INCOME AND SUBSTITUTION EFFECT OF A WAGE CHANGE 2012 CHAPTER: 1 1.1 INTRODUCTION One of the best-documented regularities in economics is that- when it affect all member of a household proportionately large, permanent differences in the real wage induce a most modest differences in the quantity of labor supplied by a household. This is tru across households, across countries, and across time. The standard explanation is that the substitution and income effects of a permanently higher real wage are of approximately the same size; that is, the motivation to give up leisure to take advantage of a higher real wage is roughly cancelled out by the extra freedom to pursue leisure afforded by the higher income that the higher real wage provides. This explanation has broad support among economists because it has the merit of accounting for a wide range of data with one restriction on the utility function. Among those economists who agree with the view that the income and substitution effects of a permanent increase in the real wage are approximately equal, there is much less agreement 1
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INCOME AND SUBSTITUTION EFFECT OF A WAGE CHANGE 2012
CHAPTER: 1
1.1 INTRODUCTION
One of the best-documented regularities in economics is that-when it affect all member of a
household proportionately large, permanent differences in the real wage induce a most modest
differences in the quantity of labor supplied by a household. This is tru across households, across
countries, and across time. The standard explanation is that the substitution and income effects of
a permanently higher real wage are of approximately the same size; that is, the motivation to give
up leisure to take advantage of a higher real wage is roughly cancelled out by the extra freedom to
pursue leisure afforded by the higher income that the higher real wage provides. This explanation
has broad support among economists because it has the merit of accounting for a wide range of
data with one restriction on the utility function. Among those economists who agree with the view
that the income and substitution effects of a permanent increase in the real wage are
approximately equal, there is much less agreement about whether the income and substitution
effects are both large or both small. The size of the substitution effect is closely related to the
elasticity of labor supply with respect to fluctuations in the real wage that are too short-lived to
have substantial income effects. The size of the substitution effect is also a key factor in the
magnitude of distortions induced by labor-income taxation and by other government policies that
affect the margin between consumption and leisure or consumption and work. Hence, having a
good estimate of the elasticity of labor supply has very broad and significant implications for
understanding economic fluctuations and for assessing the effects of changes in public policy.1
1 ADVANCED ECONOMIC THEORY- Microeconomic Analysis, Dr. H.L. AHUJA
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INCOME AND SUBSTITUTION EFFECT OF A WAGE CHANGE 2012
Drawing with a broad brush, one can paint the picture that macroeconomists, trying to explain
substantial cyclical movements in labor hours in the face of modest cyclical movements in the
real wage, see evidence that the substitution effect is large. Labor economists, looking at
regressions of labor hours on fluctuations in the real wage or regressions of labor hours on the
variation in the real wage over the life cycle, see evidence that the substitution effect is small.
Direct evidence on the size of the substitution effect is muddied by several difficulties with the
evidence.
1) It is hard to find temporary, exogenous movements in the real wage that could identify
movements in labor supply;
2) Fluctuations in the shadow wage within a long-term relationship between firms and workers can
look quite different from fluctuations in the observed wage in standard data series; and
3) Many workers may face constraints on their labor hours imposed by their employers, so that they
are not able to respond freely to variations in the real wage. These issues affect the evidence
contemplated both in the macroeconomics and labor economics literatures.
In this paper we propose an alternative to directly inferring the substitution effect from the
relationship between wages and labor supply. The equality of income and substitution effects
implies that one can infer the size of the substitution effect from the size of the income effect.
Thus, we estimate the income effect and use that estimate, together with restrictions from a theory
of labor supply, to infer the substitution effect. We estimate the size of the income effect using a
module designed by us in the Health and Retirement Study (HRS) which asks respondents to
imagine what they would do if they won a sweepstakes that would pay them an amount equal to
last year's family income every year as long as they live. We analyze this data using a structural
model of household labor supply that imposes the restriction that income and substitution effects
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cancel. The model is based on the dynamic optimization problem of the household. It has several
other features needed to capture important features of behavior. First, it allows for
nonseparabilities between consumption and labor. These can account for a drop in observed
consumption at retirement because working increases the marginal utility of consumption.
Second, it integrates the decisions of married partners about consumption and labor supply.
