CHPTER 19 Indifference Curve nalysis of Labor Supply PPENDIX In the body of this chapter, we explained why the labor supply curve can slope downward instead of upward: the substitution effect of a higher wage rate, which provides an incentive to work longer hours, can be outweighed by the income effect of a higher wage rate, which may lead individuals to consume more leisure. In this appendix we show how this analysis can be carried out using the indifference curves introduced in the appendix to Chapter 1. The Time llocation Budget Line Let s return to the example of Clive, who likes leisure but also likes having money to spend. We now assume that Clive has a total of 8 hours per week that he could spend either working or enjoying as leisure time. (The remaining hours in his week, we assume, are taken up with necessary activities, mainly sleeping.) Let s also assume, initially, that his hourly wage rate is $1. His consumption possibilities are defined by the time allocation budget line in Figure 19-1, a budget line that shows Clive s trade-offs between consumption of leisure and income. Hours of leisure per week are measured on the horizontal axis, and the money he earns from working is measured on the vertical axis. The horizontal intercept, point X, is at 8 hours: if Clive didn t work at all, he would have 8 hours of leisure per week but would not earn any money. The vertical intercept, point, is at $8: if Clive worked all the time, he would earn $8 per week. Why can we use a budget line to describe Clive s time allocation? The budget lines found in Chapter 1 and its appendix represent the trade-offs facing time allocation budget line shows an individual s trade-off between consumption of leisure and the income that allows consumption of marketed goods. 19-1 The Time llocation Budget Line Clive s time allocation budget line shows his tradeoff between work, which pays a wage rate of $1 per hour, and leisure. t point X he allocates all his time, 8 hours, to leisure but has no income. t point he allocates all his time to work, earning $8, but consumes no leisure. His hourly wage rate of $1, the opportunity cost of an hour of leisure, is equal to minus the slope of the time allocation budget line. We have assumed that point, at 4 hours of leisure and $4 in income, is Clive s optimal time allocation. It obeys the optimal time allocation rule: the additional utility Clive gets from one more hour of leisure must equal the additional utility he gets from the goods he can purchase with one hour s wages. $8 4 Optimal time allocation Time allocation X budget line, BL 4 8 Quantity of leisure (hours per week) 559 PGES NOT FINL KrugWellsEC3e_Econ_CH19.indd 559
56 PRT 9 FCTOR MRKETS ND RISK PGES NOT FINL The optimal time allocation rule says that an individual should allocate time so that the marginal utility gained from the income earned from an additional hour worked is equal to the marginal utility of an additional hour of leisure. consumers deciding how to allocate their income among different goods. Here, instead of asking how Clive allocates his income, we ask how he allocates his time. But the principles underlying the allocation of income and the allocation of time are the same: each involves allocating a fixed amount of a resource (8 hours of time in this case) with a constant trade-off (Clive must forgo $1 for each additional hour of leisure). So using a budget line is just as appropriate for time allocation as it is for income allocation. s in the case of ordinary budget lines, opportunity cost plays a key role. The opportunity cost of an hour of leisure is what Clive must forgo by working one less hour $1 in income. This opportunity cost is, of course, Clive s hourly wage rate and is equal to minus the slope of his time allocation budget line. ou can verify this by noting that the slope is equal to minus the vertical intercept, point, divided by the horizontal intercept, point X that is, $8/(8 hours) = $1 per hour. To maximize his utility, Clive must choose the optimal point on the time allocation budget line in Figure 19-1. In Chapter 1 we saw that a consumer who allocates spending to maximize utility finds the point on the budget line that satisfies the utility-maximizing principle of marginal analysis: the marginal utility per dollar spent on two goods must be equal. lthough Clive s involves allocating time rather than money, the same principles apply. Since Clive spends time rather than money, the counterpart of the utilitymaximizing principle of marginal analysis