E XERCISES FOR C HAPTER 5
7. Firms, investors and capital markets 8. Producer choice
6.4 Applications of indifference analysis
Adjusting to price changes
Next, consider the impact of a price change from the initial equilibrium E0in Figure6.10. Suppose that jazz now costs more. This reduces the purchasing power of the given budget of $200. The new jazz intercept is therefore reduced. The budget constraint becomes steeper and rotates around the snowboard intercept H, which is unchanged because its price is constant. The new equilibrium is at E2, which reflects a lower level of satisfaction because the affordable set has been reduced by the price increase. As explained in Section6.2, E0and E2define points on the demand curve for jazz (J0and J2): They reflect the consumer response to a change in the price of jazz with all other things held constant. In contrast, the price increase for jazz shifts the demand curve for snowboarding:
As far as the demand curve for snowboarding is concerned, a change in the price of jazz is one of those things other than own-price that determine its position.
Philanthropy
Individuals in the foregoing analysis aim to maximize their utility, given that they have a fixed budget. Note that this behavioural assumption does not rule out the possibility that these same individuals may be philanthropic – that is, they get utility from the act of giving to their favourite charity or the United Way or Centre-aide. To see this suppose that donations give utility to the individual in question – she gets a ‘warm glow’ feeling as a result of giving, which is to say she gets utility from the activity. There is no reason why we cannot put charitable donations on one axis and some other good or combination of goods on the remaining axis. At equilibrium, the marginal utility per dollar of contributions to charity should equal the marginal utility per dollar of expenditure on other goods; or, stated in terms of ordinal utility, the marginal rate of substitution between philanthropy and any other good should equal the ratio of their prices. Evidently the price of a dollar of charitable donations is one dollar.
6.4. Applications of indifference analysis 143
Income impacts: Normal and inferior goods
We know from Chapter 4 that the quantity demanded of a normal good increases in response to an income increase, whereas the quantity demanded of an inferior good declines. Clearly, both jazz and boarding are normal goods, as illustrated in Figure 6.10, because more of each one is demanded in response to the income increase from I0to I1. It would challenge the imagination to think that either of these goods might be inferior. But if J were to denote junky (inferior) goods and S super goods, we could envisage an equilibrium E1 to the northwest of E0in response to an income increase, along the constraint I1; less J and more S would be consumed in response to the income increase.
Policy: Income transfers and price subsidies
Government policies that improve the purchasing power of low-income households come in two main forms: Pure income transfers and price subsidies. Social Assistance payments (“welfare”) or Employment Insurance benefits, for example, provide an increase in income to the needy. Sub-sidies, on the other hand, enable individuals to purchase particular goods or services at a lower price—for example, rent or daycare subsidies.
In contrast to taxes, which reduce the purchasing power of the consumer, subsidies and income transfers increase purchasing power. The impact of an income transfer, compared with a pure price subsidy, can be analyzed using Figures6.11and6.12.
Figure 6.11: Income transfer
I1 I2
U1
U2
Other goods
Daycare
E1
E2
An increase in income due to a government transfer shifts the budget con-straint from I1to I2. This parallel shift increases the quantity consumed of the target good (daycare) and other goods, unless one is inferior.
In Figure 6.11, an income transfer increases income from I1 to I2. The new equilibrium at E2 reflects an increase in utility, and an increase in the consumption of both daycare and other goods.
Suppose now that a government program administrator decides that, while helping this individual to purchase more daycare accords with the intent of the transfer, she does not intend that govern-ment money should be used to purchase other goods. She therefore decides that a daycare subsidy program might better meet this objective than a pure income transfer.
A daycare subsidy reduces the price of daycare and therefore rotates the budget constraint out-wards around the intercept on the vertical axis. At the equilibrium in Figure 6.12, purchases of other goods change very little, and therefore most of the additional purchasing power is allocated to daycare.
