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Chapter 3.e.
Income Elasticity and the Engel Curve
Income Elasticity (of Demand)
 Definition: A measure of the responsiveness of the demand curve to changes in the income of the people
demanding the good
 Equation: (∆X/X) × (∆I/I); often simplified to (∆X/∆I) × (I/X)
 The equation in plain English: the ratio of the percentage change in demand for a good (X) to the
percentage change in income of consumers
Income elasticity is a tool used to figure out consumer purchasing behavior regarding a certain product when
incomes are raised or lowered. This is typically done by drawing a graph with consumer indifference curves at
different levels of utility and budget constraint lines. When we do this and connect all the different points of
tangency between indifference curves and budget constraint lines, we get an Income Expansion Path (I.E.P.) that
represents all the utility-maximizing combinations of the good we are interested in (good X) and money spent on all
other goods (good Y). See the graph below for an example.
Quantity of Y
I.E.P.
47
U=30
29
U=20
15
I100
10
14 17
U=10
I240
I175
Quantity of X
It is important to note that this is a normal good. Most goods behave normally, which means that as a consumer's
income rises, they purchase more of a given good. This graph gives us enough information to create an Engel Curve
for good X.
The Engel Curve
 Definition: Curve plotting Expenditure on Good X (which is the same as the Quantity of X times a constant
price) versus Income
Below we have the Engel Curve for the good X shown in the graph above. Note the points here correspond to the
points on the I.E.P. from the previous graph and the curve has a positive slope, indicative of a normal good. The
price of good X has been set as $1. (Be careful. Textbooks usually put income I on the horizontal axis and
consumption of X on the vertical axis. The diagram below has them in the reverse of the usual positions.)
Income
240
175
100
10
14
17
Expenditure on
Good X
A luxury good is a specific type of normal good and is sometimes classified differently. It is a good that behaves
like a normal good, but as income rises, a higher percentage of total income is spent on the good (it has a high
income elasticity). Examples include jewelry, fashionable clothing, and fine alcohols.
Inferior Goods
 Definition: As income rises, consumers purchase less of an inferior good
Below we have the I.E.P. for an inferior good, along with the standard indifference curves and budget lines.
Quantity of Y
I.E.P.
43
U=30
I310
30
U=20
I230
9
U=10
I100
5
7
10
Quantity of X
Engel Curve for an Inferior Good:
Income
310
230
100
5
7
10
Expenditure on
Good X
Assume a price of $1 for good X. Note the negative slope of the curve, a characteristic of an inferior good.
Examples include used cars, Ramen noodles, and bus fare.