Labor Economics

Textbook: Labor Economics Seventh Edition — George J. Borjas, Harvard University


CHAPTER 1: Introduction to Labor Economics

  • Labor economics studies how labor markets work.

  • Models in labor economics typically contain three actors: workers, firms, and governments.

  • A good theory should have realistic assumptions and can be tested with real-world data.

  • The tools of economics are helpful in answering positive questions.

CHAPTER 2: Labor Supply

Measuring the Labor Force

Labor Force = Employed + Unemployed

  • LF = E + U

  • Size of LF does not tell us about “intensity” of work.

Labor Force Participation Rate

  • LFPR = LF/P

  • P = adult population (16 years or older not in institutions).

Employment Rate: percent of population that is employed.

  • EPR = E/P

Unemployment Rate

  • UR = U/LF

  • How to define unemployment?

    • To be considered unemployed, a person must either be on temporary layoff or claim that he has “actively looked for work” in the past four weeks.

    • Hidden unemployed: persons who have given up searching for work and have therefore left the labor force.

    Labor force measurement relies on subjectivity and likely understates the depths of a recession.

Facts about Labor Supply

  • Men: labor force participation rates declined from 80% in 1900 to 71% in 2010.

  • Women: labor force participation rates rose from 21% in 1900 to 59% in 2010.

  • Hours worked fell from 55 to 34 per week during the same time period.

Labor Force Participation Facts

  • Men have larger labor force participation (LFP) rates than women.

  • More women than men work part-time.

  • LFP increases with education.

  • LFP is greatest for all groups during the ages of 25 to 54.

  • White men have higher participation rates and hours of work than black men.

Neo-Classical Model of Labor-Leisure Choice

Utility Function: \(U=f(C,L)\)

  • Measure of satisfaction individuals receive from consumption of goods (C) and leisure (L).

Indifference Curve

  • Slope: \(MRS=\frac{\Delta C}{\Delta L}=-\frac{MU_L}{MU_C}\)

The Budget Constraint: \(C=w\times h+V=w\times (T-L)+V=-wL+(V+wT)\)

  • Hourly wage rate = $w
  • Total number of hours = T
    • Number of working hours = h
    • Total number of leisure hours = L
    • T = h + L
  • Consumption (dollars) = C
  • Non-labor income = V

Optimal Choice: \(\frac{MU_L}{MU_C}=w\)

Rewrite as: \(\frac{MU_L}{w}=MU_C\)

  • Marginal utility increase experienced by spending the last dollar on leisure should be equal to that by spending the last dollar on consumption.
  • Both the tangency condition and the budget constraint must be satisfied

Mathematical example

Utility function: \(U(C,L) = 0.7lnC + 0.3lnL\);

\(]Wage\ rate\ per\ hour = \$9; Total\ hours = 24\);

\(Non-labor\ income = \$204\).

Try to solve the optimization problem.

  • \(MU_C = 0.7/C; MU_L = 0.3/L\)
  • Budget constraint: \(C = 9(24-L) + 204\).

  • Tangency condition: \(MU_L / MU_C = w \to 3C/7L = 9 \to C/L = 21 \to C = 21L\)

  • From budget constraint: \(21L = 9(24-L) + 204 \to 30L = 420 \to L = 14 \to H = 10 hours; C = \$294\)

Additional questions:

  • What happens to hours of work when non-labor income changes?
    • (e.g., if non-labor income increases?)
  • What happens to hours of work when the wage changes?
    • (e.g., if wage increases?)

Effects of wage rate changes on hours of work: Summarize

  • Income effect:

    • Wage rate and demand for leisure move in the same direction.
  • Substitution effect:

    • Wage rate and demand for leisure move in the opposite direction.
  • Total effects depend on which effect dominates.

Reservation wage

The lowest wage rate that would make the person indifferent between working and not working.

  • If the market wage is less than the reservation wage, then the person will not work.

Reservation wage (= MRSE) is determined by

  • the individual’s preference

    • Steeper indifference curve = Higher value on leisure \(\to\) Higher reservation wage
  • the individual’s non-labor income

    • Non-labor income ­and Reservation wage move in the same direction .

Mathematical example

At point E, \(MRS(V,T) = MU_L(V,T)/MU_C(V,T)\).

  • \(Reservation\ wage = MRS(V,T)\)

Utility function: \(U(C,L) = 0.7ln C + 0.3ln L\)

  • \(MU_C = 0.7/C; MU_L = 0.3/L\)

\(Total\ hours = 24; Non-labor\ income = \$204\).

