Income Elasticity, Cross Elasticity and What Elasticity Is For

Worked calculation. The price of tea rises by 20 per cent. The quantity of coffee bought rises by 8 per cent. Ec is 8 divided by 20, that is positive 0.4.

What the sign tells you. Here the sign is the whole point and must not be dropped.

The size tells you how close the relationship is. A cross elasticity of 4 between two brands of the same soap means they are near perfect substitutes. A cross elasticity of 0.1 between rail and air travel on a route means they barely compete.

Why competition authorities care. Defining the relevant market is the first step in every abuse of dominance case, and cross elasticity is the standard tool for it. If the cross elasticity between two products is high, they are in the same market and neither producer is dominant; if it is near zero, the market is narrower and a producer may be dominant within it. The Competition Act 2002 requires the Commission to determine the relevant product market, and section 19(7) lists the factors, which include physical characteristics, end use, consumer preferences and price. That is cross elasticity expressed in statutory language, and [Monopoly] returns to it.

The three elasticities compared

Elasticity of supply, in one paragraph

For completeness, because a question sometimes pairs them. Elasticity of supply is the percentage change in quantity supplied divided by the percentage change in price, and it is normally positive because supply curves slope upward. It is treated fully in [Supply and the Law of Supply].

What elasticity is actually for

This section answers the question "of what use is the concept of elasticity", which MU can set on its own. Eight uses, each with the reasoning rather than the assertion.

1. Pricing by a firm. A seller facing inelastic demand raises total revenue by raising the price; a seller facing elastic demand raises total revenue by lowering it. This is the total outlay rule of [Elasticity of Demand] read from the seller's side, and it is why a monopolist never prices in the inelastic range of its demand curve.

2. Taxation. Two separate points. A tax laid for revenue should fall on goods with inelastic demand, because the base survives the tax. And the incidence of any indirect tax, meaning who really bears it, is decided by the relative elasticities of demand and supply: the more inelastic side of the market bears the larger share. A tax on a good with perfectly inelastic demand is paid entirely by the buyer.

3. Price discrimination. A seller who can separate buyers into groups with different elasticities charges more to the group with the more inelastic demand. Railway fares by class, cinema tickets by time of day, and the different prices of the same medicine in different countries are all this. It is lawful in India only within limits; section 4(2)(a) of the Competition Act 2002 treats discriminatory pricing by a dominant enterprise as abuse.

4. Devaluation of a currency and the balance of payments. Devaluation makes exports cheaper abroad and imports dearer at home. It improves the trade balance only if the demands for exports and imports are sufficiently elastic. This is the Marshall Lerner condition, and it is the reason devaluation is not an automatic cure for a deficit. [Correcting a Disequilibrium] works it through with India's own experience.

5. Wage bargaining and the demand for labour. The demand for labour is a derived demand: it depends on the demand for what the labour makes. Where the demand for the product is inelastic and labour is a small part of total cost, a union can win a wage rise without much loss of jobs. Where the product's demand is elastic, the same demand costs jobs. Any argument about a minimum wage is at bottom an argument about these elasticities.

6. Public utility pricing and subsidy. A government supplying water, electricity or transport uses elasticity to decide how much of the cost can be recovered from the user and how much must be subsidised, and to predict how much consumption a tariff change will actually save.

7. Agricultural policy and the paradox of a good harvest. The demand for most foodgrains is inelastic. A bumper harvest therefore lowers the price by proportionately more than it raises the quantity, and the farmers' total revenue falls. A poor harvest can raise it. This is the paradox that makes minimum support prices and procurement necessary rather than merely generous, and [Government Measures to Raise Agricultural Productivity] takes it up.

8. Forecasting and planning. Income elasticity tells a planner which industries will grow fastest as national income rises. Goods with income elasticity above one, such as consumer durables, private transport and air travel, grow faster than the economy; goods with elasticity below one, such as foodgrains, grow more slowly. Every long term projection of demand for power, steel or housing rests on estimated income elasticities.

A worked example: the paradox of the good harvest

The facts. Growers in a district produce 10,000 quintals of onions a year and sell them at 40 rupees a kilogram. Rain is favourable and output rises 25 per cent to 12,500 quintals. The price elasticity of demand for onions is 0.5.

Step 1. Quantity has risen 25 per cent, and the whole crop must be sold. Step 2. With elasticity 0.5, a one per cent fall in price raises quantity demanded by half a per cent. To absorb 25 per cent more onions, the price must fall by 50 per cent. Step 3. The new price is 20 rupees. Step 4, the revenue. Before: 10,000 quintals at 40 rupees a kilogram. After: 12,500 quintals at 20 rupees. Quantity is up by a quarter and price is down by a half, so revenue falls to 62.5 per cent of what it was.

