The income elasticity of demand is the percent change in the quantity of a good demanded when a consumer’s income changes divided by the percent change in the consumer’s income.

In the days of the Founding Fathers, the great majority of Americans lived on farms. As recently as the 1940s, one American in six—or approximately 17%—still did. But in the most recent U.S. Department of Agriculture census taken in 2012, the number of American farmers was estimated to be around 0.67% of the total population. Why do so few people now live and work on farms in the United States? There are two main reasons, both involving elasticities.

First, the income elasticity of demand for food is much less than 1—it is income-inelastic. As consumers grow richer, other things equal, spending on food rises less than income. As a result, as the U.S. economy has grown, the share of income it spends on food—and therefore the share of total U.S. income earned by farmers—has fallen.

Second, the demand for food is price-inelastic. This is important because technological advances in American agriculture have steadily raised yields over time and led to a long-term trend of lower U.S. food prices for most of the past century and a half. The combination of price inelasticity and falling prices led to falling total revenue for farmers. That’s right: progress in farming has been good for American consumers but bad for American farmers.

The combination of these effects explains the long-term relative decline of farming in the United States. The low income elasticity of demand for food ensures that the income of farmers grows more slowly than the economy as a whole. And the combination of rapid technological progress in farming with price-inelastic demand for foodstuffs reinforces this effect, further reducing the growth of farm income.

That is, up until now. Starting in the mid-2000s, increased demand for foodstuffs from rapidly growing developing countries like China has pushed up the prices of agricultural products around the world. And American farmers have benefited, with U.S. farm income rising nearly 90% from 2009 to 2013. Eventually, as the growth in developing countries tapers off and agricultural innovation continues to progress, it’s likely that the agricultural sector will resume its downward trend. But for now and for the foreseeable future, American farmers are enjoying the sector’s revival.

The demand for a good is income-elastic if the income elasticity of demand for that good is greater than 1.

The demand for a good is income-inelastic if the income elasticity of demand for that good is positive but less than 1.

If the income elasticity of demand for food is less than 1, we would expect to find that people in poor countries spend a larger share of their income on food than people in rich countries. And that’s exactly what the data show. In this graph, we compare per capita income—a country’s total income, divided by the population—with the share of income that is spent on food. (To make the graph a manageable size, per capita income is measured as a percentage of U.S. per capita income.)

In very poor countries, like Pakistan, people spend a large percent of their income on food. In middle-income countries, like Israel and Mexico, the share of spending that goes to food is much lower. And it’s even lower in rich countries like the United States.

Source: U.S. Department of Agriculture and IMF World Economic Outlook.

The U.S. Bureau of Labor Statistics carries out extensive surveys of how families spend their incomes. This is not just a matter of intellectual curiosity. Quite a few government benefit programs involve some adjustment for changes in the cost of living; to estimate those changes, the government must know how people spend their money. But an additional payoff to these surveys is data on the income elasticity of demand for various goods.

What stands out from these studies? The classic result is that the income elasticity of demand for “food eaten at home” is considerably less than 1: as a family’s income rises, the share of its income spent on food consumed at home falls. Correspondingly, the lower a family’s income, the higher the share of income spent on food consumed at home.

In poor countries, many families spend more than half their income on food consumed at home. Although the income elasticity of demand for “food eaten at home” is estimated at less than 0.5 in the United States, the income elasticity of demand for “food eaten away from home” (restaurant meals) is estimated to be much higher—close to 1.

Families with higher incomes eat out more often and at fancier places. In 1950, about 19% of U.S. income was spent on food consumed at home, a number that has dropped to 6.1% in 2012. But over the same time period, the share of U.S. income spent on food consumed away from home has stayed constant at 5%. In fact, a sure sign of rising income levels in developing countries is the arrival of fast-food restaurants that cater to newly affluent customers. For example, McDonald’s can now be found in Hanoi, Jakarta, and Mumbai.

There is one clear example of an inferior good found in the surveys: rental housing. Families with higher income actually spend less on rent than families with lower income, because they are much more likely to own their own homes. And the category identified as “other housing”—which basically means second homes—is highly income-elastic. Only higher-income families can afford a luxury like a vacation home, so “other housing” has an income elasticity of demand greater than 1.

Solutions appear at back of book.