Answers To Chapter 6. Review Questions

Answers To Chapter 6 Review Questions 1 Answer d Individuals can also affect their hours through working more than one job, vacations, and leaves of absence 2 Answer d Typically when one observes indifference curves crossing on a graph, for example in Figure 6-4, they represent the preferences of different individuals If they pertain to the same person, than the point of intersection simultaneously yields two different levels of happiness, which violates the basic notion that the person can consistently rank different combinations of leisure and income Steep indifference curves indicate a high value for leisure, since the person requires a large amount of income to offset a small sacrifice of leisure 3 Answer a The wage rate is reflected in the slope of the constraint Note that nonlabor income is $200 and the optimal number of hours to supply is 100 4 Answer d When indifference curves are drawn with a convex shape, it ensures that when one moves from an extreme combination (one where there is a lot of one good but not much of the other) to one where the goods are more evenly consumed, a higher indifference curve will be attained In other words, the convex shape of the indifference curves is a way to make the statement that people prefer variety to extremes 5 Answer c The objective of the consumer is not to maximize income or leisure but to find that combination of income and leisure that is consistent with the budget constraint and leads to the highest level of utility Since higher indifference curves represents higher levels of utility, maximizing utility can be thought of as trying to get on the highest attainable indifference curve Note that it is impossible for both leisure and income to be maximized at the same point 6 Answer d When this condition holds, a window of opportunity exists for the individual to attain a higher level of utility by moving to a point involving less than the maximum leisure time Very steep indifference curves can result in a corner solution 7 Answer c When work is viewed as something good, leisure implicitly becomes something bad Leisure is bad here when it exceeds 350 hours: when one gets more of it, income must go up, not down, to keep the person at the same level of satisfaction This creates the upward slope to the indifference curves 8 Answer c Usually when the budget constraint has a flat segment, representing a guaranteed income, the optimum occurs at the point of maximum leisure But because after a point, leisure is viewed as bad, the optimum occurs at 50 hours of work The market wage is $4, with an implicit tax of 100% on the first $400 of earnings, zero thereafter

274 Ehrenberg/Smith Modern Labor Economics: Theory and Public Policy, Tenth Edition 9 Answer b For a person working zero hours, an increase in the wage cannot lead them to reduce hours even further So, although there is theoretically an income effect if the person makes any changes, her income will rise in practical terms it must be dominated by the substitution effect 10 Answer a If leisure were an inferior good, then the income effect associated with the wage increase would actually cause the person to cut back on leisure This, together with a positive substitution effect, would ensure work hours would go up 11 Answer d Typically, goods do not switch from being normal to inferior, but even if they did, the curve described in answer c could never turn back, since leisure being inferior guarantees that portion of the curve would be upward sloping 12 Answer a Hours supplied should go up because such a change creates a pure substitution effect The lower marginal tax rate is like an increase in the wage, but the assumption that the total taxes paid by workers remains constant means that income remained constant 13 Answer a A lump sum payment unrelated to earnings is an increase in nonlabor income that shifts the budget constraint out parallel to the old constraint, thus creating a pure income effect 14 Answer b Scheduled benefits unrelated to earnings create a parallel shift of the constraint Hence, the opportunity cost of leisure remains the market wage rate, and so an incentive to work is preserved 15 Answer d The maximum subsidy (S) is $600, and the breakeven income (S/t) is $1,200 Therefore, the value of t must be 05 With an implicit tax rate of 05, the initial subsidy will be completely taken away by the time earnings reach $1,200 16 Answer d The new optimum occurs at 350 (H = 50) The actual subsidy equals S t(wh) = $600 5($200) = $500 17 Answer b The substitution effect is the movement from the point ( 247, Y = $990) to the point ( 350, Y = $700) 18 Answer b The income effect is the movement from the point ( 200, Y = $800) to the point ( 247, Y = $990) 19 Answer b As the implicit tax rate increases, the effective wage rate decreases, lowering the opportunity cost of leisure, and reducing work incentives for most individuals An exception to this tendency is exhibited in Problem 30 20 Answer d While reducing the implicit tax rate tends to preserve work incentives, it extends the reach of the program (potentially to everyone if t = 0) As more people are eligible for the program, the cost of the program tends to go up 21 Answer c The lowest income recipients actually face an above-market wage, creating a substitution effect in favor of working, working against the income effect allowing more leisure Without knowing about preferences, one cannot predict the net response For higher income eligibles, either a zero implicit tax, or a positive implicit tax on earnings exists, so there is nothing to counteract the income effect, and a substitution effect may even reinforce it, reducing work effort

