick revision

1. Price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price. Introduced by Marshall, 1890. The sign is negative and by convention the absolute value is quoted.
2. Five degrees: perfectly elastic (infinity, horizontal), relatively elastic (greater than 1), unitary (equal to 1, rectangular hyperbola), relatively inelastic (less than 1), perfectly inelastic (zero, vertical).
3. Four methods: percentage, total outlay, point (lower segment divided by upper segment), and arc (using the sums of prices and quantities as the base).
4. Total outlay rule: when price falls, outlay rising means elastic, unchanged means unitary, falling means inelastic. Reverse it for a price rise.
5. Six determinants: substitutes, nature of the good, share of income, number of uses, time, and habit or postponability.
6. On a straight line demand curve elasticity is greater than one on the upper half, one at the midpoint and less than one on the lower half.
7. Tax rule: revenue is raised on inelastic goods, behaviour is changed on elastic ones, and the more inelastic the demand the more of the tax the buyer bears.

Test yourself

1. Define price elasticity of demand and give the formula. It is the degree of responsiveness of the quantity demanded of a commodity to a change in its price. Ed equals the percentage change in quantity demanded divided by the percentage change in price, which can be written as the change in quantity divided by the change in price, multiplied by the original price divided by the original quantity. The ratio is negative and is conventionally quoted as a positive figure.

2. At 20 rupees, 400 units are sold; at 16 rupees, 500 units are sold. Calculate elasticity by the percentage method and by the total outlay method. By the percentage method: quantity rises by 100 on a base of 400, which is 25 per cent; price falls by 4 on a base of 20, which is 20 per cent; elasticity is 25 divided by 20, that is 1.25, so demand is elastic. By the total outlay method: outlay was 20 multiplied by 400, that is 8,000, and becomes 16 multiplied by 500, that is 8,000. Outlay is unchanged, which indicates unitary elasticity. The two answers differ because the percentage method measures at the starting point while total outlay compares two positions across a wide range, and this is precisely why the arc method exists.

3. Name and explain the five degrees of elasticity with the numerical value of each. Perfectly elastic, elasticity infinite, where any rise in price reduces demand to nothing and the curve is horizontal. Relatively elastic, elasticity greater than one, where quantity changes proportionately more than price. Unitary elastic, elasticity exactly one, where the two change in the same proportion and total outlay is constant. Relatively inelastic, elasticity between zero and one, where quantity changes proportionately less than price. Perfectly inelastic, elasticity zero, where quantity is unaffected by price and the curve is vertical.

4. State six determinants of elasticity of demand. The availability and closeness of substitutes; whether the good is a necessity, a comfort or a luxury; the proportion of income spent on it; the number of uses to which it can be put; the period of time allowed for adjustment; and habit or the extent to which the purchase can be postponed.

5. "Elasticity is the same as the slope of the demand curve." Is this correct? No. Slope is the ratio of the change in price to the change in quantity in absolute units, while elasticity is a ratio of percentage changes and therefore depends on the point at which it is measured as well as on the slope. On a straight line demand curve the slope is constant but elasticity falls continuously from infinity at the price axis to zero at the quantity axis, passing through unity at the midpoint. Comparison of steepness is only reliable when two curves are drawn on the same axes and scale.

6. A government wishes to raise revenue from a new indirect tax. Which goods should it choose, and why? Goods with inelastic demand, such as fuel, tobacco and liquor, because a rise in price reduces quantity only slightly, so the tax base survives and collections rise. A tax on elastic goods produces a large fall in quantity and disappointing revenue, and it falls heavily on the seller through lost sales. The same reasoning in reverse explains why a tax intended to discourage consumption rather than to collect revenue works better on goods with elastic demand.

7. Explain the total outlay method and apply it: a shopkeeper raises the price of an umbrella and finds his takings from umbrellas have fallen. The total outlay method compares the buyer's total spending, which is the seller's revenue, before and after the price change. When the price rises, a fall in total outlay indicates elastic demand, an unchanged outlay indicates unitary elasticity, and a rise in outlay indicates inelastic demand. Here the price rose and takings fell, so the demand for umbrellas at that shop is elastic, which is what one would expect where buyers can go to another shop or postpone the purchase.