Question

Sudi spends his income on two goods. His income elasticity of demand for the first good is ~1 = 0.2, while his income elasticity of demand for the second good is ~ 1 = 2. Illustrate in one diagram how a 10% increase in his income would affect the quantity he demands of the two goods that shows an incomeconsumption curve, and create another diagram for each of the two goods that shows an Engel curve. How do the slopes of the Engel curves compare?

Answer 1

Let the 2 goods be X1and X2. His income elasticity for good 1(n1) = 0.2 while his income elasticity for good 2 (n2) = 2. Let the initial level of income be M, and the initial consumption be (x1,x2).

There is a 10% increase in income. SO the new income is 1.1M. At this new income, the consumption of good 1 and good2 is 1.02x1 and 1.20x2 respectively.

or,

or,

where dM/M gives the percentage change in income and dx1/x1 gives the percentage change in consumption of good 2. So, due to a 10% change in income, the consumption of x1 increases by 2%.

Similarly, for x2,

So, due to a 10% change in income, the consumption of x2 increases by 20%.

Income consumption curve (ICC) is defined as the locus of equilibrium combinations of good 1 and good2 when the income of the consumer changes, other things remaining constant. The shape of ICC depends on the income elasticity of demand, that is, how the consumption of the good changes in response to a change in income. Based on the given information, the ICC curve is shown in figure (1).

Here, as income increases from M to 1.1M, both consumption of good 1 and good 2 increases as income elasticity of both the goods are positive.

Engel curve(EC) of a good shows the locus of combinations of equilibrium consumption of the good at different income level. The Engel curve for each good 1 and good 2 are shown in figure (2) and figure (3). Note that the slope of EC_x2 is much higher than EC_x1 due to higher elasticity of demand.