Finally, to match the observed fact that few people work less than 20 hours per week, our
structural model allows for fixed utility costs of going to work. This final feature is very
important for the analysis of the labor supply response to the sweepstakes because many
households report that they would quit work entirely rather than smoothly reducing hours.2
2 ibid
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INCOME AND SUBSTITUTION EFFECT OF A WAGE CHANGE 2012
CHAPTER: 2
2.1 INCOME AND SUBSTITUTION EFFECTS
Although the idea of utility is, we believe, a helpful way of thinking about the choice process,
there is an explanation for downward-sloping demand curves that does not rely on the concept of
utility or the assumption of diminishing marginal utility. This explanation centers on income and
substitution effects. Keeping in mind that consumers face constrained choices, consider the
probable response of a household to a decline in the price of some heavily used product, ceteris
paribus. How might a household currently consuming many goods be likely to respond to a fall in
the price of one of those goods if its income, its preferences, and all other prices remained
unchanged? The household would face a new budget constraint, and its final choice of all goods
and services might change. A decline in the price of gasoline, for example, may affect not only
how much gasoline you purchase but also what kind of car you buy, when and how much you
travel, where you go.
2.1.1 The Income Effect
Price changes affect households in two ways. First, if we assume that households confine their
choices to products that improve their well-being, then a decline in the price of any product,
ceteris paribus, makes the household unequivocally better off. In other words, if a household
continues to buy the exact same amount of every good and service after the price decrease, it will
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have income left over. That extra income may be spent on the product whose price has declined,
hereafter called good X, or on other products. The change in consumption of X due to this
improvement in well-being is called the income effect of a price change.
Suppose that I live in Guwahati and that four times a year I fly to Jorhat to visit my mother.
Suppose further that last year a round-trip ticket to Jorhat cost Rs 400. Thus, I spend a total of Rs
1,600 per year on trips to visit Mom. This year, however, increased competition among the Buses
has led one bus to offer round-trip tickets to Jorhat for Rs 200. Assuming that the price remains at
Rs 200 all year, I can now travel home exactly the same number of times, and I will have spent Rs
800 less for bus tickets than I did last year. Now that I am better off, I have additional
opportunities. I could fly home a fifth time this year, leaving Rs 600 (Rs 800 – Rs 200) to spend
on other things, or I could fly home the same number of times (four) and spend all the extra Rs
800 on other things. Therefore;
“When the price of something we buy falls, we are better off. When the price of something we
buy rises, we are worse off.”3
2.1.2 The Substitution Effect
The fact that a price decline leaves households better off is only part of the story. When the
price of a product falls, that product also becomes relatively cheaper. That is, it becomes more
attractive relative to potential substitutes. A fall in the price of product X might cause a household
3 ADVANCED ECONOMIC THEORY- Microeconomic Analysis, Dr. H.L. AHUJA
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INCOME AND SUBSTITUTION EFFECT OF A WAGE CHANGE 2012
to shift its purchasing pattern away from substitutes toward X. This shift is called the substitution
effect of a price change.
Earlier, we made the point that the "real" cost or price of a good is what one must sacrifice to
consume it. This opportunity cost is determined by relative prices.
To see why this is so, consider again the choice that I face when a round-trip ticket to Jorhat
costs Rs 400. Each trip that I take requires a sacrifice of Rs 400 worth of other goods and
services. When the price drops to Rs 200, the opportunity cost of a ticket has dropped by Rs 200.
In other words, after the price decline, I have to sacrifice only Rs 200 (instead of Rs 400) worth of
other goods and services to visit Mom.
To clarify the distinction between the income and substitution effects in your mind, imagine
how I would be affected if two things happened to me at the same time. First, the price of round-
trip air travel between Guwahati and Jorhat drops from Rs 400 to Rs 200. Second, my income is
reduced by Rs800. I am now faced with new relative prices, but—assuming I flew home four
times last year—I am no better off now than I was before the price of a ticket declined. The
decrease in the price of air travel has exactly offset my decrease in income.
I am still likely to take more trips home because the opportunity cost of a trip home is now
lower, ceteris paribus—that is, assuming no change in the prices of other goods and services. A
trip to Jorhat now requires a sacrifice of only Rs 200 worth of other goods and services, not the
Rs 400 worth that it did before. Thus, I will substitute away from other goods toward trips to see
my mother.
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Everything works in the opposite direction when a price rises, ceteris paribus. A price increase
makes households worse off. If income and other prices do not change, spending the same amount
of money buys less, and households will be forced to buy less. This is the income effect. In
addition, when the price of a product rises, that item becomes more expensive relative to potential
substitutes, and the household is likely to substitute other goods for it. This is the substitution
effect.
What do the income and substitution effects tell us about the demand curve?
Both the income and substitution effects imply a negative relationship between price and
quantity demanded—in other words, downward-sloping demand. When the price of something
falls, ceteris paribus, we are better off, and we are likely to buy more of that good and other
goods (income effect). Because lower price also means "less expensive relative to substitutes," we
are likely to buy more of the good (substitution effect). When the price of something rises, we are
worse off, and we will buy less of it (income effect). Higher price also means "more expensive
relative to substitutes," and we are likely to buy less of it and more of other goods (substitution
effect).4
4 ibid
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Figure 1 summarizes the income and substitution effects of a price change.
