Chapter 7

Competitive Equilibrium

Chapter Study Outline

7.1 Competitive Equilibrium

  • Assuming a single industry consisting of a large number of perfectly competitive firms, n, each firm’s profit-maximizing demand for labor is governed by W = p ∙ MPL, where MPL is the marginal product of labor.
    • In competitive equilibrium, each firm in the assumed single industry perceives that it faces a perfectly elastic supply of labor at the wage, W0*.
      • All firms are price takers.
      • The firm’s optimal level of employment is l0*.
    • Each worker in the large number of m equally talented workers derives utility only from consumption, c, and leisure, l.
      • All workers are price takers.
      • The marginal rate of substitution is MRS = w/p, which determines the labor-supply schedule, h(m), for each of the workers.
      • Each worker perceives a perfectly elastic demand, D0, for his labor hours at this wage.
      • The worker’s optimal supply of labor hours is h0*.
    • Assuming that all m workers are participants, MPL = W0* = MRS.
      • Under this condition, L0* is Pareto efficient since it is impossible to adjust the allocation of labor to make anyone better off without hurting someone else.
  • The two-industry model is a bit more realistic.
    • Assumption 7.1: Free Mobility: workers can switch employers or sectors instantly and without cost.
    • The equilibrium levels of employment will occur at LA for Firm A and LB for Firm B, but all firms in the industry will pay the same wage rate, W0*.
      • This single wage, W0*, is the law of one price.
    • The profit-maximizing employment levels are still governed by the wage equals marginal revenue product conditions, W0* = pA ∙ MPLA = pB ∙ MPLB.
      • This implies that the equilibrium is Pareto efficient since it is impossible to reallocate labor across the two industries to increase overall output.

7.2 Policy Applications

  • Payroll taxes are levied on firms rather than workers. The best known examples in the United States are those pertaining to Social Security and Medicaid.
  • Before a tax, firms employ L' workers at wage W'.
    • After a $T0 payroll tax, firms employ L' workers at the wage (W' - T0).
      • This shifts the labor demand schedule downward by $T0.
        • Although the payroll tax is levied on employers, in the new equilibrium workers share part of the tax burden.
        • The wage declines from W0* to W1* and the level of employment declines from L0* to L1*.
        • Workers end up bearing at least part of the payroll tax.
      • Meanwhile, an income tax of $T0 will shift the labor supply schedule up by $T0.
        • The wage declines from W0* to W1* and the level of employment declines from L0* to L1*.
        • The after-tax wage and employment outcomes are identical under a payroll and equal income tax, assuming other things equal.
    • There is mixed evidence on whether employers or workers end up bearing the majority of a payroll tax.
    • If there is a tax-benefit linkage, in which the taxes that employees pay are later returned to them as benefits, the equilibrium will change again.
      • If the benefit equals $0, the competitive equilibrium shifts downward.
      • If the benefit equals exactly the value of the tax, $T0, the equilibrium remains the same.
        • In reality, the benefit is somewhere between $0 and $T0. Due to government inefficiencies, workers only see a fraction of the potential returns from payroll taxes.
  • Employment subsidies are explicit dollar payments or tax credits given to firms for hiring workers.
    • Employment subsidies are intended to provide assistance to economically disadvantaged workers by making it cheaper for employers to hire low-wage workers.
    • General employment subsidy: available to all workers
    • Categorical employment subsidy: targets a specific group of individuals
      • Other things equal, the subsidy will raise both the equilibrium wage and the level of employment.
      • Empirical evidence shows that subsidies will achieve their goals in the perfectly competitive model.
        • However, categorical subsidies have had low firm participation rates.
        • Evidence shows that wage subsidy vouchers can lower a worker’s chances of obtaining a job, perhaps because of voucher stigma or a longer period of job searching by workers with vouchers.

7.3 Compensating Wage Differentials

  • Wage differences can be partly explained by workers’ differing preferences for different types of jobs once the homogeneity assumption is relaxed.
  • Assume there are two types of jobs in two industries that provide different fixed levels of nonwage attributes for which workers have heterogeneous preferences.
    • One is safe/salubrious, s.
    • The other is dangerous/disagreeable, d.
      • The compensating difference, Δw* = wd* - ws*, is the wage premium that the disagreeable industry must provide in order to attract sufficient workers.
      • us = (ws)s is a given worker’s fixed utility from employment in the agreeable industry.
      • ud = (wd)d = u(us + Δw)d is a given worker’s fixed utility from employment in the disagreeable industry.
      • v is a worker’s reservation value, at which he is just indifferent between working in one industry or the other, such that us = u(us + v)d.
        • If v ≤ Δw, he works in industry d.
        • If v > Δw, he works in industry s.
        • if v = Δw, he is the marginal worker.
    • Due to difficulty in determining what attributes of a job are disagreeable on a priori grounds, economists often use the fatality/injury rate.
  • Industry d’s labor supply schedule will be the positively sloped curve S(Δw)d, as derived from the distribution of reservation values.
    • Industry d’s labor demand schedule will be the negatively sloped curve D(wd)d= D(Δw)d.
    • The equilibrium compensating differential is governed by the preferences of the marginal worker.

7.4 Fringe Benefits

  • Fringe benefits are an increasingly important component of total compensation.
    • $b = the value of the fringe benefit that the employer offers each of its n employees
    • $w = the wage
    • $u = the worker’s utility, which depends positively on both her consumption level, $c, and her fringe benefits, $b.
    • $C = n ∙ (w + b) is the sum of the firm’s total costs, ignoring capital and tax complications
  • The fundamental principle is that the firm is concerned only with C and not how C is distributed between w and b.
    • The isocost schedule is a negatively sloped straight line with a slope of -1, in accordance with the fundamental principle.
      • Workers are free to select a point on the line corresponding to their wage-benefit combination.
      • The model predicts that, other things equal, all combinations of w and b will lie on this line.
  • Policies requiring compulsory increases in employee benefits are predicted to be offset by a corresponding wage reduction, leading to no change in worker utility.
    • Many studies support the negative relationship between wages and benefits, while others do not on the basis of omitted variable bias.
    • Fringe benefits may be popular because they receive favorable tax treatment compared to wages.
  • The basic theory predicts that workers with greater health benefits will earn lower wages.
    • Yet unobserved heterogeneity among workers may hide this relationship. Workers with greater innate ability may not only earn higher wages but also desire more fringe benefits like health care, assuming health care is a normal good.
    • This may lead to a spurious positive correlation between benefits and earnings even when the true relationship is negative.