Income–consumption curve

Figure 2: Income-consumption curve for normal goods

In the figure 2 to the left, B1, B2 and B3 are the different budget lines and I¹, I² and I³ are the indifference curves that are available to the consumer. As shown earlier, as the income of the consumer rises, the budget line moves outwards parallel to itself. In this case, from initial bundle X^*, with an increase in the income of the consumer the budget line moves from B1 to B2 and the consumer would choose X^' bundle and subsequently, with a further rise in consumer's income the budget line moves from B2 to B3 and the consumer would choose X^" bundle and so on. The consumer would thus maximize his utility at the points X^*, X^' and X^", and by joining these points, the income-consumption curve can be obtained.

Figure 3: with an increase of income, demand for normal good X² rises while, demand for inferior good X¹ falls.

The figure on the right (figure 3), shows the consumption patterns of the consumer of two goods X¹ and X², the prices of which are p₁ and p₂ respectively, where B1 and B2 are the budget lines and I¹ and I² are the indifference curves. Figure 3 clearly shows that, with a rise in the income of the consumer, the initial budget line B1 moves outward parallel to itself to B2 and the consumer now chooses X^' bundle to the initial bundle X^*. The figure shows that, the demand for X² has risen from X²₁ to X²₂ with an outward shift of the budget line from B1 to B2 (caused due to rise in the income of the consumer). This essentially means that, good X² is a normal good as the demand for X² rose with an increase in the income of the consumer.

In contrast, it is to be noted from the figure, that the demand for X¹ has fallen from X¹₁ to X¹₂ with an outward shift of the budget line from B1 to B2 (caused due to rise in the income of the consumer). This implies that, good X¹ is an inferior good as the demand for X¹ fell with an increase in the income of the consumer.

The consumer maximizes his utility at points X^* and X^' and by joining these points, the income–consumption curve can be obtained.[2] In figure 3, the income–consumption curve bends back on itself as with an increase income, the consumer demands more of X² and less of X¹.[3] The income–consumption curve in this case is negatively sloped and the income elasticity of demand will be negative.[4] Also the price effect for X² is positive, while it is negative for X¹.[3]

${\displaystyle \Delta X_{n}^{1}}$ is the change in the demand for good 1 when we change income from ${\displaystyle m'}$ to ${\displaystyle m}$, holding the price of good 1 fixed at ${\displaystyle p_{1}}$:

${\displaystyle \Delta X_{n}^{1}=X^{1}(p_{1},m)-X^{1}(p_{1},m').}$