Figure 1 Income and Substitution Effects of a Price Change
For normal goods, the income and substitution effects work in the same direction. Higher prices
lead to a lower quantity demanded, and lower prices lead to a higher quantity demanded.
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CHAPTER: 3
3.1 CONSUMER SURPLUS
The argument, made several times already, that the market forces us to reveal a great deal about
our personal preferences is an extremely important one, and it bears repeating at least once more
here. If you are free to choose within the constraints imposed by prices and your income, and you
decide to buy (say) a hamburger for $2.50, you have "revealed" that a hamburger is worth at least
$2.50 to you.
A simple market demand curve such as the one in Figure 5.8(a) illustrates this point quite
clearly. At the current market price of $2.50, consumers will purchase 7 million hamburgers per
month. There is only one price in the market, and the demand curve tells us how many
hamburgers households would buy if they could purchase all they wanted at the posted price of
$2.50. Anyone who values a hamburger at $2.50 or more will buy it. Anyone who does not value
it that highly will not.
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Figure
5.8
Market Demand, Revealed Preference, and Consumer
Surplus
The difference between the maximum amount that a person is willing to pay for a good
and its current market price is the person's consumer surplus. The total consumer
surplus suggested by the data in Figure 5.8(a) is represented by the shaded area in
Figure 5.8(b)
Some people, however, value hamburgers at more than $2.50. As Figure 5.8(a) shows, even if
the price were $5.00, consumers would still buy 1 million hamburgers. If these people were able
to buy the good at a price of $2.50, they would earn a consumer surplus. Consumer surplus is the
difference between the maximum amount a person is willing to pay for a good and its current
market price. The consumer surplus earned by the people willing to pay $5.00 for a hamburger is
approximately equal to the shaded area between point A and the price, $2.50.
The second million hamburgers in Figure 5.8(a) are valued at more than the market price as
well, although the consumer surplus gained is slightly less. Point B on the market demand curve
shows the maximum amount that consumers would be willing to pay for the second million
hamburgers. The consumer surplus earned by these people is equal to the shaded area between B
and the price, $2.50. Similarly, for the third million hamburgers, maximum willingness to pay is
given by point C; consumer surplus is a bit lower than it is at points A and B, but it is still
significant.
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The total value of the consumer surplus suggested by the data in Figure 5.8(a) is roughly equal
to the area of the shaded triangle in Figure 5.8(b). To understand why this is so, think about
offering hamburgers to consumers at successively lower prices. If the good were actually sold for
$2.50, those near point A on the demand curve would get a large surplus; those at point B would
get a smaller surplus. Those at point E would get none.
The idea of consumer surplus helps to explain an old paradox that dates back to Plato. Adam
Smith wrote about it in 1776:
The things which have the greatest value in use have frequently little or no value in exchange;
and on the contrary, those which have the greatest value in exchange have frequently little or no
value in use. Nothing is more useful than water: but it will purchase scarce any thing; scarce
anything can be had in exchange for it. A diamond, on the contrary, has scarce any value in use;
but a very great quantity of other goods may frequently be had in exchange for it.
Although diamonds have arguably more than "scarce any value in use" today (e.g., they are
used to cut glass), Smith's diamond/water paradox is still instructive, at least where water is
concerned.
The low price of water owes much to the fact that it is in plentiful supply. Even at a price of
zero we do not consume an infinite amount of water. We consume up to the point where marginal
utility drops to zero. The marginal value of water is zero. Each of us enjoys an enormous
consumer surplus when we consume nearly free water. At a price of zero, consumer surplus is the
entire area under the demand curve. We tend to take water for granted, but imagine what would
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happen to its price if there were simply not enough for everyone. It would command a high price
indeed.
Consumer surplus measurement is a key element in cost-benefit analysis, the formal technique
by which the benefits of a public project are weighed against its costs. To decide whether to build
a new electrical power plant, we need to know the value, to consumers, of the electricity that it
will produce. Just as the value of water to consumers is not just its price times the quantity that
people consume, the value of electricity generated is not just the price of electricity times the
quantity the new plant will produce. The total value that should be weighed against the costs of
the plant includes the consumer surplus that electricity users will enjoy if the plant is built.
3.2 HOUSEHOLD CHOISE IN INPUT MARKETS
So far, we have focused on the decision-making process that lies behind output demand curves.
