Question

3. Show what happens to consumption demand after a fall in permanent income. You should both the indifference curve graph and the consumption demand graph.

4. Isolate graphically the income affect of a decline in real interest rates.

Answer 1

3. Show what happens to consumption demand after a fall in permanent income. You should both the indifference curve graph and the consumption demand graph.

In this section we are going to study income effect. In other words, understand how the optimal consumption combination changes as a result of change in consumer's income. Prices of goods X (P_X) and Y (P_Y)remaining unchanged.

An income effect represents change in consumer’s optimal consumption combination on account of change in her/his income and thereby changes in her/his quantity purchased, prices of goods X (P_X) and Y (P_Y)remaining unchanged. The consumer is better-off when optimal consumption combination is located on a higher indifference curve and vice versa.

Understand that like price effect, a consumer's responses to income changes also differ depending upon the nature of the good, viz. a normal good, inferior good or a neutral good. These are summarized in chart.1:

CHART.1 TYPE OF INCOME EFFECTS

Thus, an income effect is positive in case of normal goods. There is direct relationship between income and quantity demanded. It is negative in case of inferior goods (including Giffen goods) where we find inverse relationship between income and quantity demanded. Finally, income effect is zero in case of neutral goods where consumer's quantity demanded is fixed.

Positive, negative and zero price effects are discussed with the help of indifference curves in the following subsections.

Positive Income Effect

In this section we are going to study how the optimal consumption combination changes as a result of change in consumer's income. Goods X and Y are normal goods. Prices of goods X (P_X)and Y (P_Y) remaining unchanged. Figure.1 starts with the initial optimal consumption combination attained at point e at which OX units of good X and OY units of good Y are purchased.

Figure.1: Positive Income Effect

Whenever income of the consumer change, the entire budget constraint shifts outwards or inwards. With decrease in income the entire budget constraint shifts inwards and it is a parallel shift. Similarly, when income increases then entire budget constraint shifts outwards and it is a parallel shift. This is shown by budget constraint P₂L₂ in Figure.1.

When consumer's income decreases, the budget constraint moves inwards. This is shown by budget constraint P₁L₁ in Figure.1. The optimal consumption is located at point e₁ at which the consumer buys OX₁ units of good X and OY₁ units of good Y . Consumer’s total utility decreases as the optimal consumption combination is located on a lower indifference curve U₁.

Similarly, when consumer's income increases, the budget constraint moves outwards. This is shown by budget constraint P₂L₂. The optimal consumption is now located at point e₂, at which the consumer buys OX₂ units of good X and OY₂ units of good Y. Consumer’s total utility increases as the optimal consumption combination is now located on a higher indifference curve U₂.

Chart.2 presents a summary of Figure.1.

CHART.2 Positive Income Effect: Sum Up

The curve obtained by joining optimal consumption combinations such as e₁, e and e₂ is called the income consumption curve (ICC). The ICC in Figure.1 is rising upwards to the right. It shows that the consumer successively moves on a higher indifference curve and becomes better off, with increase in her/his income and she/he also increases consumption of of goods X and Y. Here income effect is positive for goods X and Y.

Negative Income Effect

We now study negative income effect. Good X is an inferior good and good Y is a normal good. You will now understand how consumer's optimal consumption combination changes as a result of change in her/his income. Prices of goods X (P_X)and Y (P_Y)remaining unchanged. Figure.2 starts with the initial optimal consumption combination attained at point e at which OX units of good X and OY units of good Y are purchased.

Figure.2: Negative Income Effect

When income of the consumer increases, then entire budget constraint shifts outwards and it is a parallel shift. This is shown by budget constraint P₁L₁. The optimal consumption is now located at point e₁, at which the consumer now buys OX₁ units of good X and OY₁ units of good Y.

Understand that consumer’s total utility has increased as the optimal consumption point is now located on a higher indifference curve. The consumer is better-off in terms of total utility. However, she/he reduces consumption of good X to OX₁ units as good X is an inferior good. As mentioned in chart.1 we observe inverse relationship between income and quantity demanded of good X.The consumer increases quantity demanded of good Y as good Y is a normal good. Here income effect is negative for good X.