is the optimal time allocation rule: the marginal utility Clive gets from the extra money earned from an additional hour spent working must equal the marginal utility of an additional hour of leisure. The Effect of a Higher Wage Rate Depending on his tastes, Clive s utility - maximizing of hours of leisure and income could lie anywhere on the time allocation budget line in Figure 19-1. Let s assume that his optimal is point, at which he consumes 4 hours of leisure and earns $4. Now we are ready to link the analysis of time allocation to labor supply. When Clive chooses a point like on his time allocation budget line, he is also choosing the quantity of labor he supplies to the labor market. By choosing to consume 4 of his 8 available hours as leisure, he has also chosen to supply the other 4 hours as labor. Now suppose that Clive s wage rate doubles, from $1 to $2 per hour. The effect of this increase in his wage rate is shown in Figure 19-2. His time allocation budget line rotates outward: the vertical intercept, which represents the amount he could earn if he devoted all 8 hours to work, shifts upward from point to point Z. s a result of the doubling of his wage, Clive would earn $1,6 instead of $8 if he devoted all 8 hours to working. But how will Clive s time allocation actually change? s we saw in the chapter, this depends on the income effect and substitution effect that we learned about in Chapters 1 and its appendix. The substitution effect of an increase in the wage rate works as follows. When the wage rate increases, the opportunity cost of an hour of leisure increases; this induces Clive to consume less leisure and work more hours that is, to substitute hours of work in place of hours of leisure as the wage rate rises. If the substitution effect were the whole story, the individual labor supply curve would look like any ordinary supply curve and would always slope upward a higher wage rate leads to a greater quantity of labor supplied. What we learned in our analysis of demand was that for most consumer goods, the income effect isn t very important because most goods account for only a very small share of a consumer s spending. In addition, in the few cases of goods where KrugWellsEC3e_Econ_CH19.indd 56
PGES NOT FINL CHPTER 19 PPENDIX INDIFFERENCE CURVE NLSIS OF LBOR SUPPL 561 19-2 n Increase in the Wage Rate The two panels show Clive s initial optimal, point, on BL 1, the time allocation budget line corresponding to a wage rate of $1. fter his wage rate rises to $2, his budget line rotates out to the new budget line, BL 2 : if he spends all his time working, the amount of money he earns rises from $8 to $1,6, reflected in the movement from point to point Z. This generates two opposing effects: the substitution effect pushes him to consume less leisure and to work more hours; the income effect pushes him to consume more leisure and to work fewer hours. Panel (a) shows the change in time allocation when the substitution effect is stronger: Clive s new optimal is point B, representing a decrease in hours of leisure to 3 hours and an increase in hours of labor to 5 hours. In this case the individual labor supply curve slopes upward. Panel (b) shows the change in time allocation when the income effect is stronger: point C is the new optimal, representing an increase in hours of leisure to 5 hours and a decrease in hours of labor to 3 hours. Now the individual labor supply curve slopes downward. $1,6 8 Z (a) The Substitution Effect Dominates B 3 New optimal Initial optimal BL 2 BL 1 X 4 8 Quantity of leisure (hours per week) (b) The Effect Dominates $1,6 Z Initial optimal 8 C New optimal BL 2 BL 1 X 4 5 8 Quantity of leisure (hours per week) the income effect is significant for example, major purchases like housing it usually reinforces the substitution effect: most goods are normal goods, so when a price increase makes a consumer poorer, he or she buys less of that good. In the labor/leisure, however, the income effect takes on a new significance, for two reasons. First, most people get the great majority of their income from wages. This means that the income effect of a change in the wage rate is not small: an increase in the wage rate will generate a significant increase in income. Second, leisure is a normal good: when income rises, other things equal, people tend to consume more leisure and work fewer hours. So the income effect of a higher wage rate tends to reduce the quantity of labor supplied, working in opposition to the substitution effect, which tends to increase the quantity of labor supplied. So the net effect of a higher wage rate on the quantity of labor Clive supplies could go either way depending on his preferences, he might choose to supply more labor, or he might choose to supply less labor. The two panels of Figure 19-2 illustrate these two outcomes. In each panel, point represents Clive s initial consumption. Panel (a) shows the case in which KrugWellsEC3e_Econ_CH19.indd 561