What is the reservation wage?

\(MRS(V, T)=(0.3/24)/(0.7/204)≈3.64\) \(Reservation\ wage ≈ \$3.64\)

Labor Supply Curve

Individual labor supply curve

Market labor supply curve: Horizontal sum of individual labor supply curves

  • The labor supply curve in the aggregate labor market is then given by adding up the hours that all persons in the economy are willing to work at a given wage.

*Labor supply elasticity:** \(\sigma=\frac{Percent\ change\ in\ hours\ of\ work}{Percent\ change\ in\ wage\ rate}=\frac{\Delta h/h}{\Delta w/w}\)

Labor Supply of Women

  • Over time, women’s participation rates have increased.
  • In most studies on female labor supply, the substitution effect dominates the income effect for women, implying an upward sloped labor supply curve.

Reasons for the increase in women’s labor force participation rate

  • Rising real wage of women.

    • Comparison of the market wage with the reservation wage.
  • Reductions in fertility.

  • Technological advances in household production.

  • Changes in cultural and legal attitudes toward working women.

  • The prevalence of home-based work.

Policy Application: Welfare Programs and Work Incentives

(1) Effect of a Cash Grant on Work Incentives

  • A grant of $1000 is given (e.g., to single mothers) if work hours=0; no benefit is given otherwise.
    • Encourages the (low-wage) worker to leave the labor force.

(2) Effect of a Welfare Program on Hours of Work: a cash grant and 50% tax

  • A program gives the worker a grant of $1,000 and imposes a 50% tax on labor earnings.
    • Reduce hours of work


  • Cash grants reduce wage incentives.
  • Welfare programs create work disincentives.
  • Welfare reduces supply of labor by increasing non-labor income, which raises the reservation wage.

Labor Supply over the Life Cycle

  • Wage rates change over the worker’s life (or life cycle).

    • Wages are low when young.
    • Wages rise with time and peak around age 50.
    • Wages decline or remain stable after age 50.
  • The changes in wages over the life cycle are “evolutionary” wage changes that alter the price of leisure.

Theoretical Issues of Evolutionary Wages

  • A person will work more hours when wages are higher (i.e., the substitution effect tends to dominate the income effect).
  • The profile of hours of work over the life cycle will have the same shape as the age-earnings profile.
  • Intertemporal substitution hypothesis: people substitute their time over the life cycle to take advantage of changes in the price of leisure.

Hours of Work over the Life Cycleimage-20200805170854678

  • Joe’s wage exceeds Jack’s at every age.
  • Joe works more hours than Jack if the substitution effect dominates.
  • Joe works fewer hours than Jack if the income effect dominates.

Labor Supply Over the Business Cycle

  • Added-worker effect

    • In a recession, the main breadwinner becomes unemployed or faces a wage cut.

    • A secondary worker (currently out of the labor market, such as young persons or mothers with small children) may choose to enter the labor force during these bad times. As a result, family income falls and the secondary workers get jobs to make up the loss.

    • The labor force participation rate of secondary workers (i.e., the added worker effect) is counter-cyclical.

  • Discouraged worker effect (dominates)

    • Unemployed workers find it very difficult to find jobs during a recession, so they give up searching.

    • Discouraged workers exit the labor force during bad times.

    • The labor force participation rate of discouraged workers is pro-cyclical.


  • Lifetime income is higher the longer a worker puts off retirement.
  • An increase in pension benefits reduces the price of retirement, increasing the demand for leisure and encouraging the worker to retire earlier.

Chapter 3: Labor Demand

The Firm’s Production Function

  • Q: firm’s output;
  • E: the number of employee-hours (the number of workers, for simplicity);
  • K: capital (land, machines, etc.)

Profit Maximization

  • \(Total\ Revenue=pq\)
  • \(Total\ Costs=(wE+rK)\)

Short-run and Long-run

  • In the short-run, only labor input can be adjusted, while capital input is fixed and given.

    • The firm chooses the optimal amount of only labor input.
  • In the long-run, any input (labor or capital) can be adjusted.

    • The firm chooses the optimal amounts of all inputs for production.

Short Run Hiring Decision

\(VMP_E=MP_E\times p\)
  • Value of Marginal Product of Employment (\(VMP_E\)) equals the marginal product of labor times the price of the output.
  • \(VMP_E\)indicates the dollar benefit derived from hiring an additional worker, holding capital constant.
  • Value of Average Product of Employment (\(VAP_E\)) is the dollar value of output per worker.
    • \(VAP_E=AP_E\times p\)

Profit Maximization and Firm’s Hiring Decision:

  • \(VMP_E=w\)
  • \(VMP_E\) is declining.

