Chapter 2: The Theory of Individual Labour Supply PDF

Chapter 2 The Theory of Individual Labor Supply McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. 1. The Work-Leisure Decision: Basic Model 2-2  Assumptions Individuals choose between work and...

Chapter 2 The Theory of Individual Labor Supply McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. 1. The Work-Leisure Decision: Basic Model 2-2  Assumptions Individuals choose between work and leisure. – Work is time spent on a paying job. – Leisure includes activities where one is not paid. Education Rest Work within the household 2-3  Indifference Curve Income/day The indifference curve shows work and leisure combinations that yield the same amount of total utility. More hours of leisure implies fewer hours of work. 0 24 Leisure Hr 24 0 Work Hr 2-4  Indifference Curve Properties Negative slope – To keep the level of utility the same, if one get more leisure, some of income must be given up. Convex to origin – With low hours of leisure, individuals are willing to give up a large amount of income to get 1 more leisure hour. 2-5 Indifference Curve Properties – With high hours of leisure, individuals are willing to give up a small amount of income to get 1 more leisure hour. 2-6  Marginal Rate of Substitution The marginal rate of Income/day substitution (MRS) is the amount of income one must give up to compensate for 1 more 4 hour if leisure. At 3 hours of leisure (21 hours of work), one must give up 4 units of income 1 to compensate for 1more hour of leisure. At 8 hours of leisure (16 hours of work), one must give up 1 unit of income to compensate for 1 more hour of leisure. 0 34 89 24 Leisure The MRS falls as one 24 0 Work moves southeast along an indifference curve. 2-7  Indifference Map Income/day Curves further from the origin indicate higher utility. Combination L2Y2 is preferred to combination L1Y1 since one gets both Y2 more income and more Y1 I3 leisure. I2 A person will maximize I1 utility by getting to the highest attainable indifference curve. 0 L1 L2 24 Leisure 2-8  Work-Leisure Preferences Income/day “Leisure lovers” place a high value on leisure. The have a steep indifference curve. They are willing to sacrifice a IB large amount of income IA to get a small increase in leisure. “Workaholics” place a low value on leisure. The have a flat indifference I2 curve. They must be I1 given a large increase in leisure to compensate for a small decrease in income. 0 24 Leisure 2-9  Budget Constraint The budget constraint Income/day shows the combinations of income and leisure that a worker could get given a wage rate. At a wage rate of $5, a $360 worker could get a maximum income of $120 $240 per day ($5/hour * 24 ). At a wage rate of $10, a worker could get a $120 maximum income of $240 per day. At a wage rate of $15, a worker could get a maximum income of 0 24 Leisure $360 per day. The slope of the budget 2-10 constraint is–wage rate.  Utility Maximization The optimal or utility maximizing point is where Income/day the budget constraint is tangent to the highest attainable indifference curve (U). At U, the MRS (slope of the indifference curve) is the equal to the wage rate $240 (slope of the budget constraint) B U At B, the MRS is greater $80 I3 than the wage rate. The I2 individual values leisure A I1 more than the wage rate. At A, the MRS is less than 0 16 24 Leisure the wage rate. The individual values leisure less than the wage rate. 2-11  Backward Bending Labor Supply Curve For a given person, Wage Rate hours of work may SL increase as the wage rate rises. If the wage rate rises from $10 to $25 per $25 hour hours of work rises from 8 to 10 hours per day. $10 Above $25 per hour, hours of work fall. The backward bending labor supply curve is the result of the income and substitution effects 0 8 10 24 Hours of of a wage change. Work 2-12  Income Effect Income Effect – The change in desired hours of work resulting from a change in income, holding the wage constant. Leisure is a normal good, so higher income implies a desire for more leisure (fewer hours of work). For a wage increase, income is raised and so the income effect lowers desired work hours. 2-13  Substitution Effect Substitution Effect – The change in desired hours of work resulting from a change in the wage rate, holding income constant. A higher wage rate raises the relative price of leisure. For a wage increase, the substitution effect raises desired work hours. 2-14  Net Effect For Wage Increases – If substitution effect > income effect, then hours of work rise. – If income effect > substitution effect, then hours of work fall. For Wage Decreases – If substitution effect > income effect, then hours of work fall. – If income effect > substitution effect, then hours of work rise. 2-15  Income and Substitution Effects At a wage rate of $10/hour, the optimal hours of leisure is 16 (8 hours of work) at point Income/day U1. If the wage rate rises to $15/hour, the optimal $360 hours of leisure is 15 at point U2. The income effect (IE) is U2 measured through a $240 parallel shift of the old U2’ budget constraint. The IE I2 U1 is from U1 to U2’ (from 16 to 17 hours of leisure). I1 The substitution effect (SE) is measured by movement along I2. The SE is from U2’ to U2 (from 0 15 16 17 24 Leisure 17 to 15 hours of leisure). The net effect is an increase 2-16 of hours of work by 1 hour. Backward Bending Labor Supply Rationale The substitution effect dominates at low wage rates. – The MRS is low because income is scarce relative to leisure. The income effect dominates at higher wage rates. – The MRS is high because leisure is scarce relative to income. 2-17  Empirical Evidence The labor supply curve is slightly backward bending for men. – The income effect is slightly greater than the substitution effect. 