The conclusion. The growers have a larger crop and much smaller earnings. This is not a failure of the market; it is arithmetic, and it follows from inelastic demand. It is the standing economic justification for procurement at a support price, for buffer stocks, and for export permission in a glut year, all of which appear again in [Food Security: What It Means and How India Provides It].

What beginners get wrong

"A negative income elasticity means demand is falling." It means demand falls as income rises. Demand may be rising for other reasons.

"Inferior goods are bad goods." Inferior is a technical label about the response to income, nothing more.

"Cross elasticity is quoted without the sign, like price elasticity." No. In cross elasticity the sign is the answer, because it distinguishes a substitute from a complement.

"Elasticity is a fixed number for a good." It varies with price, with income level, with the period and with the availability of substitutes at the time.

Limits and criticism

Estimates come from the past and assume the relationships hold in future.

They assume other things constant, and in a real economy income, tastes and related prices all move together, which makes disentangling the three elasticities difficult.

Aggregate elasticities hide different households. The income elasticity of demand for milk is very different for a household near the poverty line and for one in the top decile, and a national average describes neither.

Quick revision

1. Income elasticity Ey equals percentage change in quantity divided by percentage change in income. Negative means inferior; zero neutral; between 0 and 1 a necessity; above 1 a luxury.
2. Engel's law: as income rises, the proportion of it spent on food falls, though the absolute amount rises. That is a positive income elasticity below one.
3. Cross elasticity Ec equals percentage change in quantity of X divided by percentage change in the price of Y. Positive means substitutes, negative means complements, near zero means unrelated. The sign is never dropped.
4. Uses: pricing, taxation and incidence, price discrimination, devaluation and the Marshall Lerner condition, wage bargaining, utility pricing, agricultural support, and forecasting.
5. The paradox of the good harvest: with inelastic demand, a larger crop reduces total farm revenue. It is the economic case for procurement and support prices.
6. Competition law uses cross elasticity to define the relevant product market, which is where a dominance inquiry begins.

Test yourself

1. Define income elasticity of demand and state how it classifies goods. It is the ratio of the percentage change in quantity demanded to the percentage change in the consumer's income, other things being equal. A negative value marks an inferior good, of which less is bought as income rises. A value of zero marks a neutral good. A positive value below one marks a necessity, since spending on it rises proportionately less than income. A value above one marks a luxury or superior good.

2. A family's income rises from 30,000 to 36,000 rupees and its purchase of butter rises from 2 kilograms to 3 kilograms a month. Calculate income elasticity and classify the good. Income rises by 6,000 on a base of 30,000, which is 20 per cent. Quantity rises by 1 on a base of 2, which is 50 per cent. Income elasticity is 50 divided by 20, that is 2.5. Since it exceeds one, butter is for this family a luxury or superior good.

3. Define cross elasticity and explain what its sign tells you. Cross elasticity of demand is the ratio of the percentage change in the quantity demanded of one good to the percentage change in the price of a related good. A positive value means the two are substitutes, because a rise in the price of one causes buyers to move to the other. A negative value means they are complements, used together, so a rise in the price of one reduces the quantity of both. A value at or near zero means the goods are unrelated.

4. State Engel's law and say what it implies for a growing economy. Engel's law states that as a household's income rises, the proportion of income spent on food falls, although the absolute amount spent may rise. It implies that as national income grows, the share of agriculture in total consumption expenditure declines and the shares of manufactured goods and services rise, which is one of the mechanisms behind the structural change of an economy from agriculture towards industry and services.

5. Explain four practical uses of elasticity. In pricing, because a firm facing inelastic demand raises revenue by raising price and a firm facing elastic demand by lowering it. In taxation, because a revenue tax should fall on inelastic goods and because the more inelastic side of a market bears more of the burden of an indirect tax. In devaluation, because a devaluation improves the trade balance only if the demands for exports and imports are sufficiently elastic. And in forecasting, because income elasticity indicates which industries will grow faster than national income. Price discrimination, wage bargaining and agricultural support policy are further uses.

6. Why do farmers sometimes earn less from a bigger crop? Because the demand for foodgrains and vegetables is inelastic. A larger crop can be sold only at a much lower price, since a given percentage fall in price increases the quantity demanded by a smaller percentage. If elasticity is 0.5, absorbing a 25 per cent larger crop requires a 50 per cent fall in price, so total revenue falls even though output rose. This is the economic justification for minimum support prices, procurement and buffer stocks.

7. How does cross elasticity help a competition authority? It measures whether two products compete. A high positive cross elasticity shows that buyers switch readily between them, so they belong to the same relevant product market and neither seller can behave independently of the other. A cross elasticity near zero shows that the products do not constrain each other, so the market is narrower and a seller within it may hold a dominant position. Since dominance under the Competition Act 2002 is assessed within a relevant market, and section 19(7) directs attention to characteristics, end use, consumer preferences and price, the statutory test is cross elasticity reasoning in legal form.