Chapter 6

Question 1

How to calculate Delta(little Triangle)

Answer 1

How to calculate Delta(little Triangle)

(X final- X initial)/x Initial

*100

Question 2

Hours of work

Short run :

Long Run:

Answer 2

Hours of work

Short-run: the employers( demand) have the most power on hours of work

Long-run: employee preferences(supply) has more influence on long run

Question 3

A theory of the decision to work

Demand for a good is a function of three Factors:

1. t
   
   • the Opportunity cost of an hour of leisure is equal to …

Total income indicator of

Answer 3

A theory of the decision to work

Demand for a good is a function of three Factors:

1. The opportunity cost of the good:
   
   • the Opportunity cost of an hour of leisure is equal to your wage rate( the extra earning a worker can take home form extra hour of work)
2. One’s level of wealth
3. One’s set of preferences

Total income indicator of total wealth

Question 4

Income effect

• • Based on the simple notion that
• the income effect is … because

Answer 4

Income effect

• If income increases while wages and preferences are held constant, number of leisure hours demanded will rise and desired hours of work will go down. and vise versa
• Based on the simple notion that as income rise people want to consume more leisure
• the income effect is negative because the sign of the fraction in equation (6.1) is negative.If income goes up , hours of work fall. If income goes down, hours of work increase. The numerator ( H) and denominator (Y ) in equation move in opposite directions, giving a negative sign to the income effect.

Question 5

Substitution effect

• • substitution effect occurs because
• the substitution effect is

Answer 5

Substitution effect

• if income is held constant, an increase in the wage rate will raise the price and reduce the demand for leisure, thereby increasing work incentives.
• substitution effect occurs because as the cost of leisure changes, income held constant, leisure and work hours are substituted for each other.
• the substitution effect is positive, Because the numerator (H) and denominator (W) always move in the same direction, at least in theory, the substitution effect has a positive sign.

Question 6

Observing Income and Substitution Effects Separately

Usually, both effects are

Example, Receiving inheritance: Substitution or Income?

Answer 6

Substitution Effects Separately

Usually, both effects are simultaneously present, often working against each other.

Example, Receiving inheritance: Substitution or Income?

The bequest enhances wealth (income) independent of the hours of work. Thus, income is increased without a change in the compensation received from an hour of work. In this case, the income effect induces the person to consume more leisure, thereby reducing the willingness to work.

Question 7

Both Effects Occur When Wages Rise

Consider the case of a person who receives a wage increase

The labor supply response to a simple wage increase will involve both an …. The income effect is the result … after the increase. For a given level of work effort, he or she now has a …. The substitution effect results from the fact that …. Because the actual labor supply response …, we … in advance; theory simply does not tell us which effect is stronger. If the income effect is stronger, the person will respond…. This decrease will be smaller than if the same change in wealth were due …, because the … However, as seen in Example 6.2, when the income effect dominates, …. It is entirely plausible, of course, that the substitution effect will dominate. If so, the actual response to wage increases …. Should the substitution effect dominate, the person’s labor supply curve— relating, say, his or her desired hours of work to wages—will be …. That is, l… will increase with the wage rate. If, on the other hand, the income effect dominates, the person’s labor supply curve ….. Economic theory cannot say which …, and in fact, individual labor supply curves could be p…

Answer 7

Both Effects Occur When Wages Rise

The labor supply response to a simple wage increase will involve both an income effect and a substitution effect. The income effect is the result of the worker’s enhanced wealth (or potential income) after the increase. For a given level of work effort, he or she now has a greater command over resources than before (because more income is received for any given number of hours of work). The substitution effect results from the fact that the wage increase raises the opportunity costs of leisure. Because the actual labor supply response is the sum of the income and substitution effects, we cannot predict the response in advance; theory simply does not tell us which effect is stronger. If the income effect is stronger, the person will respond to a wage increase by decreasing his or her labor supply. This decrease will be smaller than if the same change in wealth were due to an increase in nonlabor wealth, because the substitution effect is present and acts as a moderating influence. However, as seen in Example 6.2, when the income effect dominates, the substitution effect is not large enough to prevent labor supply from declining. It is entirely plausible, of course, that the substitution effect will dominate. If so, the actual response to wage increases will be to increase labor supply. Should the substitution effect dominate, the person’s labor supply curve— relating, say, his or her desired hours of work to wages—will be positively sloped. That is, labor supplied will increase with the wage rate. If, on the other hand, the income effect dominates, the person’s labor supply curve will be negatively sloped. Economic theory cannot say which effect will dominate, and in fact, individual labor supply curves could be positively sloped in some ranges of the wage and negatively sloped in others

Question 8

Figure 6.1

When does substitution and income effect dominate?

Answer 8

In Figure 6.1, for example, the person’s desired hours of work increase (substitution effect dominates) when wages go up as long as wages are low (below W*). At higher wages, however, further increases result in reduced hours of work (the income effect dominates); economists refer to such a curve as backward-bending.

Question 9

Graph 6.2

suppose a thoughtful consumer/worker were asked to decide how happy he or she would be with a daily income of $64 combined with 8 hours of leisure (point a in Figure 6.2). This level of happiness could be called …A. Our consumer/worker could name other combinations of money income and leisure hours that would also yield …A. Assume that our respondent named five other combinations. All six combinations of money income and leisure hours that yield… A are represented by heavy dots in Figure 6.2. The curve connecting these dots is called .., which … (The term indifference curve is derived from …) Our worker/consumer could no doubt achieve a higher level of happiness if he or she could combine the 8 hours of leisure with an income of $100 per day instead of just $64 a day. This higher satisfaction level could be called … B. The consumer could name other combinations of money income and leisure that would also yield this higher level of utility. These combinations are denoted by the Xs in Figure 6.2 that are connected by a second indifference curve

Answer 9

suppose a thoughtful consumer/worker were asked to decide how happy he or she would be with a daily income of $64 combined with 8 hours of leisure (point a in Figure 6.2). This level of happiness could be called utility level A. Our consumer/worker could name other combinations of money income and leisure hours that would also yield utility level A. Assume that our respondent named five other combinations. All six combinations of money income and leisure hours that yield utility level A are represented by heavy dots in Figure 6.2. The curve connecting these dots is called an indifference curve, which connects the various combinations of money income and leisure that yield equal utility. (The term indifference curve is derived from the fact that since each point on the curve yields equal utility, a person is truly indifferent about where on the curve he or she will be.) Our worker/consumer could no doubt achieve a higher level of happiness if he or she could combine the 8 hours of leisure with an income of $100 per day instead of just $64 a day. This higher satisfaction level could be called utility level B. The consumer could name other combinations of money income and leisure that would also yield this higher level of utility. These combinations are denoted by the Xs in Figure 6.2 that are connected by a second indifference curve​

Question 10

Indifference curves have certain specific characteristics

• Utility Level … represents more happiness than level …. Any such curve that lies to the … of another one is preferred to any curve to the … because …
• Indifference curves do not …. We assume …
• Indifference curves are … because if either income or leisure hours are increased, the other….. If the slope is steep, as at segment … in Figure 6.3, a given loss of income…..When the curve is relatively flat, however, as at segment … in Figure 6.3, a given decrease in income ….. Thus, when indifference curves are relatively steep, people d…as when such curves are relatively flat; when they are flat, a loss of income can only be compensated by …
• Indifference curves are ..—…. This shape reflects the assumption that…. At segment … in Figure 6.3, a great loss of income () can be compensated for by j…, whereas a little loss of leisure time would require a …. …
• Conversely, when income is low and leisure is abundant (segment… in Figure 6.3), income is more …. Losing income (by moving from ..to.., for example) would require a …. To repeat, what is relatively scarce is …
• Finally, different people have …. The curves drawn in Figures 6.2 and 6.3 were for one person. Another person would have a….

