Chapter Study Outline

  • Neoclassical Approach
    • Static: the choices workers make during the given time period are considered in isolation from other periods.
    • Neoclassical: workers are rational utility maximizers who derive utility from both consuming goods and enjoying leisure time.
      • The decision maker is either an individual or a household who values consumption and leisure time.
      • The goal of the decision maker is to maximize his utility (or welfare) over a given period of time.
      • The restrictions on the individual’s actions stem from
        • an identity: there are only T = 24 hours in a day
        • market constraints: paid work means that more leisure results in lower consumption of goods and services
        • legal and policy constraints: tax structure and occupational restrictions
  • The length of the average workweek has declined substantially, from almost 60 hours a week in 1890 to about 38 hours a week today.
  • Though the average number of hours worked per week has been relatively stable over the last 50 years, there have been profound changes in the work patterns of various demographic groups.
    • From 1950 to 2009, the participation rate of women over 20 approximately doubled.
    • Over the same period, the participation rate of men over 20 declined by about 16%.

4.1 Preferences

  • Utility function: u = U(c, l) represents the individual’s tastes over different consumption-leisure pairs.
    • u = utils, representing the satisfaction derived from every conceivable consumption-leisure bundle
      • c = consumption
    • T = h + l, where T is the time endowment of 24 hours
      • h = hours worked
      • l = leisure time
    • u0 = the indifference curve of combinations of c and l over which the individual is indifferent. The combination of all indifference curves, un, forms an indifference curve map.
      • Indifference curves do not cross.
      • Indifference curves lying further to the northeast are always preferred to indifference curves lying to the southwest, since utility increases with c and l.
      • There is an indifference curve that runs through every combination of (c, l).
      • Indifference curves are negatively sloped and convex to the origin.
        • Convexity indicates that workers prefer averages to extremes in combinations of (c, l).
    • The slope of the indifference curve represents the individual’s willingness to trade consumption for additional leisure time.
      • Slope = (Δc/Δl)u0 dollars per hour
        • Δc = a small change in consumption
        • Δl = a small change in leisure
        • u0 = utility is held constant in this trade-off
      • Marginal rate of substitution, MRS = −(Δc/Δl)u0 > 0
        • The MRS is the absolute value of the slope of the indifference curve.
        • The MRS measures how much of a “bribe” the individual must be paid to compensate him for the loss of one hour of leisure.
        • The behavior of the MRS justifies the convexity of the indifference curve.
      • The MRS also provides a means to compare individuals’ work attitudes.
        • It is possible for different individuals’ indifference curves to cross. A single individual’s indifference curves will not.
        • A hardworking individual might generally have a flatter indifference curve than a lazy person, since the lazy person’s higher MRS indicates that she requires a huge increase in consumption to induce her to work more.
    • Marginal utilities
      • The marginal utility of leisure (MUl) = Δc Δl, holding c constant
      • The marginal utility of consumption (MUc) = Δc/Δl, holding l constant
        • The marginal utility of consumption represents the increase in utility from a $1 increase in consumption, holding leisure fixed.
      • ΔuMUl ∙ Δl + MUcΔc
        • Along a single indifference curve, by definition 0 = Δu MUl ∙ Δl + MUcΔc
        • Rearrangement yields the slope of the indifference curve, (Δc/Δl)u0 =MUl / MUc
        • The definition of the MRS yields MRS = MUl / MUc > 0

4.2 The Constraints

  • Assumption 4.1: Time Allocation
    • The worker enjoys l hours of leisure and works for h hours such that T = h + l = 24 hours in a day.
      • One additional hour of leisure must reduce the number of hours worked by one hour.
    • Assumption 4.2: Legal and Policy Environment
      • The only function of the government is to enforce property rights and contracts, a task that it does flawlessly.
        • This assumes away taxes and welfare payments, thereby allowing subsequent evaluation of these policies.
    • Assumption 4.3: Market Constraints
      • The worker is free to choose the number of hours (h) that he works. The hourly wage rate is a constant $W, and his initial wealth plus earned income is $A0.
        • The worker’s labor earnings are W h = W ∙ (T − l), which captures the trade-off that the opportunity cost of an additional leisure hour is forgoing $W in consumption.
      • The worker’s budget line determines the set of consumption-leisure bundles he can afford by summing labor earnings and initial wealth.
        • The budget line is given by c = A0 + W (T − l)
        • The slope of the budget line is −$W/h
        • The budget line intercepts the vertical l = T at c = $A0
          • An increase in initial wealth (A0) shifts the budget line outward, leaving the slope unchanged.
          • An increase in the wage ($W/h) pivots the budget line outward around P(T, A0), making the slope steeper.