Answers To Chapter 6 275 22 Answer d Many who work for minimum wages do not live in low-income households, and although their impact on work incentives may be positive (they are theoretically ambiguous), they may result in reduced hours because of employer cutbacks As noted in the text, subsidies given to employers to hire low-income workers have not been very successful, and in some cases appear to have worsened the target population s chances of finding employment by identifying them as potential problem employees Problems 23a See the solid line in Figure 6-9 Figure 6-9 23b See the dashed line in Figure 6-9 23c Increased appreciation for leisure relative to income tends to make the indifference curves steeper It takes larger amounts of income to compensate for a given sacrifice of leisure 24a See the solid line in Figure 6-10 Figure 6-10

276 Ehrenberg/Smith Modern Labor Economics: Theory and Public Policy, Tenth Edition 24b See the dashed line in Figure 6-10 25a Full income (WT + V ) for the original budget line is $2,700 Noticing that V = $300 and T = 400, the original wage was $6 Similarly, after the wage decrease the new level of full income is $1,500, which implies a wage of $3, given the same values of V and T 25b The income effect is the movement from the point ( 225, Y = $1350) to the point ( 177, $Y = 1061), a decrease of 48 leisure hours The substitution effect is the movement from the point ( 177, Y = $1061) to the point ( 250, Y = $750), an increase of 73 leisure hours 25c The two points would be (W = $6, H = 175), and (W = $3, H = 150) The curve is positively sloped The substitution effect is stronger than the income effect in 25b 26a Given that preferences are represented by the Cobb-Douglas utility function, the expression for the optimal level of leisure is * α WT + V Substituting the values that apply before the injury yields 8 (H = 8), Y = $40, and U = 320 26b If all the income is replaced after an injury, then 16, Y = $40, and U = 640, a higher level of utility than that attained while working 26c To keep the worker at U = 320, solve the equation (16)(Y) = 320 This implies Y = $20 Therefore, to keep utility constant, only 50% of the original income needs to be replaced This whole analysis, of course, assumes that all leisure time is identical That is, leisure time obtained through injury yields the same utility as leisure time taken while healthy This may not be the case, for example, if the injury is painful or limiting 27a Given that preferences are represented by the Cobb-Douglas utility function, the expression for the optimal level of leisure is * α WT + V (Note that both α and β = 1 in this example) Substituting the values that apply before the welfare program, the original optimum is 200 leisure hours (200 work hours) With t = 1, the effective wage, given by the expression (1 t)w, becomes zero and while we cannot divide by zero, the optimum occurs at the maximum of 400 leisure hours (zero work hours) With t = 05, the effective wage rate is $2 Combining this with $500 in nonlabor income yields an optimum of 325 leisure hours (75 work hours) With t = 0, the effective wage remains the market wage of $4 Combining this with the nonlabor income of $500 yields an optimum of 2625 leisure hours (1375 work hours) Summarizing, t = 1 implies H falls by 200, t = 05 implies H falls by 125, and t = 0 implies H falls by 625

