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In this article we will discuss about the reasons for changes in equilibrium choice of consumers.
The Demand Function:
From the model of consumer equilibrium developed, several characteristics of the demand function can be derived. The demand function derived from this model will exhibit an absence of money illusion, and the income, price and cross price effects obtained will be free of sign restrictions. Thus this model can account for inferior as well as non-inferior goods; Giffen as well as normal goods; complements as well as substitutes.
Absence of Money Illusion:
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This can be argued as follows. First, the indifference map which reflects the consumer’s tastes is not affected by changes in the financial parameters. Secondly, an equi-proportionate change in all prices and the consumer’s budget leaves his budget constraint, eqn. [3a], unaffected. Hence we may conclude that since the budget constraint as well as the indifference map is unchanged, the point of tangency will remain the same. Thus the same combination of goods will be purchased by the consumer when all the prices and the consumer’s budget change in the same proportion. This shows an absence of ‘the money illusion’.
The Income Effect – Income Consumption Curves:
If the consumer’s money income or budget changes, the height of the budget line shifts. As result, new points of equilibrium are established on new indifference curves. The line connecting all these points of equilibrium established at different levels of income for given price is called the Income Consumption Curve (ICC). The income consumption curve shows how the consumer’s demand for two goods changes as his money income or budget changes, at given prices. Such a change in the budget is graphically depicted by parallel budget lines, as in Figs. 5.15 and 5.17.
Non-Inferior Goods:
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If the ICC slopes up to the right as in Fig. 5.15, it shows that the demand for both goods rises as the consumer’s money income or budget increases. Hence both goods are non-inferior in this case.
Necessities and Luxuries:
Figure 5.16 shows a further classification of non-inferior goods. On ICC0, which has a constant slope, the demand for both goods rises in the same proportion as the budget increases. Since the entire budget is spent on the two goods, this implies that their demand grows in the same proportion as the budget. Since the budget is equal to the money income, the income elasticity of demand for both the goods is equal to one.
In contrast, on ICCl, the demand for x grows faster than the demand for y, and hence faster than the budget. It follows that the income elasticity of demand for x is larger than one on ICCl. Hence, x is a luxury good. For analogous reasons, x is a necessity if ICCn obtains. Thus ICCs can be used to describe the income effects for luxuries and necessities.
Inferior Goods:
Figure 5.17 illustrates the case of the good x, which turns inferior above the budget level implied by BB. It can be seen that the demand for x does not fall as income rises until BB.
Once the budget constraint crosses the level BB, the demand for x decreases as the budget or money income increases. Hence, x is inferior in this range. When x is inferior, the ICC slopes back to the left.
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Thus, we see that the model of consumer behaviour based on the Ordinal utility theory is versatile and can accommodate all kinds of income effects.
The Price Effect – Price Consumption Curve:
If the price of one good alone changes, while the consumer’s budget and other prices are constant, the slope of the budget line changes. As a result, new points of equilibrium are established on new indifference curves. The line connecting all these points of equilibrium established at different prices of one good, cet. par. is called the Price Consumption Curve (PCC). The price consumption curve gives the consumer’s demand for the two goods as the price of one good alone changes, while his budget and other prices remain constant.
Normal and Giffen Goods:
The PCC can be used to show the own price effect for normal goods as well as for Giffen goods. Thus Fig. 5.18 shows the own price effect for good x, whose demand is normal. We see that as the price of x decreases, the slope of the budget line declines. When this happens, the demand for x increases. Hence the PCCx drawn for changes in price of x slopes to the right. This is true of any normal good. The exceptional case of Giffen goods is illustrated by Fig. 5.19. Here PCCx slopes backward to the left as the price of x decreases. This indicates that when x is cheaper, less of it is demanded.
Thus we see that the own price effects of normal as well as Giffen goods can be described by this model of consumer behaviour.