Labor Demand Curve

  • The demand curve for labor indicates how many workers the firm hires for each possible wage rate, holding capital constant.

  • The demand curve for labor coincides with the relevant downward-sloping portion of the firm’s value of marginal product curve.


Maximizing Profits: Two Rules

  • MC=MR: The profit maximizing firm should produce up to the point where the cost of producing an additional unit of output (marginal cost) is equal to the revenue obtained from selling that output (marginal revenue).
  • Marginal Productivity Condition (\(VMP_E=w\)): hire labor up to the point where the value of marginal product equals the wage rate.

The Short-Run Demand Curve for the Industry


  • \(w\downarrow\to Q\uparrow\to P\downarrow\)
  • \(P\downarrow\Rightarrow\) The Short-Run Demand Curve for Individual Firms move downward.

The Employment Decision in the Long Run

Cost Minimization & Long-run Profit Maximization

  • \(\frac{MP_E}{MP_K}=\frac{w}{r}\Rightarrow\frac{MP_E}{w}=\frac{MP_K}{r}\)
  • Output increased by last dollar spent on labor should be equal to that by last dollar spent on capital.

  • Profit maximization is a special case of cost minimization.

    • Profit maximization implies cost minimization.

    • Cost minimization does not necessarily imply profit maximization!

Long Run Demand Curve for Labor


  • The long-run demand curve for labor gives the firm’s employment at a given wage and is downward sloping (r is held constant).
  • At each point of the labor demand curve, the firm has realized profit maximization.

When the wage drops (r is held constant):

  • The firm takes advantage of the lower price of labor by expanding production.

    • the scale effect
  • The firm takes advantage of the wage change by rearranging its mix of inputs, by employing more labor and less of other inputs, even if holding output constant.

    • the substitution effect

Labor Demand Elasticity: \(\sigma=\frac{Percent\ change\ in\ employment}{Percent\ change\ in\ wage}=\frac{\Delta E/E}{\Delta w/w}\)

  • LRLD is more elastic than SRLD.


Relationship between Two Inputs in Production Process: Substitutes and Complements

  • Two factors are substitutes in production if they can be used interchangeably (not necessarily one to one).
  • Two factors are complements in production if both are needed for production.

Elasticity of Substitution

\(Elasticity\ of\ substitution=\frac{percent\ change\ in\ (K/E)}{percent\ change\ in\ (w/r)}\)
  • relative price of labor

Cross-elasticity of factor demand

\(Cross-elasticity\ of\ factor\ demand=\frac{percent\ change\ in\ x_i}{percent\ change\ in\ w_j}\)
  • If cross-elasticity is positive, the two inputs are substitutes in production.
  • If cross-elasticity is negative, the two inputs are complements in production.

Application: Affirmative Action and Production Costs

  • The “initial conditions” determine the inferences that one draws about the labor market impact of affirmative action programs.
  • If one assumes that the typical competitive firm discriminates against black workers, an affirmative action program increases the firm’s profits.
  • If one assumes that the typical firm does not discriminate, an affirmative action program may reduce the profitability of competitive firms.
  • The empirical evidence on whether the programs increase or reduce firms’ costs is inconclusive.

Marshall’s Rules of Derived Demand*

  • Describe the situations that are likely to generate elastic labor demand.

  • Labor Demand is more elastic in a industry when:

    1. The elasticity of substitution is greater.

      • The greater the elasticity of substitution, the more the isoquant looks like a straight line, and the more “similar” labor and capital are.
      • This allows the firms to easily substitute labor for capital as the wage increases.
    2. The elasticity of demand for the firm’s output is greater.

      • A wage increase raises the industry’s price and reduces consumers’ demand for the product.

      • The greater the reduction in consumer demand, the larger the cut in employment and the more elastic the industry’s labor demand.

    3. Labor’s share in total costs of production is greater.

      • A small increase in the wage rate would substantially increase the marginal cost.
      • Output price increases and consumers buy less.
      • Firms cut back on employment substantially.
    4. The elasticity of supply of other factors of production such as capital is greater.

      • Suppose there is a wage increase and firms want to substitute from labor to capital.
      • Demand curve for labor is more elastic the easier it is to increase the capital stock (i.e., the more elastic the supply curve of capital).

Policy Application: The Employment Effects of Minimum Wages

  • The unemployment rate is higher the higher the minimum wage and the more elastic the supply and demand curves.