562 PRT 9 FCTOR MRKETS ND RISK PGES NOT FINL 19-3 Backward-Bending Individual Labor Supply Curve t lower wage rates, the substitution effect dominates the income effect for this individual. This is illustrated by the movement along the individual labor supply curve from point to point B: a rise in the wage rate from W 1 to W 2 leads the quantity of labor supplied to increase from L 1 to L 2. But at higher wage rates, the income effect dominates the substitution effect, shown by the movement from point B to point C: here, a rise in the wage rate from W 2 to W 3 leads the quantity of labor supplied to decrease from L 2 to L 3. Wage rate W 3 W 2 Individual labor supply curve C B W 1 L 1 L 3 L 2 Quantity of labor (hours per week) Clive works more hours in response to a higher wage rate. n increase in the wage rate induces him to move from point to point B, where he consumes less leisure than at and therefore works more hours. Here the substitution effect prevails over the income effect. Panel (b) shows the case in which Clive works fewer hours in response to a higher wage rate. Here, he moves from point to point C, where he consumes more leisure and works fewer hours than at. Here the income effect prevails over the substitution effect. When the income effect of a higher wage rate is stronger than the substitution effect, the individual labor supply curve, which shows how much labor an individual will supply at any given wage rate, slopes the wrong way downward: a higher wage rate leads to a smaller quantity of labor supplied. Economists believe that the substitution effect usually dominates the income effect in the labor supply decision when an individual s wage rate is low. n individual labor supply curve typically slopes upward for lower wage rates as people work more in response to rising wage rates. But they also believe that many individuals have stronger preferences for leisure and will choose to cut back the number of hours worked as their wage rate continues to rise. For these individuals, the income effect eventually dominates the substitution effect as the wage rate rises, leading their individual labor supply curves to change slope and to bend backward at high wage rates. n individual labor supply curve with this feature, called a backward - bending individual labor supply curve, is shown in Figure 19-3. lthough an individual labor supply curve may bend backward, market labor supply curves almost always slope upward over their entire range as higher wage rates draw more new workers into the labor market. backward - bending individual labor supply curve is an individual labor supply curve that slopes upward at low to moderate wage rates and slopes downward at higher wage rates. Indifference Curve nalysis In the appendix to Chapter 1, we showed that consumer can be represented using the concept of indifference curves, which provide a map of consumer preferences. If you have covered the appendix, you may find it interesting to learn that indifference curves are also useful for addressing the issue of labor supply. In fact, this is one place where they are particularly helpful. KrugWellsEC3e_Econ_CH19.indd 562
PGES NOT FINL CHPTER 19 PPENDIX INDIFFERENCE CURVE NLSIS OF LBOR SUPPL 563 19-4 Labor Supply Choice: The Indifference Curve pproach Point, on BL 1, is Clive s initial optimal. fter a wage rate increase, his income and utility level increase: his new time allocation budget line is BL 2 and his new optimal is point C. This change can be decomposed into the substitution effect, the fall in the hours of leisure from point to point S, and the income effect, the increase in the number of hours of leisure from point S to point C. s shown here, the income effect dominates the substitution effect: the net result of an increase in the wage rate is an increase in the hours of leisure consumed and a decrease in the hours of labor supplied. $1,6 8 Z effect Initial optimal S C New optimal I 1 I 2 BL 2 BL S BL 1 X 8 Quantity of leisure Substitution effect (hours per week) Using indifference curves, Figure 19-4 shows how an increase in