Households with limited incomes allocate those incomes across various combinations of goods
and services that are available and affordable. In looking at the factors affecting choices in the
output market, we assumed that income was fixed, or given. We noted at the outset, however, that
income is in fact partially determined by choices that households make in input markets (look
back at Figure 5.1). We now turn to a brief discussion of the two decisions households make in
input markets: the labor supply decision and the saving decision.
3.3 THE LABOUR SUPPLY DECISION
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INCOME AND SUBSTITUTION EFFECT OF A WAGE CHANGE 2012
Most income in the United States is wage and salary income paid in compensation for labor.
Household members supply labor in exchange for wages or salaries. As in output markets,
households face constrained choices in input markets. They must decide:
1. Whether to work
2. How much to work
3. What kind of a job to work at
In essence, household members must decide how much labor to supply. The choices they make
are affected by:
1. Availability of jobs
2. Market wage rates
3. Skills they possess
As with decisions in output markets, the labor supply decision involves a set of trade-offs. There
are basically two alternatives to working for a wage:
(a) not working, and
(b) unpaid work.
If I do not work, I sacrifice income for the benefits of staying at home and reading, watching
TV, swimming, or sleeping. Another option is to work, but not for a money wage. In this case, I
sacrifice money income for the benefits of growing my own food, bringing up my children, or
taking care of my house.
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As with the trade-offs in output markets, my final choice depends on how I value the
alternatives available. If I work, I earn a wage that I can use to buy things. Thus, the trade-off is
between the value of the goods and services I can buy with the wages I earn versus the value of
things I can produce at home—home-grown food, manageable children, clean clothes, and so on
—or the value I place on leisure. This choice is illustrated in Figure 5.9. In general, then: The
wage rate can be thought of as the price—or the opportunity cost—of the benefits of either unpaid
work or leisure.
Figure 5.9 The Trade-Off Facing Households
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The decision to enter the workforce involves a trade-off between wages (and the goods and
services that wages will buy) on the one hand, and leisure and the value of nonmarket production
on the other.
CHAPTER: 4
4.1 THE PRICE OF LEISURE
In our analysis in the early part of this chapter, households had to allocate a limited budget
across a set of goods and services. Now they must choose among goods, services, and leisure.
When we add leisure to the picture, we do so with one important distinction. Trading off one
good for another involves buying less of one and more of another, so households simply
reallocate money from one good to the other. "Buying" more leisure, however, means reallocating
time between work and nonwork activities. For each hour of leisure that I decide to consume, I
give up one hour's wages. Thus the wage rate is the price of leisure.
Conditions in the labor market determine the budget constraints and final opportunity sets that
face households. The availability of jobs and these job wage rates determine the final
combinations of goods and services that a household can afford. The final choice within these
constraints depends on the unique tastes and preferences of each household. Different people
place more or less value on leisure—but everyone needs to put food on the table.
4.2 INCOME AND SUBSTITUTION EFFECTS OF A WAGE CHANGE
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A labor supply curve shows the quantity of labor supplied at different wage rates. The shape of
the labor supply curve depends on how households react to changes in the wage rate.
Consider an increase in wages. First, an increase in wages makes households better off. If they
work the same number of hours—that is, if they supply the same amount of labor—they will earn
higher incomes and be able to buy more goods and services. They can also buy more leisure. If
leisure is a normal good—that is, a good for which demand increases as income increases, an
increase in income will lead to a higher demand for leisure and a lower labor supply. This is the
income effect of a wage increase.
However, there is also a potential substitution effect of a wage increase. A higher wage rate
means that leisure is more expensive. If you think of the wage rate as the price of leisure, each
individual hour of leisure consumed at a higher wage costs more in forgone wages. As a result,
we would expect households to substitute other goods for leisure. This means working more, or a
lower quantity demanded of leisure and a higher quantity supplied of labor.
Note that in the labor market the income and substitution effects work in opposite directions
when leisure is a normal good. The income effect of a wage increase implies buying more leisure
and working less; the substitution effect implies buying less leisure and working more. Whether
households will supply more labor overall or less labor overall when wages rise depends on the
relative strength of both the income and the substitution effects.
If the substitution effect is greater than the income effect, the wage increase will increase labor
supply. This suggests that the labor supply curve slopes upward, or has a positive slope, like the
one in Figure 5.10(a). If the income effect outweighs the substitution effect, however, a higher
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wage will lead to added consumption of leisure, and labor supply will decrease. This implies that
the labor supply curve "bends back," as the one in Figure 5.10(b) does.
Figure 5.10 Two Labor Supply Curves
Here, in this figure, when the substitution effect outweighs the income effect, the labor supply
curve slopes upward (a). When the income effect outweighs the substitution effect, the result is a