Chart.3 presents a summary of Figure.2.

CHART.3 Negative Income Effect: Sum Up

The ICC obtained by joining optimal consumption combinations such as e, and e₁, in Figure.2 rises upwards but bending backwards. It shows that the consumer successively moves on a higher indifference curve and becomes better off, with increase in her/his income. however, she/he also reduces purchase of good X as it is an inferior good.

Zero Income Effect

We now study zero income effect. Good X is a neutral good and good Y is a normal good. You can now see how consumer's optimal consumption combination changes as a result of change in her/his income. Prices of goods X P_X)and Y (P_Y) remaining unchanged. Figure.3 starts with the initial optimal consumption combination attained at point e at which OX units of good X and OY units of good Y are purchased.

Figure.3: Zero Income Effect

When consumer's income increases, then entire budget constraint shifts outwards and it is a parallel shift. This is shown by budget constraint P₁L₁. The optimal consumption is now located at point e₁, at which the consumer now buys same OX units of good X and OY₁ units of good Y.

Understand that consumer’s total utility has increased as the optimal consumption point is now located on a higher indifference curve U₁. The consumer is better-off in terms of total utility. However, she/he keeps consumption of good X fixed at OX units as good X is a neutral good. As mentioned in chart.1 we observe no change in quantity demanded of good X.The consumer increases quantity demanded of good Y as good Y is a normal good. Here income effect is zero for good X.

Chart.4 presents a summary of Figure.3.

CHART.4 Zero Income Effect: Sum Up

The ICC obtained by joining optimal consumption combinations such as e, and e₁, in Figure.3 is a vertical straight line. It shows that the consumer successively moves on a higher indifference curve and becomes better off, with increase in her/his income. However, she/he is keeping purchase of good X fixed as it is a neutral good. The consumer increases quantity demanded of good Y as it is a normal good.

Forms of Income Consumption Curve

In the above discussion on positive, negative and zero income effects we have considered good X to be normal good, inferior good and neutral good respectively. Similarly, we can explain income effect for different types of good Y. Figure.4 shows different forms of ICC for different natures of good X or good Y.

Figure.4: Forms of Income Consumption Curve

ICC₁ is rising upwards and bending towards Y-axis. This form of ICC is obtained when good X is an inferior good (including Giffen goods). The ICC is a vertical straight line as shown by ICC₂when good X is a neutral good. It is a rising curve from left to right as shown by ICC₃ when goods X and Y are normal goods.The ICC is a horizontal straight line as shown by ICC₄ when good Y is a neutral good. Finally, ICC₅ is rising upwards bending towards X-axis. This form of ICC is obtained when good Y is an inferior good (including Giffen goods). Chart.5 presents a summary of Figure.4.

CHART.5 Forms of Income Consumption Curve: Sum Up

4. Isolate graphically the income affect of a decline in real interest rates.

It is a well-known proposition of consumption theory that a ra­tional consumer reaches equilibrium when he chooses the bundle of goods that maximises his satisfaction. He will continue to consume the goods in the proportions indicated by the point of tangency between the budget line and an indifference curve until something changes. The price-consumption line shows increasing (declining) qualities of a commodity, such as bread being bought as its price falls (rises).

The effect of a change in the price of one of the purchasable commodities can be bro­ken down into a substi­tution effect and an income effect. In Fig. 11 we show our consumer, Ram, faced with a budget line AB. He is in equilibrium at point 1 where he consumes q, of bread. Now, let the price of bread (commodity x) fall, while money in­come and the price of eggs (commodity y) re­main the same. Ram’s new budget line is now AC and his new equilibrium is at point 3 on indifference curve h, where bread is purchased.

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We may now breakdown the effect of a change in the price of bread on the quantity demanded into what J.R. Hicks called the substitution effect and income effect. The substitution effect shows the change in the consump­tion of x which occurs when its price and hence the relative prices of x and y change. When there is a change in relative price the consumer tends to substitute x (which is now relatively cheap) for y (which is now relatively expensive), although there is no change in (the absolute price of y^α).