Answers To Chapter 6 277 27b An implicit tax rate of zero preserves work incentives the best since the opportunity cost of leisure remains the market wage Hours of work still fall under such a program because of the income effect of the subsidy, but there is no reinforcing substitution effect if implicit taxes do not reduce the effective wage rate 28a The breakeven income occurs at the value S/t So for constraint acdb we have 350/t = 350, which implies t = 1 For the constraint aceb we have 350/t = 1400, which implies t = 025 Note that when we can view the breakeven point graphically, the tax rate can be calculated as S/B = t, or in the two cases here, 350/350 = 1 and 350/1400 = 025 28b For these preferences, t = 1 provides the strongest work incentives The reason for this somewhat unusual result is that when t is reduced, the reach of the program (as illustrated by the breakeven point) is expanded dramatically In this case, the person would not even have been affected by the program with the high implicit tax rate The lower rate, however, enables the person to be eligible for the program and experience the income and substitution effects it creates 29a See Figure 6-11 The breakeven point occurs at 1,600 (H = 1,200) and Y = $6,000 Figure 6-11 29b Given that preferences are represented by the Cobb-Douglas utility function, the expression for the optimal level of leisure is * α WT + V Substituting the values that apply before the program is enacted yields an optimum of 1,400 (H = 1,400) and Y = $7,000 This is point a in Figure 6-11 The level of utility (denoted by U 1 ) is 9,800,000 29c Using the graph as a guide, it appears likely that the individual will be pulled into the program, even though they are currently above the breakeven point The optimal point appears to be the corner of the constraint which occurs at 2,000, Y = $6,000 Notice that the level of utility at this point is 12,000,000 This represents an improvement over the original point The optimum is identical to that which would have been achieved if benefits were simply cut off once earnings reached $4,000 No one who values both leisure and income would want to locate along the horizontal segment of the constraint when moving to the corner of the constraint is possible

278 Ehrenberg/Smith Modern Labor Economics: Theory and Public Policy, Tenth Edition Applications 30a See Figure 6-12 The breakeven point occurs at 175 (H = 225), Y = $900 The value of S/t = 200/04 = $500 in this case represents the additional income needed to reduce the subsidy to zero once the person qualifies for the program Note that in this case, however, the person does not qualify for the program immediately, but rather works 100 hours, and hence earns $400, before the usual type of income maintenance program begins Figure 6-12 30b Given that preferences are represented by the Cobb-Douglas utility function, the expression for the optimal level of leisure is α WT + V * For α = 065, β = 035, the optimal combination before the program was 260 (H = 140), Y = $560 This is point a in Figure 6-12 After the program, the person should end up at the corner of the new constraint (point d) Since the corner point has coordinates 300 (H = 100), Y = $600, this represents a reduction in work hours of 40 For α = 075, β = 025, the optimal combination before the program was 300 (H = 100), Y = $400 This is point b in Figure 6-12 After the program, the person should also end up at the corner of the new constraint (point d) There will be no reduction in work hours For α = 085, β = 015, the optimal combination before the program was 340 (H = 60), Y = $240 This is point c in Figure 6-12 After the program, the person should also end up at the corner of the new constraint (point d ) This represents an increase in work hours of 40 30c While some people will reduce their work hours due to the income and substitution effects such programs can create, the possibility of such individuals dropping out of the labor force is very remote Also, some individuals will actually increase their hours just enough to cross over the threshold and qualify for the program s maximum benefit Such thresholds seem like a sensible way to preserve at least some minimal work incentives