the wage rate can lead to a fall in the quantity of labor supplied. Point is Clive s initial optimal, given an hourly wage rate of $1. It is the same as point in Figure 19-2; this time, however, we include an indifference curve to show that it is a point at which the budget line is tangent to the highest possible indifference curve. Now consider the effect of a rise in the wage rate to $2. Imagine, for a moment, that at the same time Clive was offered a higher wage, he was told that he had to start repaying his student loan and that the good-news / bad - news combination left his utility unchanged. Then he would find himself at point S: on the same indifference curve as at, but tangent to a steeper budget line, the dashed line BL S in Figure 19-4, which is parallel to BL 2. The move from point to point S is the substitution effect of his wage increase: it leads him to consume less leisure and therefore supply more labor. But now cancel the repayment on the student loan, and Clive is able to move to a higher indifference curve. His new optimum is at point C, which corresponds to C in panel (b) of Figure 19-2. The move from point S to point C is the income effect of his wage increase. nd we see that this income effect can outweigh the substitution effect: at C he consumes more leisure, and therefore supplies less labor, than he did at. PROBLEMS 1. Leandro has 16 hours per day that he can allocate to work or leisure. His job pays a wage rate of $2. Leandro decides to consume 8 hours of leisure. His indifference curves have the usual shape: they slope downward, they do not cross, and they have the characteristic convex shape. a. Draw Leandro s time allocation budget line for a typical day. Then illustrate the indifference curve at his optimal. Now Leandro s wage rate falls to $1. b. Draw Leandro s new budget line. c. Suppose that Leandro now works only 4 hours as a result of his reduced wage rate. Illustrate the indifference curve at his new optimal. d. Leandro s decision to work less as the wage rate falls is the result of a substitution effect and an income effect. In your diagram, show the income effect and the substitution effect from this reduced wage rate. Which effect is stronger? KrugWellsEC3e_Econ_CH19.indd 563
564 PRT 9 FCTOR MRKETS ND RISK PGES NOT FINL 2. Florence is a highly paid fashion consultant who earns $1 per hour. She has 16 hours per day that she can allocate to work or leisure, and she decides to work for 12 hours. a. Draw Florence s time allocation budget line for a typical day, and illustrate the indifference curve at her optimal. One of Florence s clients is featured on the front page of Vague, an influential fashion magazine. s a result, Florence s consulting fee now rises to $5 per hour. Florence decides to work only 1 hours per day. b. Draw Florence s new time allocation budget line, and illustrate the indifference curve at her optimal. c. In your diagram, show the income effect and the substitution effect from this increase in the wage rate. Which effect is stronger? 3. Tamara has 8 hours per week that she can allocate to work or leisure. Her job pays a wage rate of $2 per hour, but Tamara is being taxed on her income in the following way. On the first $4 that Tamara makes, she pays no tax. That is, for the first 2 hours she works, her net wage what she takes home after taxes is $2 per hour. On all income above $4, Tamara pays a 75% tax. That is, for all hours above the first 2 hours, her net wage rate is only $5 per hour. Tamara decides to work 3 hours. Her indifference curves have the usual shape. a. Draw Tamara s time allocation budget line for a typical week. lso illustrate the indifference curve at her optimal. The government changes the tax scheme. Now only the first $1 of income is tax - exempt. That is, for the first 5 hours she works, Tamara s net wage rate is $2 per hour. But the government reduces the tax rate on all other income to 5%. That is, for all hours above the first 5 hours, Tamara s net wage rate is now $1. fter these changes, Tamara finds herself exactly equally as well off as before. That is, her new optimal is on the same indifference curve as her initial optimal. b. Draw Tamara s new time allocation budget line on the same diagram. lso illustrate her optimal. Bear in mind that she is equally as well off (on the same indifference curve) as before the tax changes occurred. c. Will Tamara work more or less than before the changes to the tax scheme? Why? www.worthpublishers.com/krugmanwells KrugWellsEC3e_Econ_CH19.indd 564