Answer 10

Indifference curves have certain specific characteristics

• Utility Level B represents more happiness than level A.el. Any such curve that lies to the northeast of another one is preferred to any curve to the southwest because the northeastern curve represents a higher level of utility.
• Indifference curves do not intersect. We assume our worker/ consumer is not so inconsistent in stating his or her preferences that this could happen.
• Indifference curves are negatively sloped because if either income or leisure hours are increased, the other is reduced in order to preserve the same level of utility. If the slope is steep, as at segment LK in Figure 6.3, a given loss of income need not be accompanied by a large increase in leisure hours to keep utility constant.When the curve is relatively flat, however, as at segment MN in Figure 6.3, a given decrease in income must be accompanied by a large increase in the consumption of leisure to hold utility constant. Thus, when indifference curves are relatively steep, people do not value money income as highly as when such curves are relatively flat; when they are flat, a loss of income can only be compensated for by a large increase in leisure if utility is to be kept constant
• Indifference curves are convex—steeper at the left than at the right. This shape reflects the assumption that when money income is relatively high and leisure hours are relatively few, leisure is more highly valued (and income less valued) than when leisure is abundant and income relatively scarce. At segment LK in Figure 6.3, a great loss of income (from Y4 to Y3, for example) can be compensated for by just a little increase in leisure, whereas a little loss of leisure time (from H3 to H4, for example) would require a relatively large increase in income to maintain equal utility. What is relatively scarce is more highly valued.
• Conversely, when income is low and leisure is abundant (segment MN in Figure 6.3), income is more highly valued. Losing income (by moving from Y2 to Y1, for example) would require a huge increase in leisure for utility to remain constant. To repeat, what is relatively scarce is assumed to be more highly valued.
• Finally, different people have different sets of indifference curves. The curves drawn in Figures 6.2 and 6.3 were for one person. Another person would have a completely different set of curves.

Question 11

Figure 6.4

People who …. for example, would have had indifference curves that were generally steeper (see Figure 6.4a). People …. would have relatively flat curves (see Figure 6.4b).

Answer 11

Figure 6.4

People who value leisure more highly, for example, would have had indifference curves that were generally steeper (see Figure 6.4a). People who do not value leisure highly would have relatively flat curves (see Figure 6.4b).

Question 12

Income and Wage Constraints

Everyone would like to …, which would be ideally done by …. Unfortunately, the resources anyone can command are …. Thus, all that is possible …. To see these resource limitations graphically requires…. Suppose the person whose indifference curves are graphed in Figure 6.2 had no source of income other than labor earnings. Suppose, further, that he or she could earn $8 per hour. Figure 6.5 includes the two indifference curves shown in Figure 6.2 as well as a straight line (ED) connecting combinations of leisure and income that are possible for a person with an $8 wage and no outside income. If 16 hours per day are available for work and leisure, and if this person consumes all 16 in leisure, then … (point .. in Figure 6.5). If 5 hours a day are devoted to work, income will be … (point …), and if 16 hours a day are worked, income will be … (point …). Other points on this line—for example, the point of 15 hours of leisure (1 hour of work) and $8 of income—are also possible. This line, which reflects… that are possible for the individual, is called the…. Any combination to the right of the budget constraint is …; the person’s command over resources is … to attain these …..

The slope of the …. is a graphical representation of t…. One’s wage rate is properly defined …

Wage rate=

Answer 12

Everyone would like to maximize his or her utility, which would be ideally done by consuming every available hour of leisure combined with the highest conceivable income. Unfortunately, the resources anyone can command are limited. Thus, all that is possible is to do the best one can, given limited resources. To see these resource limitations graphically requires superimposing constraints on one’s set of indifference curves to see which combinations of income and leisure are available and which are not. Suppose the person whose indifference curves are graphed in Figure 6.2 had no source of income other than labor earnings. Suppose, further, that he or she could earn $8 per hour. Figure 6.5 includes the two indifference curves shown in Figure 6.2 as well as a straight line (ED) connecting combinations of leisure and income that are possible for a person with an $8 wage and no outside income. If 16 hours per day are available for work​and leisure,10 and if this person consumes all 16 in leisure, then money income will be zero (point D in Figure 6.5). If 5 hours a day are devoted to work, income will be $40 per day (point M), and if 16 hours a day are worked, income will be $128 per day (point E). Other points on this line—for example, the point of 15 hours of leisure (1 hour of work) and $8 of income—are also possible. This line, which reflects the combinations of leisure and income that are possible for the individual, is called the budget constraint. Any combination to the right of the budget constraint is not achievable; the person’s command over resources is simply not sufficient to attain these combinations of leisure and money income. The slope of the budget constraint is a graphical representation of the wage rate. One’s wage rate is properly defined as the increment in income ( y) derived from an increment in hours of work (h):

Wage rate=^Y/^H

Question 13

Next part Income and Wage Constraints

Now ^y/^h is exactly the slope of the …(in absolute value). Figure 6.5 shows how the constraint rises $.. for every …-hour increase in work: if the person works 0 hours, income per day is …; if the person works 1 hour, $… in income is received; if he or she works 5 hours, … in income is achieved. The constraint rises $8 because the …. If the person could earn $16 per hour, the constraint would r…. It is clear from Figure 6.5 that our consumer/worker cannot achieve utility level …. He or she can achieve some points on the indifference curve representing utility level ….—specifically, those points between … and …. in Figure 6.5. However, if our consumer/worker is a utility maximizer, he or she will realize that a utility level above A is possible. Remembering that an …of indifference curves can be drawn between curves A and B in Figure 6.5, one representing …, we can draw a curve ( …) that is northeast of curve A and just tangent to the budget constraint at point …. Any movement along the budget constraint away from the tangency point places the person on an indifference curve lying … A’.

Workers who face the same budget constraint, but who have different preferences for leisure, will make different choices about hours of work. If the person whose preferences were depicted in Figure 6.5 had placed lower values on leisure time—and therefore had indifference curves that were comparatively …, such as the one shown in Figure 6.4..—then the point of tangency with constraint ED would have been to the … N (indicating more hours of work). Conversely, if he or she had steeper indifference curves, signifying that leisure time … (see Figure 6.4…), then the point of tangency in Figure 6.5 would have been to the … of point N, and … hours of work would have been desired. Indeed, some people will have indifference curves so steep (that is, preferences for leisure so strong) that there is no point of tangency with ED. For these people, as is illustrated by Figure 6.6, utility is maximized at the “corner” (point D); they desire no work at all and therefore are not in the labor force.