2-18  Empirical Evidence The labor supply curve is positive for women. – If substitution effect is greater than the income effect. Women substitute between work at home and market work more than men. 2-19 Elasticity of Labor Supply The elasticity of labor supply measures the responsiveness of desired hours of work to the wage rate. = % Change in Elasticity quantity of labor supplied of Labor Supply % Change in the wage rate 2-20 Elasticity of Labor Supply If the elasticity is zero, it is perfectly inelastic. If the elasticity is negative, it is backward bending. If the elasticity is positive and less than 1, it is relatively inelastic. If the elasticity is positive and more than 1, it is relatively elastic. 2-21 Questions for Thought 1. Show the effect of a wage decrease on an individual’s income-leisure choices. Isolate the income and substitution effects. Is the worker on the forward-rising or backward bending portion of the labor supply curve? 2. Indicate in each of the following instances whether specified events would cause a worker to want to work more or fewer hours: (a) The wage rates rises and the substitution effect is greater than the income effect. (b) The wage rate falls and the income effect is greater than the substitution effect. 2-22 2. Applying and Extending the Model 2-23  Non-Labor Income At a wage rate of Income/day $10/hour with no other income, the optimal hours of leisure is 16 (8 hours of work) at point U 1. $300 If the person gets an inheritance that generates $240 $60 a day of non-labor income, the budget U2 constraint has a parallel U1 I2 shift. I1 The optimal hours of leisure rises to 17 at point U2. 0 16 17 24 Leisure With an increase in non- labor income, only the income effect occurs and 2-24 so hours work must fall.  Non-Participants If a person has a low wage Income/day rate (WN is flat), higher non- I2 labor income (NH), or steep W ’ indifference curves (I1), he is less likely to participate in the labor force (U1). I1 W If a person has a high U2 wage rate (HW’), low non- labor income (0), or flat indifference curves (I2), she is more likely to participate (U2). The reservation wage is U1 the lowest wage N necessary to induce someone to work. College students are less H likely to participate in the 0 10 24 Leisure labor force than other persons. Why? 2-25  Over-Employment If an individual is free to Income/day choose the number of hours of work, she would choose point U1, with 18 hours of leisure and 6 hours of work. If the individual is W constrained to work a standard workday of 8 hours or not all, she will choose point U2. U2 U1 At U2, her MRS is more than the wage rate and so N she feels overemployed. What is a potential solution H to her overemployment 0 16 18 24 Leisure situation? 2-26  Under-Employment Income/day If an individual is free to choose the number of hours of work, she would choose point U1, with 14 hours of work and 10 hours of leisure. W If the individual is U1 constrained to work a standard workday of 8 hours or not all, she will choose point U2. U2 At U2, her MRS is less than the wage rate and so she N feels underemployed. What is a potential solution H to her underemployment 0 10 16 24 Leisure situation? 2-27 Income Maintenance Programs There are a variety of income maintenance programs such as food stamps, Medicaid, Temporary Assistance to Needy Families. We will examine the work incentives of such programs. 2-28 Income Maintenance Program Features Income Guarantee (B) – Benefit received if individual/family has no earned income. Benefit Reduction Rate (t) – Rate by which the benefit is reduced as income is increased. At t=.50, benefits are reduced by $.50 for every dollar earned. 2-29  Income Maintenance Program Features Break-Even Level of Income (Yb) – The level of earned income at which the individual/family receives no benefit. 2-30 Benefit Example The actual subsidy payment S illustrates these concepts as shown below. S = B – tY If B = $80, t =.5, earned income (Y) = $60 then… S = $80 -.5 * $60 =$50 2-31 Benefit Example The break-even level of income formula is shown below: Yb = B/t If B = $80, t =.5, then Yb = $160 2-32  Income Maintenance At a wage rate of Program $10/hour, the optimal hours of leisure is 16 (8 hours of work) at point U1. Income/day If there is a welfare program is started with a B of $80 a day, t =.5, then Yb= $160. The income effect (IE) is measured through a parallel shift of the old budget $240 constraint. The IE is from U1 to U2’ (from 16 to 18 hours of $160 U2’ leisure). U2 The substitution effect (SE) $80 I2 is measured by movement U1 I1 along I2. The SE is from U2’ to U2 (from 18 to 22 hours of leisure). The tax lowers the “price” of leisure. 0 16 18 22 24 Leisure In contrast to a wage change, both the IE and SE reduce desired hours of 2-33 work.  Welfare Reform The main elements of the 1996 Welfare Reform Act are: – Two-year time limit for receiving assistance. – Five-year lifetime time limit for collecting assistance. – Provisions to help enforce the collection of child support payments from fathers. 2-34  Welfare Reform There has been a large reduction in caseloads since 1996. 2-35 Welfare Caseloads 2-36 Why Did Caseloads Fall? The economic boom of the 1990s helped the labor prospects of welfare recipients. The expansion of tax subsidies for working low income families encouraged recipients to seek jobs. 2-37 Why Did Caseloads Fall? The benefit time limits encouraged recipients to conserve their benefits. Welfare benefit reductions, child care expansions, and changes in training programs also likely played a role. 2-38 Questions for Thought 1. One way of aiding low-income families is to increase the minimum wage. An alternative is to provide a direct grant of non-labor income. Compare the impact of these two options on work incentives. 2. How would you expect each of the following factors to affect the probability someone chooses not to participate in the labor force? (a) Education (b) Presence of preschool children (c) Level of spouse’s income (d) Marital status 2-39