4.3 Optimal Choice I: Determination

  • Assumption 4.4: Utility Maximization
    • The worker examines all feasible consumption-leisure combinations (c, l), and picks the one that maximizes her utility.
    • She chooses the point on the budget line that is tangent to the outermost indifference curve, at which she consumes c0* of goods and enjoys l0* of leisure.
      • l0* is an interior solution in this case because it lies strictly within the binding limits l = 0 and l = T.
      • Since the worker works a positive number of hours such that h0* = T l0* > 0, she is a labor force participant.
      • At the point of tangency the slope of the budget line equals the slope of the worker’s highest attainable indifference curve so that W = MRS.
        • The optimal choice (E) is characterized by a unique tangency condition.
        • By algebraic manipulation, MUl = W MUc.
        • If the worker participates in the labor force, her utility is maximized only if she equates the benefits and costs of an additional leisure hour at the margin, where MUl is the marginal benefit of an additional leisure hour.
    • Nonparticipants face the same budget constraint. A nonparticipant chooses the point P = (T, A0)
      • l0* is a corner solution in this case since it occurs at the corner of the budget constraint, where l0* = T.
      • Here, the highest attainable indifference curve is steeper than the budget line such that MRS > W.
        • By algebraic manipulation, MUl > W MUc
        • Thus, the nonparticipant would like to increase his leisure time, l, but is unable to do so because he is constrained by the maximum l* = T = 24 hours in a day.
    • If W > MRSp, then the worker participates in the labor force. If MRSpW, he does not.
    • If an individual does participate, his optimal choice is located at an interior point of tangency at which MRS = MUl/MUc = W
  • Kinked budget constraints
    • A convex budget line may be caused by a tax exemption up to a certain level of earnings, after which each dollar earned is taxed.
      • A convex kink in the budget line will cause like-minded people with different indifference curves to cluster about the outermost point in the kink.
      • Modest changes in wages or taxes may cause no change in behavior.
    • A concave budget line may be caused by the existence of overtime pay.
      • A concave kink will cause like-minded people with different indifference curves to separate to opposite sides of the budget line.
      • Small changes in the budget constraint may lead to large changes in behavior.

4.4 Optimal Choice II: Properties

  • Comparative statics: an exercise comparing the decision maker’s behavior in different states.
  • An increase in wealth will shift the budget line outward, allowing greater consumption of both c and l.
    • Wealth: unearned income
      • Normal good: the good has a positive wealth effect, since demand for the good will increase with additional wealth.
      • Inferior good: the good has a negative wealth effect, since demand for the good will decrease with additional wealth.
    • Assumption 4.5: Leisure Is a Normal Good: a ceteris paribus increase in wealth raises the demand for leisure.
  • An increase in the wage rate will rotate the budget line outward, unleashing two conflicting forces and an ambiguous effect on the worker’s demand for leisure.
    • The wealth (income) effect: an increase in the wage unambiguously increases u by allowing the worker to consume more c and l. This effect tends to increase the worker’s demand for leisure, which leads to a corresponding reduction in the number of hours worked.
      • If the wealth effect dominates, the individual will work less following an increase in the wage.
    • The substitution effect: an increase in the wage also increases the opportunity cost of leisure. This effect tends to decrease the worker’s demand for leisure, leading her to substitute away from leisure time in order to work more hours and receive a higher wage.
      • If the substitution effect dominates, the individual will work more following an increase in the wage.
  • Nonparticipants have a reservation wage (W*) at which they are completely indifferent between participating and not participating in the labor force.
    • Once the wage rate increases past this level, the nonparticipant will choose to enter the labor force by working for h1* = T l1* > 0 hours.
    • This wage increase is associated only with the substitution effect. The income effect is zero.
  • An individual’s labor supply curve begins at W* and may contain a backward-bending region beginning at W', at which point the substitution effect exceeds the income effect.
  • Aggregate supply of labor, H: the horizontal sum of the labor supply decisions of each individual in the population as a whole
    • Intensive margin: the margin along which a population’s supply of labor hours varies when labor-market participants adjust their behavior in response to a wage change
    • Extensive margin: the margin along which a population’s supply of labor hours varies when individuals in a population adjust their participation decisions in response to a wage change
    • An increase in wages will increase the aggregate supply of labor hours despite backward-bending individual supply curves.
      • Along the intensive margin, a sufficient number of current participants are predicted to increase the hours they work and undo the effects of the backward benders.
      • Along the extensive margin, the increase in the wage rate will unambiguously encourage an increase in the total number of hours worked.
      • Thus, the aggregate supply of labor schedule (Σh I = H) should be positively sloped.

4.5 The Empirical Evidence

  • The own wage elasticity of labor supply (η) is given by η = (ΔHW) ∙ (W / H)
    • η = the percentage response in the aggregate supply of labor (H) induced by a 1% change in the wage (W).
  • There is a large body of empirical research using cross-sectional, time series, panel, and experimental data to estimate elasticity.
    • The strongest empirical effects are at the extensive margin, where individuals choose to enter and exit the workforce in response to wage changes.
      • This choice contains only a substitution effect, and it is particularly strong for women.
    • Generally, the empirical conclusion is that leisure is a normal good, as hypothesized by neoclassical economic theory.
  • The Carnegie conjecture posits that individuals will decrease their labor hours supplied in response to an anticipated bequest. The conjecture is empirically supported.
  • Despite the usefulness of the neoclassical model, it suffers from two major deficiencies.
    • The single decision period makes it impossible to study life-cycle behavior.
    • The theory of individual labor supply ignores the broader context of the family.