Answer 13

Next part Income and Wage Constraints

Now ^y/^h is exactly the slope of the budget constraint (in absolute value).11 Figure 6.5 shows how the constraint rises $8 for every 1-hour increase in work: if the person works 0 hours, income per day is zero; if the person works 1 hour, $8 in income is received; if he or she works 5 hours, $40 in income is achieved. The constraint rises $8 because the wage rate is $8 per hour. If the person could earn $16 per hour, the constraint would rise twice as fast and therefore be twice as steep. It is clear from Figure 6.5 that our consumer/worker cannot achieve utility level B. He or she can achieve some points on the indifference curve representing utility level A—specifically, those points between L and M in Figure 6.5. However, if our consumer/worker is a utility maximizer, he or she will realize that a utility level above A is possible. Remembering that an infinite number of indifference curves can be drawn between curves A and B in Figure 6.5, one representing each possible level of satisfaction between A and B, we can draw a curve ( a’) that is northeast of curve A and just tangent to the budget constraint at point N. Any movement along the budget constraint away from the tangency point places the person on an indifference curve lying below A’.

Workers who face the same budget constraint, but who have different preferences for leisure, will make different choices about hours of work. If the person whose preferences were depicted in Figure 6.5 had placed lower values on leisure time—and therefore had indifference curves that were comparatively flatter, such as the one shown in Figure 6.4b—then the point of tangency with constraint ED would have been to the left of point N (indicating more hours of work). Conversely, if he or she had steeper indifference curves, signifying that leisure time was more valuable (see Figure 6.4a), then the point of tangency in Figure 6.5 would have been to the right of point N, and fewer hours of work would have been desired. Indeed, some people will have indifference curves so steep (that is, preferences for leisure so strong) that there is no point of tangency with ED. For these people, as is illustrated by Figure 6.6, utility is maximized at the “corner” (point D); they desire no work at all and therefore are not in the labor force.

Question 14

The Income Effect

Supose now that the person depicted in Figure 6.5 receives a source of income independent of work. Suppose further that this nonlabor income amounts to about $36 per day. Thus, even if this person worked 0 hours per day, his or her daily income would be …. Naturally, if the person worked more than 0 hours, his or her daily income would be equal to $36 plus …. (t…). Our person’s command over resources has clearly …, as can be shown by drawing a…. As shown by the darker blue line in Figure 6.7, the endpoints of the new … are point … (…) and point…(…). Note that the … is parallel t…. Parallel lines have the same …; since the slope of each constraint reflects …, we can infer that the increase in nonlabor income has not changed ….. We have just described a situation in which a …. should be observed. Income (wealth) has been increased, but …. The previous section noted that if wealth increased and the opportunity cost of leisure remained constant, the person would …. We thus concluded that the income effect was …, and this negative relationship is illustrated graphically in Figure 6.7. When the old budget constraint (ED) was in effect, the person’s highest level of utility was reached at point …, working …. With the new constraint (ed), the optimum hours of work are …). The new source of income, because …, has caused an income effect that results in …. Statistical analyses of people who received large inheritances (Example 6.3) or who won large lottery prizes support the prediction that labor supply …..

Answer 14

The Income Effect

Suppose now that the person depicted in Figure 6.5 receives a source of income independent of work. Suppose further that this nonlabor income amounts to about $36 per day. Thus, even if this person worked 0 hours per day, his or her daily income would be $36. Naturally, if the person worked more than 0 hours, his or her daily income would be equal to $36 plus earnings (the wage multiplied by the hours of work). Our person’s command over resources has clearly increased, as can be shown by drawing a new budget constraint to reflect the nonlabor income. As shown by the darker blue line in Figure 6.7, the endpoints of the new constraint are point d (0 hours of work and $36 of money income) and point e (16 hours ofwork and $164 of income—$36 in nonlabor income plus $128 in earnings). Note that the new constraint is parallel to the old one. Parallel lines have the same slope; since the slope of each constraint reflects the wage rate, we can infer that the increase in nonlabor income has not changed the person’s wage rate. We have just described a situation in which a pure income effect should be observed. Income (wealth) has been increased, but the wage rate has remained unchanged. The previous section noted that if wealth increased and the opportunity cost of leisure remained constant, the person would consume more leisure and work less. We thus concluded that the income effect was negative, and this negative relationship is illustrated graphically in Figure 6.7. When the old budget constraint (ED) was in effect, the person’s highest level of utility was reached at point N, working 9 hours a day. With the new constraint (ed), the optimum hours of work are 8 per day (point P). The new source of income, because it does not alter the wage, has caused an income effect that results in one less hour of work per day. Statistical analyses of people who received large inheritances (Example 6.3) or who won large lottery prizes support the prediction that labor supply is reduced when unearned income rises.

Question 15

ncome and Substitution Effects with a Wage Increase

Suppose that instead of increasing one’s command over resources by receiving a source of nonlabor income, the wage rate were to be increased from $8 to $12 per hour. This increase, as noted earlier, would cause both an i…; workers would be .. and face a … opportunity cost of leisure. Theory tells us in this case that the substitution effect .. and the income effect toward f…, but it cannot tell us which effect will dominate. Figures 6.8 and 6.9 illustrate the possible effects of the above wage change on a person’s labor supply, which we now assume is initially 8 hours per day. Figure 6.8 illustrates the case in which the observed response by a worker is to …; in this case, the substitution effect is … than the income effect. Figure 6.9 illustrates the case in which the income effect is … and the response to a wage increase is to … The difference between the two figures lies solely in the shape of the …that might describe a person’s preferences; the budget constraints,…, are exactly the same

Figures 6.8 and 6.9 both show the old constraint, AB, the slope of which reflects the wage of $8 per hour. They also show the new one, AC, which reflects the $12 wage. Because we assume workers have no source of nonlabor income, both constraints are anchored at point …, where income is …. Point C on the new constraint is now at $192 (16 hours of work times $12 per hour). With the worker whose preferences are depicted in Figure 6.8, the wage increase makes utility level …the highest that can be reached. The tangency point at …. suggests that …. When the old constraint was in effect, the utility-maximizing hours of work were … (…). Thus, the wage increase would cause this person’s desired hours of work to increase by … per day. With the worker whose preferences are depicted in Figure 6.9, the wage increase would make utility level … the highest one possible (the prime emphasizes that workers’ preferences differ and that utility levels in Figures 6.8 and 6.9 cannot be compared). Utility is maximized at …,… hours of work per day. Thus, with preferences like those in Figure 6.9, working hours fall from … to … as the wage rate increases.

Answer 15

Income and Substitution Effects with a Wage Increase

Suppose that instead of increasing one’s command over resources by receiving a source of nonlabor income, the wage rate were to be increased from $8 to $12 per hour. This increase, as noted earlier, would cause both an income effect and a substitution effect; workers would be wealthier and face a higher opportunity cost of leisure. Theory tells us in this case that the substitution effect pushes them toward more hours of work and the income effect toward fewer, but it cannot tell us which effect will dominate. Figures 6.8 and 6.9 illustrate the possible effects of the above wage change on a person’s labor supply, which we now assume is initially 8 hours per day. Figure 6.8 illustrates the case in which the observed response by a worker is to increase the hours of work; in this case, the substitution effect is stronger than the income effect. Figure 6.9 illustrates the case in which the income effect is stronger and the response to a wage increase is to reduce the hours of work. The difference between the two figures lies solely in the shape of the indifference curves that might describe a person’s preferences; the budget constraints…, are exactly the same