The income effect shows the changes in quantity demanded of x resulting from the change in real income that occurs when the price of x changes (falls) while money income is held constant (by ceteris paribus assumption). A study of demand theory reveals that income changes affect demand. Now, we have to show explicitly the effect of real income changes when prices change while money income is constant, as well as when money income changes, with relatively prices held constant.

The Price Effect (or the total effect of price change):

Since price effect is the sum total of substitution effect and income effect, we can measure the size of the substitution effect by eliminating income effect. For isolating the price-substitution effect of a fall in the price of x we have to hold Ram’s real income constant and see what he would do if just relative prices changed.

The Substitution Effect:

It was Sir John Hicks who first isolated the pure substitution effect of the price change in the following manner. Following Hicks, we hold the con­sumer’s real income constant, and see what he would do if just relative prices changed. If the consumer’s real income remains unchanged he will stay on the old indifference curve h, and continue to enjoy the same level of satisfaction or utility as before the change in relative price.

However, he will not maximise satisfaction at point 1, because there has occurred a change in relative price. The relative price is no longer given by the slope of the line AB, but by the slope of the line AC. So, to find out the best combination of eggs and bread we try to find where on his indifference curve Ii he will settle. The answer is that, he will select the point on the curve where the new relative price of bread in terms of eggs is equal to MRS.

This occurs where the indifference curve is tangent to the line representing the ratio: the price of bread – the price of eggs. To find this line we construct the line A’ C’, parallel to AC, and also tangent to h. Since A’ C’ and AC are parallel, they have the same slope; and since the point of tangency of A’ C with I₁ is the consumer’s equilibrium point, he will surely maximise satis­faction (or reach the point of maximum welfare) at point 2.

This shows that his equilibrium purchase of bread is q₂, if the price of bread falls and consumer’s real gain is eliminated. His real income gain is eliminated by a parallel shifting of the budget line AC to the left to A’ C in such a fashion that it is tangent to the old indifference curve h.

This implies that the consumer is just enable to enjoy the same (old) level of satisfaction at the new set is q₁q₂. This is the substitution effect of a change in the price of bread. In short, substitution effect measures the change in the consumption of bread that occurs when the consumer moves along the same indifference curve due to a fall in the market price of bread.

The Income Effect:

Since we have a clear idea of the total effect of the price change, we can easily determine the size of the income effect. Recall that the price effect is the sum of the income and substitution effects. Since we have already measured the substitution effect we can now deduce the size of the income effect imme­diately as q₃-q₂ bread.

It is just the difference between the total income in quantity q₃-q₂minus the substitution effect of q₂-q₁ bread. However, it is both important and interesting, at least from the conceptual point of view, to understand how the income effect is (formally) derived. Simply put, the (pure) income effect of a price change is the extent to which a change in real income affects the quantity demanded of bread, with relative price held constant.

While isolating the substitution effect we held real income constant by confining the consumer to his old (original) indifference curve, I₁. Now, in order to identify and measure the income effect we remove this restriction and allow the consumer to reach a higher indifference curve (l₂). In other words, we shift the budget line A’ C’ back to the position AC.

This enables the consumer to reach the higher indifference curve I₂ and enjoy a higher level of satisfaction or utility at point 3. So, point 3 is his new equilibrium point after the restoration of the income effect. In fact, we eliminated the income effect by shifting the budget line AC to the left to A’ C. Now, that we have been able to measure the size of the substitution effect, we follow an exactly opposite procedure. We shift the budget line back to the position AC.

Since we are now only interested in the income effect of the price change, we have to observe the behaviour of the consumer when we allow his income to rise, with no change occurring in relative price.

In order to isolate income effect we have just to observe the difference in the consumer’s consumption of bread when the price of bread is held constant, but his real income is allowed to rise as much as it would from the fall of price (of bread). To do this we have to hold the market prices of the two goods constant and raise his real income.

Differently put, all we have to do is to compare his consumption of bread at point 3 with that at point 2, because the relative price of bread is the same at both points. Only his real income has increased so as to enable him to move from I₁ to I₂.

