Although a consumer’s demand curve for any good x is likely to be downward sloping we cannot be certain of this because of the presence of the income effect of a price change. Whenever a price changes, that change will affect the demand for the good in two ways:

• The price of this good, relative to others, has changed. This induces a substitution effect. The change in relative prices will lead to a re-allocation of spending between goods. Fewer of the good which has become relatively more expensive will be purchased and more of the good which has become relatively less expensive will be bought. The substitution effect will always be negative: a change in the price of a good will lead to a change in the opposite direction in the quantity demanded of it

• A price change (with a fixed level of money income) will change the consumer’s real income (the purchasing power of the money income). As the consumer’s real income is changed, there will be a change in the amount of this good (and others) purchased. However, the direction of this change is uncertain, for the reasons we explained in Chapter 2. If the good in question is a normal good, higher real income will increase the quantity demanded. Conversely, if the good is an inferior good, higher real income will decrease the quantity demanded.

The demand curve for a good describes the overall relationship between price and quantity demanded, and so incorporates both the substitution effect and the real income effect of a price change.

We can obtain a graphical representation of the decomposition of a price change into substitution and income effects in the following way. First, the substitution effect of the price change is identified. The income effect is then obtained as the difference between the total effect and the substitution effect of the price change.

The substitution effect can be identified by asking how much demand for the good would change if

1. its price changes, and

2. the consumer is compensated for a price increase (or financially penalised for a price fall) by just the amount required to prevent the consumer from gaining more utility than he or she had prior to the price change.

Refer to Figure 3.11 which illustrates the reasoning.. Suppose the consumer initially allocates his or her money income of m by purchasing y₁ units of good y (at the price P_y1 ) and x₁ units of good x (at the price P_x1). This is a utility maximising expenditure pattern obtains utility level U₁ . We next suppose that the price of good x falls, with money income and the price of good y remaining constant. This causes the individual’s budget constraint to rotate anti-clockwise. The consumer now switches expenditure to the allocation shown by point b, at which utility is maximised at the higher level, U₂.

The consumption of x increases from x₁ to x₃. This is the total effect of the price change. Let us now conduct the following hypothetical experiment. Starting from the new (post price change) budget constraint, we take away from the consumer the maximum amount of income that is just compatible with him or her being able to get the original utility level U₁ at the new set of prices. This results in the consumer’s budget constraint moving to the line de. With this budget constraint (and at the new set of prices, P_y1 and P_x2 ), the highest level of utility level attainable is U₁, its original level. This is achieved by purchasing x₃ units of x and y₃ units of y.

This has removed the income effect of the price change. Any change in the demand for good x can, therefore, be attributed to the substitution effect alone. For good x, the substitution effect (SE) of the price fall consists of the change from x₁ to x₃. The income effect (IE) of the price change consists of the change in quantity from x₃ to x₂. To see why this is so, note that if we were to begin at the point c and, without changing relative prices, return to the consumer the money income previously taken away, the individual would move from c to b, thereby raising consumption of x from x₃ to x₂.

The following can be said by way of conclusion.

Total effect of a price change = substitution effect + income effect

(x₁ to x₂) (x₁ to x₃) (x₃ to x₂)

The case we investigated in Figure 3.11 was one in which the two component parts of the overall effect work in the same direction, so reinforcing one another. It can be deduced from this that x is a normal good, as an increase in real income has resulted in an increase in the quantity demanded of the good.

But as some goods are inferior, there are other possibilities. These are illustrated in Figures 3.12 and 3.13. In these two cases, x is an inferior good, and so the income effect of a price change works in the reverse direction to the substitution effect, thereby reducing the size of the overall effect. Figure 3.12 shows the case where the income effect only partially offsets the substitution effect. Overall, a price fall of good x results in a greater quantity being demanded, even though the size of the overall change has been reduced by the income effect.

Figure 3.13 illustrates a theoretically plausible, but very unlikely, situation. The extent of the income effect is so great that it not only reduces the overall effect, it actually reverses it. Here, a fall in the price of good x results in a fall in the quantity demanded of that good. The demand curve has a positive slope!

Empirical evidence shows that there are few, if any, Giffen goods in practice. Theory also suggests the probability of Giffen goods is extremely small. Most goods are normal goods. But even where a good is inferior, the income effect is likely to be small in magnitude in comparison with the substitution effect. Unless a very large proportion of income is spent on one good, the income effect will be small for moderate sized price changes. Only in very exceptional circumstances would an income effect dominate the substitution effect in the way required for Giffen goods.