Figures 6.8 and 6.9 both show the old constraint, AB, the slope of which reflects the wage of $8 per hour. They also show the new one, AC, which reflects the $12 wage. Because we assume workers have no source of nonlabor income, both constraints are anchored at point A, where income is zero if a person does not work. Point C on the new constraint is now at $192 (16 hours of work times $12 per hour). With the worker whose preferences are depicted in Figure 6.8, the wage increase makes utility level U2 the highest that can be reached. The tangency point at N2 suggests that 11 hours of work is optimum. When the old constraint was in effect, the utility-maximizing hours of work were 8 per day (point N1). Thus, the wage increase would cause this person’s desired hours of work to increase by 3 per day. With the worker whose preferences are depicted in Figure 6.9, the wage increase would make utility level U’2 the highest one possible (the prime emphasizes that workers’ preferences differ and that utility levels in Figures 6.8 and 6.9 cannot be compared). Utility is maximized at N’2, at 6 hours of work per day. Thus, with preferences like those in Figure 6.9, working hours fall from 8 to 6 as the wage rate increases

Question 16

Isolating Income and Substitution Effects

Figure 6.10 has three panels. Panel (a) repeats Figure 6.8; it shows the final, overall effect of a wage increase on the labor supply of the person whose preferences are depicted. As we saw earlier, the effect of the wage increase in this case is to …the person’s utility from …to … and to induce this worker to i….from 8.. to … per day. Embedded in this overall effect of the wage increase, however, is an income effect pushing toward .. work and a substitution effect pushing toward …. These effects are graphically separated in panels (b) and (c). Panel (b) of Figure 6.10 shows the income effect that is embedded in the overall response to the wage change. By definition, the income effect is the change in … To reveal this embedded effect, we ask a hypothetical question: “What would have been the change in labor supply if the person depicted in panel (a) had reached the new indifference curve (U2) with a change in nonlabor income instead of a change in his or her wage rate?” We begin to answer this question graphically by moving the old constraint to the northeast, which depicts the … leisure time and goods—and hence the… level of utility—associated with greater wealth. The constraint is shifted … while maintaining its original slope (reflecting the old $8 wage), which holds …. The dashed line in panel (b), which is parallel to AB, depicts this hypothetical movement of the old constraint, and it results in a tangency point at N3. This tangency suggests that had the person received nonlabor income, with no change in the wage, sufficient to reach the …, he or she would have reduced work hours from … (N1…) to … (…) per day. This shift is graphical verification that the income effect is …, assuming that leisure is a normal good. The substitution effect is the effect on labor supply …. It can be seen in panel (c) of Figure 6.10 as the difference between where the person actually ended up on indifference curve U2 (tangency at…) and where he or she would have ended up with a pure income effect (tangency at …). Comparing tangency points on the same indifference curve is a graphical approximation to holding wealth constant. Thus, with the wage change, the person represented in Figure 6.10 ended up at point …, working …. Without the wage change, the person would have chosen to work … (point …). The wage change by itself, holding utility (or real wealth) constant, caused work hours to increase by … per day.This increase demonstrates that the substitution effect is …. To summarize, the observed effect of raising wages from $8 to $12 per hour increased the hours of work in Figure 6.10 from … to … per day. This observed effect, however, is the sum of two-component effects. The income effect, which operates because a … wage …. one’s real wealth, tended to reduce the hours of work from … to … per day. The substitution effect, which captures the pure effect of the change in …, tended to push the person toward ……. hours of work per day. The end result was an increase of … in the hours worked each day.

Answer 16

Isolating Income and Substitution Effects

Figure 6.10 has three panels. Panel (a) repeats Figure 6.8; it shows the final, overall effect of a wage increase on the labor supply of the person whose preferences are depicted. As we saw earlier, the effect of the wage increase in this case is to raise the person’s utility from U1 to U2 and to induce this worker to increase desired hours of work from 8 to 11 per day. Embedded in this overall effect of the wage increase, however, is an income effect pushing toward less work and a substitution effect pushing toward more. These effects are graphically separated in panels (b) and (c). Panel (b) of Figure 6.10 shows the income effect that is embedded in the overall response to the wage change. By definition, the income effect is the change in desired hours of work brought on by increased wealth, holding the wage rate constant. To reveal this embedded effect, we ask a hypothetical question: “What would have been the change in labor supply if the person depicted in panel (a) had reached the new indifference curve (U2) with a change in nonlabor income instead of a change in his or her wage rate?” We begin to answer this question graphically by moving the old constraint to the northeast, which depicts the greater command over leisure time and goods—and hence the higher level of utility—associated with greater wealth. The constraint is shifted outward while maintaining its original slope (reflecting the old $8 wage), which holds the wage constant. The dashed line in panel (b), which is parallel to AB, depicts this hypothetical movement of the old constraint, and it results in a tangency point at N3. This tangency suggests that had the person received nonlabor income, with no change in the wage, sufficient to reach the new level of utility, he or she would have reduced work hours from 8 (N1) to 7 (N3) per day. This shift is graphical verification that the income effect is negative, assuming that leisure is a normal good. The substitution effect is the effect on labor supply of a change in the wage rate, holding wealth constant. It can be seen in panel (c) of Figure 6.10 as the difference between where the person actually ended up on indifference curve U2 (tangency at N2) and where he or she would have ended up with a pure income effect (tangency at N3). Comparing tangency points on the same indifference curve is a graphical approximation to holding wealth constant. Thus, with the wage change, the person represented in Figure 6.10 ended up at point N2, working 11 hours a day. Without the wage change, the person would have chosen to work 7 hours a day (point N3). The wage change by itself, holding utility (or real wealth) constant, caused work hours to increase by 4 per day. This increase demonstrates that the substitution effect is positive. To summarize, the observed effect of raising wages from $8 to $12 per hour increased the hours of work in Figure 6.10 from 8 to 11 per day. This observed effect, however, is the sum of two component effects. The income effect, which operates because a higher wage increases one’s real wealth, tended to reduce the hours of work from 8 to 7 per day. The substitution effect, which captures the pure effect of the change in leisure’s opportunity cost, tended to push the person toward 4 more hours of work per day. The end result was an increase of 3 in the hours worked each day.

Question 17

Which Effect Is Stronger?

Suppose that a wage increase changes the budget constraint facing a worker from CD to CE in Figure 6.11. If the worker had a relatively flat set of indifference curves, the initial tangency along CD might be at point…, implying a relatively…. If the person had more steeply sloped indifference curves, the initial tangency might be at point …, where …. One important influence on the size of the income effect is the extent of the … of the new constraint: the more the constraint shifts …, the greater the income effect will tend to be. For a person with an initial tangency at point …, for example, the northeast movement is larger than that for a person whose initial tangency is at point …. Put in words, the increased command over resources made possible by a wage increase is only attainable i…, and the … work-oriented the person is, …. will be his or her increase in resources. Other things equal, people who are working longer hours will exhibit … income effects when wage rates change. To take this reasoning to the extreme, suppose a person’s indifference curves were … that the person was initially out of the labor force (that is, when the budget constraint was CD in Figure 6.11, his or her utility was maximized at point C). The wage increase and the resultant new constraint, CE, can induce only two outcomes: the person will either … or …. Reducing… is not possible. For those who are out of the labor force, then, the decision to participate as wage offers rise clearly reflects a dominant … effect. Conversely, if someone currently working decides to change his or her participation decision and drop out of the labor force when wages fall, the … effect has again dominated. Thus, the labor force participation decisions brought about by wage changes exhibit a dominant …. effect. We turn now to a more detailed analysis of the decision whether to join the labor force.

Answer 17

Which Effect Is Stronger?