Decomposition of the Price Effect:
We will conduct our entire discussion in terms of a lower price. A lower price acts on the demand of a good in two ways. It increases the attractiveness of the good per se. It also implies a higher real purchasing power of the money income or budget, which in turn reacts on the demand for the good. These two channels of influence of a lower price on the demand for a good are called the substitution effect and the income effect, respectively.
We can use indifference curves to decompose the price effect into these two components. But before doing so, let us clarify the effect of lower prices on real income or the real worth of the budget.
Consider Fig. 5.20. Here B2 describes a situation where apples are cheaper than in B1. Between these two situations, we find two points of difference. First, at a lower price, the consumer moves to a higher level of satisfaction. If we measure the real worth of income or budget by the satisfaction it fetches, we may say that the real income is higher.
Second, at the lower price, the consumer has a greater access to goods, with the same money income or budget. If we consider the consumer’s command over goods to be his real income, we may say that his real income is higher. Thus the real income of the consumer is higher in two different senses, when the price of apples is lower.
Compensating Variation of Income:
To isolate the substitution effect, i.e. the effects of the changed attractiveness of the good, we must first eliminate the change in the real income arising from a lower price. This can be done by hypothetically removing from the consumer’s budget as much money as will restore him to his old level of real income. This kind of hypothetical change in the consumer’s budget is called a compensating variation of income.
There are two kinds of compensating variations corresponding to the two concepts of real income. These two kinds of variations are called the Slutsky compensating variation and the Hicks’ compensating variation, after the economists who introduced them into analysis.
1. Slutsky’s Compensation:
In the Slutsky compensation, the old purchasing power over goods is restored to the consumer. This is illustrated in Fig. 5.21. Here, the consumer was purchasing the combination x0, y0 before apples became cheaper. At a lower price of apples, the slope of the budget line is smaller (B1→B2), and some other combination of goods is purchased.
We now subtract from the consumer’s budget so that the budget line falls, with its ‘new’ slope intact (B2 → B3). Enough money is removed from the budget so that the consumer is just able to purchase the old combination x0, y0. Hence, after the Slutsky compensation, the budget line passes through x0, y0, but with a lower slope reflecting the lower price of apples.
2. Hicks’ Compensation:
In the Hicks’ compensating variation, the consumer is restored to his old level of satisfaction. This is illustrated in Fig. 5.22. Here, the consumer obtains U1 level of satisfaction at the old price of apples. At a lower price of apples, he moves to some higher level of satisfaction (B1→B2).
By Hicks’ compensation, sufficient money is removed from the consumer’s budget so as to restore him to the old level of satisfaction U1 (B2 →B3). Hence, the budget line, after Hicks compensation, is tangential to the old indifference curve. It does not generally pass through the old combination x0, y0. Thus generally, Hicks and Slutsky compensations are different.
Hicks Vs. Slutsky Compensations:
In general, the Hicks and Slutsky compensations are different. If the compensation is to counteract a lower price, Slutsky’s compensation generally restores the consumer to a higher level of satisfaction. This is shown by Fig. 5.21, where the compensated budget line (B3) cuts the old indifference curve U1. In contrast, the Hicks compensation restores the consumer to the old level of satisfaction. This contrast raises the problem of choosing between the two. Which method of analysis is to be preferred?
In theory, the psychological worth of the budget or money income would seem to be a ‘truer’ measure of real income. Hence Hicks compensation is frequently preferred in theoretical analysis. However, Slutsky compensation is more frequently encountered in empirical situations. For instance, a price indexed wage will make the old combination of goods available to workers at all times. Moreover, the expenditure required for the ‘old’ combination of goods can be calculated, whereas the expenditure required for the old satisfaction cannot. This makes the Slutsky compensation more attractive in empirical work.
Mosak’s Equality:
Mosak proves that the Hicks and Slutsky compensations are virtually the same when the change in price is small. Thus, when minor changes in price are in question, there is no problem of choice. Since in graphical analysis, it is necessary to use large changes in price, we are forced to choose.