Answers To Chapter 6 279 31a See Figure 6-13 The original earnings constraint is line ab Under this EITC, the maximum subsidy first occurs where earnings equal $9,000 This occurs where 1,500 (H = 1,500) This is point c in Figure 6-13 The level of total income (including the government payment) will be Y = $11,700 (point d ) The maximum subsidy continues to be received until earnings = $12,000 (point e) This occurs where 1,000 (H = 2,000) Factoring in the subsidy, total income is $14,700 at 1,000 (point f ) The breakeven point occurs when earnings equal $18,000 (point b) Once the person has reached point e, an additional $6,000 in earnings at an implicit tax rate of 045 just eliminates the $2,700 subsidy ($6,000 045 = $2,700) To achieve the additional $6,000 in earnings, the person must increase work hours (reduce leisure) by 1,000 hours Figure 6-13 31b To the right of point d, the individual is accumulating income according to the formula income = WH + 3(WH), which makes the effective wage rate (the absolute value of the slope of the constraint) (13)(W) which equals 78 To the left of point f, the effective wage rate is (1 t)w, where t = 045 This means that the absolute value of the slope is 33 31c A person originally at point g will experience both an income effect and a substitution effect The substitution effect will push the person in the direction of more work, while the income effect will tend to counteract this At low levels of work hours, however, the income effect tends to be relatively small, and so it is likely that the substitution effect will dominate the income effect and the person will work more 31d A person originally to the left of point c will tend to reduce work hours The extent of the reduction depends on whether the person originally worked more or less than 2,000 hours If the person worked more than 1,500 hours but less than 2,000 hours, he will experience just a pure income effect If the person worked in excess of 2,000 hours, he will experience reinforcing income and substitution effects Note for H > 2,000, the position of the constraint moves out at the same time that it becomes flatter This creates a strong incentive to work less, and many workers are likely to end up near point f

280 Ehrenberg/Smith Modern Labor Economics: Theory and Public Policy, Tenth Edition *32a See Figure 6-14 Figure 6-14 *32b The 40% marginal tax rate applies after $1,000 in total income is reached With nonlabor income of $200, that income level is reached when 200 (H = 200) This is point a in Figure 6-14 The tax reduces total income by 20 percent to a total of $800 (point b) The effective wage rate (the slope of the constraint) is now (1 t)w, where t is the marginal tax rate To the right of point b, the slope is (1 2)4 = 32 To the left of point b, the slope is (1 4)4 = 24 *32c Given that preferences are represented by the Cobb-Douglas utility function, the expression for the optimal level of leisure is * α WT + V Substituting the appropriate values leads to an optimum of 225 (H = 175), Y = $900 (point c) before the tax After the tax, the level of nonlabor income falls to $160 and the effective wage rate is 32 Substituting into the L * expression again yields 225 (H = 175), but Y is now lower at $720 There is no change in labor supply since the income and substitution effects of the tax change have exactly canceled one another This combination is point d The person has paid $180 in taxes, making for an average tax rate of $180/$900 = 20% *32d What is the value of Y on the after-tax constraint when H = 400? H = 400 implies Y = $1800 When total income is $1800, the person pays $200 on the first $1,000 he earned, plus $320 on the next $800, for a total after-tax income of $1,280 If WT + V = $1,280, and W is $24 and T is 400, the implicit value of V is $320 *32e Making the appropriate substitutions into the L * expression yields 1125 (H = 2875), Y = $1,350 before the tax program (point e) After the tax program, substitute W = $24 and V = $320 into the L * expression to find 13333, (H = 26667), Y = $960 (point f ) Hours of work are reduced modestly because of the stronger substitution effect of the higher marginal tax rate The total tax paid is 20% of $1,000 plus 40% of $350, for a total of $340 Note that this is not the difference between $1,350 and $960, since the $960 reflects the lower level of work hours that the tax induced The average tax rate is $340/$1,350 = 2519%

Answers To Chapter 6 281 *32f Significantly higher marginal tax rates can result in appreciable reductions in the work hours of higher-income individuals 33a Given that preferences are represented by the Cobb-Douglas utility function, the expression for the optimal level of leisure is * α WT + V With both fixed monetary and time costs of working it is as if V is only $100 and T is 370 hours This leads to an optimum at 1975 (H = 1725) and Y = $790 This yields a utility level of 156,025 This does exceed the utility associated with not participating in the labor force since the combination 400, Y = $200 yields a utility level of 80,000 33b Telecommuting would return V to $200 and T to 400, leading to an optimum at 225 (H = 175) and Y = $900 Utility would now be 202,500 In this example, telecommuting leads to higher levels of leisure, work, income, and utility