From Fig. 11 we observe that our consumer increases his consumption of bread from q₂ to q₃ when the price of bread is held constant but his real income rises. Thus q₃-q₂ measures the income effect of the price change. In short, the income effect measures the change in the consumption of bread that occurs when the consumer moves to a higher indifference curve (representing the change in real income).

Price Effects with Inferior and Giffen Goods:

In dividing the price effect into two parts we assumed that bread was a normal and not an inferior good.

Normal goods, it may be recalled, are those for which the quantity demanded by a consumer rises when income rises and falls when income fall. In case of normal goods both the income effect and substitution effect move in the same direction. From Fig. 11 we see that bread being a normal good, the fall in its price led the consumer to buy more of it as a result of consumer’s real income gain. The substitution effect also led to an increase in consumption of bread.

In the case of inferior goods the two effects of price change actually work in opposite directions. The substitution effect is always negative. It is because holding the real income constant; the consumer will always tend to substitute a good whose price has fallen for one whose price remains the same. But, income effect is positive in case of normal goods and negative in case of inferior goods.

In case of normal goods the income effect reinforces the substitution effect. But, in case of an inferior good, income effect operates in the opposite direction to the substitution effect. If the price of an inferior good falls the substitution effect will still cause a larger commodity. This is because the fall in price raises the real income of the consumer. This, for an inferior good, means that les§ will be purchased, when price falls.

Economic theory cannot tell us whether the income effect or substitution effect will predominate. It is a matter of empirical research. However, we can consider the following two possibilities.

Case 1: Inferior Goods: The Substitution Effect Exceeding the Income Effect:

In Fig. 12 we show that the substitution effect is stronger than the income effect. Here apple is a normal good and jackfruit is an inferior good. The consumer’s equilibrium is at point 1. He buys q₁ units of jackfruit. The price of jackfruit now falls. This is indicated by the shift of the budget line from AB to AC. Now, the substitution effect shifts the consumer from point 1 to 2.

As a result of this there is an increase in the quantity bought of q₂-q₁. However, as a result of income effect, equilibrium moves from point 2 to point 3. Because jackfruit is as­sumed to be an inferior good, there is a fall in the quantity demanded of (q₂-q₁), due to in­come effect alone. The net effect (or full price effect) is an in­crease in quantity of jackfruit bought of q₃-q₁. This is made up of an increase in q₂-q₁ (sub­stitution effect) and a decrease of q₂-q₃ (income effect). The substitution effect is greater (stronger) than the income ef­fect.

  Case 2: Giffen Goods: The Income Effect Exceeding the Substitution Effect:

Fig. 13 illustrates the case of a special variety of inferior good, known as Giffen good, in which case the income effect is stronger than the substitution effect. In Fig. 13, the original equilibrium is at point 1 with quantity q₁ consumed. Now, the fall in price of the Giffen good shifts the budget line from A B to AC as usual.

The substitution effect is also the same as before q₂-q₁. The consumer buys more of the Giffen good due to substitution effect. But, income effect in this case is q₂-q₃, which is so large that it outweighs the income effect. So, the net effect of a fall in the price of a Giffen good is a fall in the quantity demanded.

Fig. 12 and 13 show price effect for inferior goods. The income effect is negative in both the diagrams. This follows from the very definition of an inferior good: an inferior good is one the quantity demanded of which falls when income rises.

In each case, the substitution effect serves to increase the quantity demanded as price falls and is partly offset by the negative in­come effect. The net effect of price change depends on the relative strengths of the two ef­fects. In Fig. 13 the negative in­come effect is less strong than the substitution effect. So the quantity demanded of an infe­rior good increases when its price falls, though not as much as for a normal good.

Thus, there is a net income in the quantity bought of an inferior good when its price falls. This produces a negatively sloped demand curve. But it is stepper (more inelastic) than that in case of a normal good, in which case the price effect is much strong (since its two components reinforce each other or go in the same direction).

In Fig. 13, the negative income effect is stronger than the substitution effect. Thus, the quantity bought of the commodity falls (rises) when its price falls (rises). This happens in case of a Giffen good. In this case, the demand curve will be positively sloped.