Suppose that a wage increase changes the budget constraint facing a worker from CD to CE in Figure 6.11. If the worker had a relatively flat set of indifference curves, the initial tangency along CD might be at point A, implying a relatively heavy work schedule. If the person had more steeply sloped indifference curves, the initial tangency might be at point B, where hours at work are fewer. One important influence on the size of the income effect is the extent of the northeast movement of the new constraint: the more the constraint shifts outward, the greater the income effect will tend to be. For a person with an initial tangency at point A, for example, the northeast movement is larger than that for a person whose initial tangency is at point B. Put in words, the increased command over resources made possible by a wage increase is only attainable if one works, and the more work-oriented the person is, the greater will be his or her increase in resources. Other things equal, people who are working longer hours will exhibit greater income effects when wage rates change. To take this reasoning to the extreme, suppose a person’s indifference curves were so steep that the person was initially out of the labor force (that is, when the budget constraint was CD in Figure 6.11, his or her utility was maximized at point C). The wage increase and the resultant new constraint, CE, can induce only two outcomes: the person will either begin to work for pay or remain out of the labor force. Reducing the hours of paid employment is not possible. For those who are out of the labor force, then, the decision to participate as wage offers rise clearly reflects a dominant substitution effect. Conversely, if someone currently working decides to change his or her participation decision and drop out of the labor force when wages fall, the substitution effect has again dominated. Thus, the labor force participation decisions brought about by wage changes exhibit a dominant substitution effect. We turn now to a more detailed analysis of the decision whether to join the labor force.

Question 18

The Reservation Wage

An implication of our labor supply theory is that if people who are not in the labor force place a value of $X on the marginal hour of leisure, then they would be unwilling to take a job unless the offered wages were … than $X. Because they will “reserve” their labor unless the wage is $X … (see Example 6.4), economists say that they have a reservation wage of $X. The reservation wage, then, is …, and in the labor/leisure context, it represents the … Refer back to Figure 6.6, which graphically depicted a person choosing not to work. The reason there was no tangency between an indifference curve and the budget constraint—and the reason the person remained out of the labor force—was that the wage was everywhere … than his or her marginal value of leisure time. Often, people are thought to behave as if they have both a reservation wage and a certain number of work hours that must be offered before they will consider taking a job. The reasons are not difficult to understand and are illustrated in Figure 6.12. Suppose that taking a job entails 2 hours of commuting time (roundtrip) per day. These hours, of course, are unpaid, so the worker’s budget constraint must reflect that if a job is accepted, 2 hours of leisure are given up before there is any increase in income. These fixed costs of working are reflected in Figure 6.12 by segment …. Segment …, of course, reflects the earnings that are possible (once at work), and the slope of … represents the person’s wage rate. Is the wage underlying … great enough to induce the person to work? Consider indifference curve …, which represents the highest level of utility this person can achieve, given budget constraint …. Utility is maximized at point …, and the person chooses not to work. It is clear from this choice that the offered wage (given the 2-hour commute) is below the person’s reservation wage, but can we show the latter wage graphically? To take work with a 2-hour commute, the person depicted in Figure 6.12 must find a job able to generate a combination of earnings and leisure time that yields a utility level equal to, or greater than,…. This is possible only if the person’s budget constraint is equal to (or to the right of) …, which is tangent to …at point X. The person’s reservation wage, then, is equal to the slope of …, and you can readily note that in this case, the slope of… exceeds the slope of …, which represents the currently offered wage. Moreover, to bring utility up to the level of … (the utility associated with not working), the person shown in Figure 6.12 must be able to find a job at the reservation wage that offers …hours of work per day. Put differently, at this person’s reservation wage, he or she would want to consume … hours of leisure daily, and with a 2-hour commute, this implies … hours of work.

Answer 18

The Reservation Wage

An implication of our labor supply theory is that if people who are not in the labor force place a value of $X on the marginal hour of leisure, then they would be unwilling to take a job unless the offered wages were greater than $X. Because they will “reserve” their labor unless the wage is $X or more (see Example 6.4), economists say that they have a reservation wage of $X. The reservation wage, then, is the wage below which a person will not work, and in the labor/leisure context, it represents the value placed on an hour of lost leisure time. Refer back to Figure 6.6, which graphically depicted a person choosing not to work. The reason there was no tangency between an indifference curve and the budget constraint—and the reason the person remained out of the labor force—was that the wage was everywhere lower than his or her marginal value of leisure time. Often, people are thought to behave as if they have both a reservation wage and a certain number of work hours that must be offered before they will consider taking a job. The reasons are not difficult to understand and are illustrated in Figure 6.12. Suppose that taking a job entails 2 hours of commuting time (roundtrip) per day. These hours, of course, are unpaid, so the worker’s budget constraint must reflect that if a job is accepted, 2 hours of leisure are given up before there is any increase in income. These fixed costs of working are reflected in Figure 6.12 by segment AB. Segment BC, of course, reflects the earnings that are possible (once at work), and the slope of BC represents the person’s wage rate. Is the wage underlying BC great enough to induce the person to work? Consider indifference curve U1, which represents the highest level of utility this person can achieve, given budget constraint ABC. Utility is maximized at point A, and the person chooses not to work. It is clear from this choice that the offered wage (given the 2-hour commute) is below the person’s reservation wage, but can we show the latter wage graphically? To take work with a 2-hour commute, the person depicted in Figure 6.12 must find a job able to generate a combination of earnings and leisure time that yields a utility level equal to, or greater than, U1. This is possible only if the person’s budget constraint is equal to (or to the right of) ABD, which is tangent to U1 at point X. The person’s reservation wage, then, is equal to the slope of BD, and you can readily note that in this case, the slope of BD exceeds the slope of BC, which represents the currently offered wage. Moreover, to bring utility up to the level of U1 (the utility associated with not working), the person shown in Figure 6.12 must be able to find a job at the reservation wage that offers 4 hours of work per day. Put differently, at this person’s reservation wage, he or she would want to consume 10 hours of leisure daily, and with a 2-hour commute, this implies 4 hours of work.

Question 19

Budget Constraints with “Spikes”

To understand the consequences of paying benefits only to those who are not working, let us suppose that a workers’ compensation program is structured so that, after injury, workers receive their pre-injury earnings for as long as they are off work. Once they work even one hour, however, they are no longer considered disabled and cannot receive further benefits. The effects of this program on work incentives are analyzed in Figure 6.13, in which it is assumed that the pre-injury budget constraint was AB and pre-injury earnings were e0(=AC) .