Figure 6.12: Price subsidy
I2
I1
U1
U2
Other goods
Daycare
E1
E2
A subsidy to the targeted good, by reducing its price, rotates the budget constraint from I1to I2. This induces the consumer to direct expenditure more towards daycare and less towards other goods than an income transfer that does not change the relative prices.
Let us take the example one stage further. From the initial equilibrium E1 in Figure6.12, suppose that, instead of a subsidy that took the individual to E2, we gave an income transfer that enabled the consumer to purchase the combination E2. Such a transfer is represented in Figure 6.13 by a parallel outward shift of the budget constraint from I1 to I1′, going through the point E2. We now have a subsidy policy and an alternative income transfer policy, each permitting the same consumption bundle (E2). The interesting aspect of this pair of possibilities is that the income transfer will enable the consumer to attain a higher level of satisfaction—for example, at point E′—and will also induce her to consume more of the good on the vertical axis. The higher level of satisfaction comes about because the consumer has more latitude in allocating the additional real
6.4. Applications of indifference analysis 145
income.
Application Box 6.3: Daycare subsidies in Quebec
The Quebec provincial government subsidizes daycare very heavily. In the network of day-cares that are part of the government-sponsored “Centres de la petite enfance”, lower- and middle-income households can place their children in daycare for about $10 per day. This policy is designed to enable households to limit the share of their income expended on day-care (though higher-income households are also heavily subsidized). This policy is described accurately in Figure6.13.
The consequences of strong subsidization are not negligible: Excess demand, to such an extent that children are frequently placed on waiting lists for daycare places long before their parents intend to use the service. Annual subsidy costs amount to almost $2 billion per year.
At the same time, it has been estimated that the policy has enabled many more parents to enter the workforce than otherwise would have.
Figure 6.13: Subsidy-transfer comparison
I1′
I2
I1
U1
U2U3
Other goods
Daycare
E1
E2
E′
A price subsidy to the targeted good induces the individual to move from E1to E2, facing a budget constraint I2. An income transfer that permits him to consume E2is given by I1′; but it also permits him to attain a higher level of satisfaction, denoted by E′on the indifference curve U3.
The price of giving
Imagine now that the good on the horizontal axis is charitable donations, rather than daycare, and the government decides that for every dollar given the individual will see a reduction in their income tax of 50 cents. This is equivalent to cutting the ‘price’ of donations in half, because a donation of one dollar now costs the individual half of that amount. Graphically the budget constraint rotates outward with the vertical intercept unchanged. Since donations now cost less the individual has increased spending power as a result of the price reduction for donations. The price reduction is designed to increase the attractiveness of donations to the utility maximizing consumer.
Key Terms 147
K EY T ERMS
Cardinal utility is a measurable concept of satisfaction.
Total utility is a measure of the total satisfaction derived from consuming a given amount of goods and services.
Marginal utility is the addition to total utility created when one more unit of a good or service is consumed.
Diminishing marginal utility implies that the addition to total utility from each extra unit of a good or service consumed is declining.
Consumer equilibrium occurs when marginal utility per dollar spent on the last unit of each good is equal.
Law of demand states that, other things being equal, more of a good is demanded the lower is its price.
Ordinal utility assumes that individuals can rank commodity bundles in accordance with the level of satisfaction associated with each bundle.
Budget constraint defines all bundles of goods that the consumer can afford with a given budget.
Affordable set of goods and services for the consumer is bounded by the budget line from above; the non-affordable set lies strictly above the budget line.
Indifference curve defines combinations of goods and services that yield the same level of satisfaction to the consumer.
Indifference map is a set of indifference curves, where curves further from the origin denote a higher level of satisfaction.
Marginal rate of substitution is the slope of the indifference curve. It defines the amount of one good the consumer is willing to sacrifice in order to obtain a given increment of the other, while maintaining utility unchanged.
Diminishing marginal rate of substitution reflects a higher marginal value being associated with smaller quantities of any good consumed.
Consumer optimum occurs where the chosen consumption bundle is a point such that the price ratio equals the marginal rate of substitution.