The Substitution Effect:
In Fig. 5.23, we carry out the Hicksian compensating variation of income. This reveals that at a lower price the consumer purchases more of the good x, when he is restored to the old indifference curve (x1→ x2). Thus, on the same level of satisfaction, the consumer will always purchase more of a good if it is cheaper. This is called the substitution effect, and there are no exceptions to this rule. The substitution effect is always negative in relation to price change.
Although Fig. 5.23 reveals this, one may still wonder why it should be so. The negative substitution effect results from the conditions of consumer equilibrium. In equilibrium, the price ratio equals the slope of the indifference curve. When apples are cheaper, the price ratio falls, so that the slope of the indifference curve must also be lower at the new point of equilibrium. We know that the slope of the indifference curve decreases as the quantity of apples increases (by DMRS). Hence, more apples are demanded along an indifference curve, when apples are cheaper. The substitution effect is always negative.
The Income Effect:
The compensating variation of income is only a hypothetical cut in the consumer’s budget. Once we restore this amount to the consumer’s budget, his budget increases, so that the income effect comes into play. This is shown in the Figs. 5.24, 5.25, 5.26.
a. Normal Non-Inferior Good:
Figure 5.24 illustrates the usual case of normal, non-inferior goods. Here, the income effect and the substitution effect act in the same direction, so that a larger quantity of apples is purchased at a lower price.
Hence the Conclusion:
If more is demanded by the consumer at a higher income, more will be demanded at a lower price.
Changes in demand due to:
b. Normal Inferior Good:
Figure 5.25 illustrates the case of a normal inferior good. Here, the ICC bends backwards, indicating that apples are inferior over this range. The income effect works at cross purposes with the substitution effect. However, since the good is normal, i.e. non-Giffen, the income effect is too weak to overcome the substitution effect. Hence the net effect of a lower price is that more apples are purchased.
c. Giffen Good:
Figure 5.26 illustrates the abnormal case of an inferior, Giffen good. Here we see that the ICC slopes backwards as price falls since the good is inferior. As in other inferior goods, the income effect and the substitution effects work at cross purposes. However, in the Giffen good, the income effect is stronger than the substitution effect. As a result, fewer apples are demanded at a lower price.
We have graphically decomposed the price effect into its two components- the income effect and substitution effect. This decomposition can also be performed mathematically. The results of this analysis can be shown in the Slutsky equation.
The Slutsky Equation:
Eugene Slutsky first decomposed the price effect into its component parts—the substitution and income effects—through mathematical analysis in 1915. The result of his analysis is called the Slutsky Equation.
We present the Slutsky equation in the following convenient form:
On the right hand side, the first term is the substitution effect. It is always negative.
The second term on the right hand side represents the total impact of the income effect. Its sign is negative when IE is positive, as is the case in non-inferior goods. In these cases, the income effect joins the substitution effect in contributing to a negative price effect.
On the other hand, in inferior goods, the total impact of the income effect is positive because the income effect is negative (minus x minus = plus). Hence in inferior goods the income effect counteracts the negative substitution effect. However if the good is ‘normal’ but inferior, the total impact of the income effect is smaller than the substitution effect, so that the price effect remains negative. This does not happen in Giffen goods.
The Giffen Good:
In light of eqn. [10], we may say that the Giffen good may arise from two conditions:
(a) The good must be strongly inferior. That is, the magnitude of the income effect (IE) should be large enough to overcome the substitution effect.
(b) Large quantities of the good must be purchased. That is, x should be large enough to magnify the impact of inferiority of the good.
The Giffen good is rarely observed in practice. Its first sighting is attributed to Sir Giffen. Sir Giffen observed during the Irish potato famine of the 19th century, that despite high potato prices many poor families increased their consumption of potatoes.
Since then, however, empirical studies of market behaviour have not provided any evidence on Giffen goods. One reason for this extreme rarity of the phenomenon could be that individual consumers, who treat a good as a Giffen good, are outnumbered by consumers who exhibit a normal demand. Hence, the aggregate market demand curve nearly always slopes down to the right.
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