Furthermore, we assume that the worker’s “market” budget constraint (that is, the constraint in the absence of a workers’ compensation program) is unchanged, so that after recovery, the pre-injury wage can again be earned. Under these conditions, the post-injury budget constraint is …, and the person maximizes utility at point …—a point of no work. Note that constraint … contains the segment …, which looks like a spike. It is this spike that creates severe work-incentive problems, for two reasons. First, the returns associated with the first hour of work are …. That is, a person at point … who returns to work for 1 hour would find his or her income to be …. Earnings from this hour of work would be more than offset by the …. in benefits, which creates a negative “net wage.” The … effect associated with this program characteristic clearly discourages work. Second, our assumed no-work benefit of AC is equal to …, the pre-injury level of earnings. If the worker values leisure at all (as is assumed by the standard downward slope of indifference curves), being able to receive the old level of earnings while also enjoying more leisure clearly enhances utility. The worker is better off at point … than at point …, the pre-injury combination of earnings and leisure hours, because he or she is on indifference curve U2 rather than U1. Allowing workers to reach a higher utility level without working generates an income effect that … the return to work. Indeed, the program we have assumed raises a worker’s…. above his or her pre-injury wage, meaning that a return to work is possible only if the worker qualifies for a higher-paying job. To see this graphically, observe the dashed blue line in Figure 6.13 that begins at point A and is tangent to indifference curve U2 (the level of utility made possible by the social insurance program). The slope of this line is equal to the person’s …., because if the person can obtain the desired hours of work at this or a greater wage, utility will be at least equal to that associated with point …. Note also that for labor force participation to be induced, the reservation wage must be received for at least R* hours of work. Given that the work-incentive aspects of income replacement programs often quite justifiably take a backseat to the goal of making unfortunate workers “whole” in some economic sense, creating programs that avoid work disincentives is not easy. With the preferences of the worker depicted in Figure 6.13, a benefit of slightly less than Ag would ensure minimal loss of utility while still providing incentives to return to work as soon as physically possible (work would allow indifference curve U1 to be attained—see point f—while not working and receiving a benefit of less than Ag would not). Unfortunately, workers differ in their preferences, so the optimal benefit—one that would provide work incentives yet ensure only minimal loss of utility—differs for each individual. With programs that create spikes, the best policymakers can do is set a nowork benefit as some fraction of previous earnings and then use administrative means to encourage the return to work among any whose utility is greater when not working. Unemployment insurance (UI), for example, replaces something like half of lost earnings for the typical worker, but the program puts an upper limit on the weeks each unemployed worker can receive benefits. Workers’ compensation replaces two-thirds of lost earnings for the average worker but must rely on doctors—and sometimes judicial hearings—to determine whether a worker continues to be eligible for benefits. (For evidence that more-generous workers’ compensation benefits do indeed induce longer absences from work, see Example 6.6.)

Answer 19

Budget Constraints with “Spikes”

To understand the consequences of paying benefits only to those who are not working, let us suppose that a workers’ compensation program is structured so that, after injury, workers receive their pre-injury earnings for as long as they are off work. Once they work even one hour, however, they are no longer considered disabled and cannot receive further benefits. The effects of this program on work incentives are analyzed in Figure 6.13, in which it is assumed that the pre-injury budget constraint was AB and pre-injury earnings were E0(=AC) .

Furthermore, we assume that the worker’s “market” budget constraint (that is, the constraint in the absence of a workers’ compensation program) is unchanged, so that after recovery, the pre-injury wage can again be earned. Under these conditions, the post-injury budget constraint is BAC, and the person maximizes utility at point C—a point of no work. Note that constraint BAC contains the segment AC, which looks like a spike. It is this spike that creates severe work-incentive problems, for two reasons. First, the returns associated with the first hour of work are negative. That is, a person at point C who returns to work for 1 hour would find his or her income to be considerably reduced by working. Earnings from this hour of work would be more than offset by the reduction in benefits, which creates a negative “net wage.” The substitution effect associated with this program characteristic clearly discourages work.19 Second, our assumed no-work benefit of AC is equal to E0, the pre-injury level of earnings. If the worker values leisure at all (as is assumed by the standard downward slope of indifference curves), being able to receive the old level of earnings while also enjoying more leisure clearly enhances utility. The worker is better off at point C than at point f, the pre-injury combination of earnings and leisure hours, because he or she is on indifference curve U2 rather than U1. Allowing workers to reach a higher utility level without working generates an income effect that discourages, or at least slows, the return to work. Indeed, the program we have assumed raises a worker’s reservation wage above his or her pre-injury wage, meaning that a return to work is possible only if the worker qualifies for a higher-paying job. To see this graphically, observe the dashed blue line in Figure 6.13 that begins at point A and is tangent to indifference curve U2 (the level of utility made possible by the social insurance program). The slope of this line is equal to the person’s reservation wage, because if the person can obtain the desired hours of work at this or a greater wage, utility will be at least equal to that associated with point C. Note also that for labor force participation to be induced, the reservation wage must be received for at least R* hours of work. Given that the work-incentive aspects of income replacement programs often quite justifiably take a backseat to the goal of making unfortunate workers “whole” in some economic sense, creating programs that avoid work disincentives is not easy. With the preferences of the worker depicted in Figure 6.13, a benefit of slightly less than Ag would ensure minimal loss of utility while still providing incentives to return to work as soon as physically possible (work would allow indifference curve U1 to be attained—see point f—while not working and receiving a benefit of less than Ag would not). Unfortunately, workers differ in their preferences, so the optimal benefit—one that would provide work incentives yet ensure only minimal loss of utility—differs for each individual. With programs that create spikes, the best policymakers can do is set a nowork benefit as some fraction of previous earnings and then use administrative means to encourage the return to work among any whose utility is greater when not working. Unemployment insurance (UI), for example, replaces something like half of lost earnings for the typical worker, but the program puts an upper limit on the weeks each unemployed worker can receive benefits. Workers’ compensation replaces two-thirds of lost earnings for the average worker but must rely on doctors—and sometimes judicial hearings—to determine whether a worker continues to be eligible for benefits. (For evidence that more-generous workers’ compensation benefits do indeed induce longer absences from work, see Example 6.6.)

Question 20

Programs with Net Wage Rates of Zero

These programs factor income needs into their eligibility criteria and then pay benefits based on the difference between one’s … and …. We will see that paying people the difference between their earnings and their needs creates a net wage rate …; thus, the work-incentive problems associated with these welfare programs result from the fact that they increase the …. of program recipients while also drastically reducing the price of leisure.

Nature of Welfare Subsidies

Welfare programs have historically taken the form of a guaranteed annual income, under which the welfare agency determines the income needed by an eligible person (Yn in Figure 6.14) based on family size, area living costs, and local welfare regulations. … are then subtracted from this …, and a check is issued to the person each month for the difference. If the person does not work, he or she receives a subsidy of …. If the person works, and if earnings cause dollar-for-dollar reductions in welfare benefits, then a budget constraint like … in Figure 6.14 is created. The person’s income remains Yn as long as he or she is subsidized. If receiving the subsidy, then, an extra hour of work yields n…., because the extra earnings result in an … . The net wage of a person on the program—and therefore his or her price of leisure—is …, which is graphically shown by the segment of the constraint having a slope of zero (…).

Thus, a welfare program like the one summarized in Figure 6.14 increases the income of the poor by moving the lower end of the budget constraint out from … to …; as indicated by the dashed hypothetical constraint in Figure 6.14, this shift creates an income effect tending to reduce … from the hours associated with point … to those associated with point …. However, it also causes the wage to effectively drop to zero; every dollar earned is matched by a dollar reduction in welfare benefits. This dollar-for-dollar reduction in benefits induces a huge … effect, causing those accepting welfare to reduce their hours of work to zero (point …). Of course, if a person’s indifference curves were sufficiently flat so that the curve tangent to segment … passed above point … (see Figure 6.15), then that person’s utility would be maximized by choosing work instead of welfare.

