Economics, 3rd Edition

The Income Expansion Path Where Cola is an 

Inferior Good

The increase in income has caused the consumer optimum 

to change from point A to point B. The demand for cola has 

fallen but the demand for pizza has risen indicating that 

cola is an inferior good in this example.

Th I

E

i

FIGURE 5.20

Quantity

of cola

Quantity

of pizza

Income expansion path

A

B

BC

2

BC

1

I

1

I

2

The Engel Curve

The income expansion path allows us to see an interesting discovery made by German statistician, Ernst 

Engel (1821–1896). Engel spent some time investigating the relationship between changes in income 

and spending on broad categories of goods such as food. In 1857, Engel proposed a theory referred to 

as Engel’s law. Engel observed that as income rises the proportion of income spent of food decreases, 

whereas the proportion of income devoted to other goods, such as leisure, increases. For example, imagine 

a family of four has a combined annual income of 

€45,000 and spends €15,000 of that income on food. This 

represents a third of the family’s income spent on food. If the combined income then doubled to 

€90,000 

it is unlikely that spending on food will rise to 

€30,000; it might rise to €20,000 and if it did then the propor-

tion spent on food would now be just over 22 per cent. Engel’s findings have been observed and supported 

many times since his discovery and have important implications for government policy and for businesses. 

For example, if incomes are rising, firms selling food will not see their revenues rising in proportion to the 

change in incomes. In economies where per capita income is very low, any increase in incomes may see 

higher proportions initially spent on food but then start to decline as these economies change to become 

emerging economies. Equally, in many countries the poor will spend a higher proportion of their income 

on food than will those on middle and high incomes. Businesses selling other goods such as those in the 

leisure industry may find that as incomes rise expenditure on their goods and services increases.

Note that as incomes increase, families may spend a small proportion of their income on food but 

that does not mean to say that food is not a normal good. At low levels of income, spending on food is 

important – families have to live. As income increases spending on food increases but the rate at which 

it increases starts to fall. The income elasticity of demand for food is likely to become more inelastic as 

income increases. Conversely, the income elasticity of demand for other goods (which we shall call lux-

uries) increases as income increases and at a faster rate – the income elasticity of demand for luxuries 

becomes more elastic as income rises.

The upper graph in Figure 5.21 shows two goods: food on the vertical axis and luxuries on the horizontal 

axis. As income increases, as shown by the three budget constraints BC

1

 to BC

3

, the change in consumer 

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CHAPTER 5  BACKGROUND TO DEMAND: THE THEORY OF CONSUMER CHOICE  125

optimum is shown by the three points A, B and C. As income increases, the demand for food and luxuries 

both increase – both are normal goods. However, the amount of food demanded is increasing at a dimin-

ishing rate whereas the increase in the demand for luxuries is greater as income increases. The implication, 

therefore, is that the demand for food is income inelastic whereas the demand for luxuries is income elastic.

The relationship between income and the demand for luxuries is plotted on the lower graph in 

Figure 5.21 showing how the demand for luxuries increases as income increases. The line joining points 

A, B and C is the