Lifetime Limits

Both lifetime limits and work requirements can be analyzed using the graphical tools developed in this chapter. Lifetime limits on the receipt of welfare have the effect of ending eligibility for transfer payments, either by forcing recipients off welfare or by inducing them to leave so they can “save” their eligibility in case they need welfare later in life. Thus, in terms of Figure 6.14, the lifetime limit ultimately removes … from the potential recipient’s budget constraint, which then reverts to the market constraint of …. Clearly, the lifetime limit increases work incentives by ultimately eliminating the income subsidy. However, within the limits of their eligible years, potential welfare recipients must choose when to receive the subsidy and when to “save” their eligibility in the event of a future need. Federal law provides for welfare subsidies only to families with children under the age of 18; consequently, the closer one’s youngest child is to 18 (when welfare eligibility ends anyway), the smaller are the incentives of the parent to forgo the welfare subsidy and save eligibility for the future.

Work Requirements

Figure 6.16 illustrates the budget constraint associated with a minimum work requirement of 6 hours a day (30 hours per week). If the person fails to work the required 6 hours a day, no welfare benefits are received, and he or she will be along segment … of the constraint. If the work requirement is met, but earnings are less than Yn, welfare benefits are received (see segment BCD). If the work requirement is exceeded, income (earnings plus benefits) remains at Yn—the person is along …—until earnings rise above needed income and the person is along segment … of the constraint and no longer eligible for welfare benefits. The work-incentive effects of this work requirement can be seen from analyzing Figure 6.16 in the context of people whose skills are such that they are potential welfare recipients. At one extreme, some potential recipients may have such steeply sloped indifferences curves (reflecting a…) that utility is maximized along segment AB, where so little market work is performed that they do not qualify for welfare. At the opposite extreme, others may have such flat indifference curves (reflecting a s…) that their utility is maximized along segment DE; they work so many hours that their earnings disqualify them for welfare benefits. In the middle of the above extremes will be those whose preferences lead them to work enough to qualify for welfare benefits. Clearly, if their earnings reduce their benefits dollar for dollar—as shown by the horizontal segment… in Figure 6.16—they will want to work just the minimum hours needed to qualify for welfare, because their utility will be maximized at point … and not along …. (For labor supply responses to different forms of a work requirement—requisitions of food from farmers during wartime—see Example 6.7 on page 204.)

Answer 20

Programs with Net Wage Rates of Zero

The programs just discussed were intended to confer benefits on those who are unable to work, and the budget-constraint spike was created by the eligibility requirement that to receive benefits, one must not be working. Other social programs, such as welfare, have different eligibility criteria and calculate benefits differently. These programs factor income needs into their eligibility criteria and then pay benefits based on the difference between one’s actual earnings and one’s needs. We will see that paying people the difference between their earnings and their needs creates a net wage rate of zero; thus, the work-incentive problems associated with these welfare programs result from the fact that they increase the income of program recipients while also drastically reducing the price of leisure.

Nature of Welfare Subsidies

Welfare programs have historically taken the form of a guaranteed annual income, under which the welfare agency determines the income needed by an eligible person (Yn in Figure 6.14) based on family size, area living costs, and local welfare regulations. Actual earnings are then subtracted from this needed level, and a check is issued to the person each month for the difference. If the person does not work, he or she receives a subsidy of Yn. If the person works, and if earnings cause dollar-for-dollar reductions in welfare benefits, then a budget constraint like ABCD in Figure 6.14 is created. The person’s income remains Yn as long as he or she is subsidized. If receiving the subsidy, then, an extra hour of work yields no net increase in income, because the extra earnings result in an equal reduction in welfare benefits. The net wage of a person on the program—and therefore his or her price of leisure—is zero, which is graphically shown by the segment of the constraint having a slope of zero (BC).

Lifetime Limits

Both lifetime limits and work requirements can be analyzed using the graphical tools developed in this chapter. Lifetime limits on the receipt of welfare have the effect of ending eligibility for transfer payments, either by forcing recipients off welfare or by inducing them to leave so they can “save” their eligibility in case they need welfare later in life. Thus, in terms of Figure 6.14, the lifetime limit ultimately removes ABC from the potential recipient’s budget constraint, which then reverts to the market constraint of AD. Clearly, the lifetime limit increases work incentives by ultimately eliminating the income subsidy. However, within the limits of their eligible years, potential welfare recipients must choose when to receive the subsidy and when to “save” their eligibility in the event of a future need. Federal law provides for welfare subsidies only to families with children under the age of 18; consequently, the closer one’s youngest child is to 18 (when welfare eligibility ends anyway), the smaller are the incentives of the parent to forgo the welfare subsidy and save eligibility for the future.

Work Requirements

Figure 6.16 illustrates the budget constraint associated with a minimum work requirement of 6 hours a day (30 hours per week). If the person fails to work the required 6 hours a day, no welfare benefits are received, and he or she will be along segment AB of the constraint. If the work requirement is met, but earnings are less than Yn, welfare benefits are received (see segment BCD). If the work requirement is exceeded, income (earnings plus benefits) remains at Yn—the person is along CD—until earnings rise above needed income and the person is along segment DE of the constraint and no longer eligible for welfare benefits. The work-incentive effects of this work requirement can be seen from analyzing Figure 6.16 in the context of people whose skills are such that they are potential welfare recipients. At one extreme, some potential recipients may have such steeply sloped indifferences curves (reflecting a strong preference, or a need, to stay at home) that utility is maximized along segment AB, where so little market work is performed that they do not qualify for welfare. At the opposite extreme, others may have such flat indifference curves (reflecting a strong preference for income and a weak preference for leisure) that their utility is maximized along segment DE; they work so many hours that their earnings disqualify them for welfare benefits. In the middle of the above extremes will be those whose preferences lead them to work enough to qualify for welfare benefits. Clearly, if their earnings reduce their benefits dollar for dollar—as shown by the horizontal segment DC in Figure 6.16—they will want to work just the minimum hours needed to qualify for welfare, because their utility will be maximized at point C and not along DC. (For labor supply responses to different forms of a work requirement—requisitions of food from farmers during wartime—see Example 6.7 on page 204.)

Question 21

Subsidy Programs with Positive Net Wage Rates

So far, we have analyzed the work-incentive effects of income maintenance programs that create net wage rates for program recipients that are either negative or zero (that is, they create constraints that have either a spike or a horizontal segment). Most current programs, however, including those adopted by states under PRWORA, create positive net wages for recipients. Do these programs offer a solution to the problem of work incentives? We will answer this question by analyzing a relatively recent and rapidly growing program: the Earned Income Tax Credit (EITC). The EITC program makes income tax credits available to low-income families with at least one worker. A tax credit of $1 reduces a person’s income taxes by $1, and in the case of the EITC, if the tax credit for which workers qualify exceeds their total income tax liability, the government will mail them a check for the difference. Thus, the EITC functions as an earnings subsidy, and because the subsidy goes only to those who work, the EITC is seen by many as an income maintenance program that preserves work incentives. This view led Congress to vastly expand the EITC under President Bill Clinton and it is now the largest cash subsidy program directed at low-income households with children. The tax credits offered by the EITC program vary with one’s earnings and the number of dependent children. For purposes of our analysis, which is intended to illustrate the work-incentive effects of the EITC, we will focus on the credits in the year 2009 offered to unmarried workers with two children. Figure 6.17 graphs the relevant program characteristics for a worker with two children who could earn a market (unsubsidized) wage reflected by the slope of AC. As we will see later, for such a worker, the EITC created a budget constraint of … . For workers with earnings of $12,570 or less, the tax credit was calculated at … percent of earnings. That is, for every dollar earned, a tax credit of … cents was also earned; thus, for those with earnings of under $12,570, net wages (Wn) were … percent higher than market wages (W). Note that this tax credit is represented by segment AB on the EITC constraint in Figure 6.17 and that the slope of AB exceeds the slope of the market constraint AC. The maximum tax credit allowed for a single parent with two children was $5,028 in 2009. Workers who earned between $12,570 and $16,420 per year qualified for this maximum tax credit. Because these workers experienced no increases or reductions in tax credits per added dollar of earnings, their net wage is equal to their market wage. The constraint facing workers with earnings in this range is represented by segment BD in Figure 6.17, which has a slope equal to that of segment AC. For earnings above $16,420, the tax credit was gradually phased out, so that when earnings reached $40,295, the tax credit was zero. Because after $16,420 each dollar earned reduced the tax credit by … cents, the net wage of EITC recipients was only …percent of their market wage (note that the slope of segment DE in Figure 6.17 is flatter than the slope of AC).

Looking closely at Figure 6.17, we can see that EITC recipients will be in one of three “zones”: along AB, along BD, or along DE. The incomes of workers in all three zones are enhanced, which means that all EITC recipients experience an income effect that pushes them in the direction of … work. However, the program creates quite different net wage rates in the zones, and therefore the substitution effect differs across zones. For workers with earnings below $12,570, the net wage is … than the market wage (by 40 percent), so along segment AB, workers experience an … in the price of leisure. Workers with earnings below $12,570, then, experience a … effect that pushes them in the direction of more work. With an income effect and a substitution effect that push in opposite directions, it is uncertain which effect will dominate. What we can predict, though, is that some of those who would have been out of the labor force in the absence of the EITC program will now decide to seek work (earlier, we discussed the fact that for nonparticipants in the labor force, the substitution effect dominates). Segments BD and DE represent two other zones, in which theory predicts that labor supply will …. Along BD, the net wage is equal to the market wage, so the price of leisure in this zone is …while income is …. Workers in this zone experience a … effect. Along segment DE, the net wage is actually below the market wage, so in this zone, both the income and the substitution effects push in the direction of … labor supply. Using economic theory to analyze labor supply responses induced by the constraint in Figure 6.17, we can come up with two predictions. First, if an EITC program is started or expanded, we should observe that the labor force participation rate of low-wage workers will … . Second, a new or expanded EITC program should lead to a reduction in working hours among those along… and … (the effect on hours along … is ambiguous). Several studies have found evidence consistent with prediction that the EITC should increase labor force participation, with one study finding that over half of the increase in labor force participation among single mothers from 1984 to 1996 was caused by expansions in the EITC during that period. The evidence so far, however, does not indicate a measurable drop in hours of work by those receiving the tax credit.26 Thus, the labor supply responses to the EITC are very similar to those found in labor supply studies cited earlier (see footnote 17 and Example 6.5), in that labor force participation rates seem to be more responsive to wage changes than are the hours of work.

Answer 21

Subsidy Programs with Positive Net Wage Rates

So far, we have analyzed the work-incentive effects of income maintenance programs that create net wage rates for program recipients that are either negative or zero (that is, they create constraints that have either a spike or a horizontal segment). Most current programs, however, including those adopted by states under PRWORA, create positive net wages for recipients. Do these programs offer a solution to the problem of work incentives? We will answer this question by analyzing a relatively recent and rapidly growing program: the Earned Income Tax Credit (EITC). The EITC program makes income tax credits available to low-income families with at least one worker. A tax credit of $1 reduces a person’s income taxes by $1, and in the case of the EITC, if the tax credit for which workers qualify exceeds their total income tax liability, the government will mail them a check for the difference. Thus, the EITC functions as an earnings subsidy, and because the subsidy goes only to those who work, the EITC is seen by many as an income maintenance program that preserves work incentives. This view led Congress to vastly expand the EITC under President Bill Clinton and it is now the largest cash subsidy program directed at low-income households with children. The tax credits offered by the EITC program vary with one’s earnings and the number of dependent children. For purposes of our analysis, which is intended to illustrate the work-incentive effects of the EITC, we will focus on the credits in the year 2009 offered to unmarried workers with two children. Figure 6.17 graphs the relevant program characteristics for a worker with two children who could earn a market (unsubsidized) wage reflected by the slope of AC. As we will see later, for such a worker, the EITC created a budget constraint of ABDEC. For workers with earnings of $12,570 or less, the tax credit was calculated at 40 percent of earnings. That is, for every dollar earned, a tax credit of 40 cents was also earned; thus, for those with earnings of under $12,570, net wages (Wn) were 40 percent higher than market wages (W). Note that this tax credit is represented by segment AB on the EITC constraint in Figure 6.17 and that the slope of AB exceeds the slope of the market constraint AC. The maximum tax credit allowed for a single parent with two children was $5,028 in 2009. Workers who earned between $12,570 and $16,420 per year qualified for this maximum tax credit. Because these workers experienced no increases or reductions in tax credits per added dollar of earnings, their net wage is equal to their market wage. The constraint facing workers with earnings in this range is represented by segment BD in Figure 6.17, which has a slope equal to that of segment AC. For earnings above $16,420, the tax credit was gradually phased out, so that when earnings reached $40,295, the tax credit was zero. Because after $16,420 each dollar earned reduced the tax credit by 21 cents, the net wage of EITC recipients was only 79 percent of their market wage (note that the slope of segment DE in Figure 6.17 is flatter than the slope of AC).

Looking closely at Figure 6.17, we can see that EITC recipients will be in one of three “zones”: along AB, along BD, or along DE. The incomes of workers in all three zones are enhanced, which means that all EITC recipients experience an income effect that pushes them in the direction of less work. However, the program creates quite different net wage rates in the zones, and therefore the substitution effect differs across zones. For workers with earnings below $12,570, the net wage is greater than the market wage (by 40 percent), so along segment AB, workers experience an increase in the price of leisure. Workers with earnings below $12,570, then, experience a substitution effect that pushes them in the direction of more work. With an income effect and a substitution effect that push in opposite directions, it is uncertain which effect will dominate. What we can predict, though, is that some of those who would have been out of the labor force in the absence of the EITC program will now decide to seek work (earlier, we discussed the fact that for nonparticipants in the labor force, the substitution effect dominates). Segments BD and DE represent two other zones, in which theory predicts that labor supply will fall. Along BD, the net wage is equal to the market wage, so the price of leisure in this zone is unchanged while income is enhanced. Workers in this zone experience a pure income effect. Along segment DE, the net wage is actually below the market wage, so in this zone, both the income and the substitution effects push in the direction of reduced labor supply. Using economic theory to analyze labor supply responses induced by the constraint in Figure 6.17, we can come up with two predictions. First, if an EITC program is started or expanded, we should observe that the labor force participation rate of low-wage workers will increase. Second, a new or expanded EITC program should lead to a reduction in working hours among those along BD and DE (the effect on hours along AB is ambiguous). Several studies have found evidence consistent with prediction that the EITC should increase labor force participation, with one study finding that over half of the increase in labor force participation among single mothers from 1984 to 1996 was caused by expansions in the EITC during that period. The evidence so far, however, does not indicate a measurable drop in hours of work by those receiving the tax credit.26 Thus, the labor supply responses to the EITC are very similar to those found in labor supply studies cited earlier (see footnote 17 and Example 6.5), in that labor force participation rates seem to be more responsive to wage changes than are the hours of work.