The Impact of Minimum Wages on the Covered and Uncovered Sectors


  • If the minimum wage applies only to the covered sector, the displaced workers might move to the uncovered sector, shifting the supply curve to the right and reducing the uncovered sector’s wage.

  • If it is easy to get a minimum wage job, workers in the uncovered sector might quit their jobs and wait in the covered sector until a job opens up, shifting the supply curve in the uncovered sector to the left.

  • The migration of workers across the two sectors would stop when the expected wage in the covered sector equals the for-sure wage in the uncovered sector.

Adjustment costs

  • The expenditures that firms incur as they adjust the size of their workforce.

  • Costs of increasing the number of employees

    • Costs of hiring exercise: Costs of vacancy advertisement, interviews, assessments, selection, etc.
    • Costs of training new employees: Costs of hiring trainers and preparing for training materials, etc.
    • Other costs: Costs of administrative work, paperwork, etc.
  • Costs of reducing the number of employees

    • Severance pay, if required.
    • Costs of adjusting the work schedule for remaining employees.
    • Psychological impacts on remaining employees, etc.

Adjustment costs may be fixed or variable.

  • Fixed costs: Costs that are incurred regardless of the size of adjustment.
    • e.g., expenses in running a personnel office
  • Variable costs: Costs that vary with the size of adjustment.
    • e.g., costs of training new workers

Asymmetric Variable Adjustment Costs


  • Changing employment quickly is costly, and these costs increase at an increasing rate.

  • If government policies prevent firms from firing workers, the costs of trimming the workforce will rise even faster than the costs of expanding the firm.

Dynamics of Employment in the Labor Market

  • If variable adjustment costs are important, employment changes occur slowly.

  • If fixed adjustment costs dominate, the firm will either remain at its current employment level or switch immediately to a different employment level.

  • Evidence suggests that both variable and fixed adjustment costs play an important role in determining labor demand.

Chapter 4: Labor Market Equilibrium

Equilibrium in a Single Competitive Labor Market

  • Competitive equilibrium occurs when supply equals demand, generating a competitive wage and employment level.

  • It is unlikely that the labor market is ever in an equilibrium, as supply and demand are dynamic.

  • The concept of labor market equilibrium remains useful because it helps us understand why wages and employment seem to go up or down in response to particular economic or political events.

  • As the labor market reacts to a particular shock, wages and employment will tend to move toward their new equilibrium level.

Competitive Equilibrium in Two Labor Markets Linked by Migration


  • Suppose the wage in the northern region (\(w_N\)) exceeds the wage in the southern region (\(w_S\)).

  • Southern workers want to move north, shifting the southern supply curve to the left and the northern supply curve to the right.

  • In the emigration increases the total value of output in the national economy by the triangle ABC.

  • Wages are equated across regions at w*.

Competitive Equilibrium Across Labor Markets

  • As long as either workers or firms are free to enter and exit labor markets, a competitive economy will be characterized by a single wage.

    • In a competitive equilibrium the wage equals the value of marginal product of labor.
    • As firms and workers move to the region that provides the best opportunities, they eliminate regional wage differentials.
    • Workers of given skills have the same value of marginal product of labor in all markets.
  • The allocation of workers to firms that equates the value of marginal product across markets is also the sorting that leads to an efficient allocation of labor.

  • The “invisible hand” theorem: self-interested workers and firms accomplish a social goal that no one had in mind, i.e., efficient allocation of resources.

Policy Application: Impact of payroll taxes (for social security or medical care)


The Impact of an Employment Subsidy


Policy Application: Mandated Benefits

  • Suppose that the mandated provision of benefits costs C dollars per worker.
  • Suppose that each worker values the provision of the benefits at B dollars, where B <C.


Policy Application: The Labor Market Impact of Immigration


  • Immigrants and natives have the same types of skills;

  • Immigrants and natives have different types of skills.

The Short-Run Impact of Immigration When Immigrants and Natives Are Perfect Substitutes


The Short-Run Impact of Immigration when Immigrants and Natives are Complements


The Short-Run Effect on Native-Born Workers

  • Immigration reduces the wages and employment of similarly-skilled native-born workers, but native-born workers may be able to increase their productivity by specializing in tasks better suited to their skills.

  • Competing native workers will have lower wages; complementary native workers will have higher wages.

The Long-Run Impact of Immigration When Immigrants and Natives Are Perfect Substitutes


The Cobweb Model

  • Previously, we assume markets adjust instantaneously.
    • Wages and employment change quickly from the old equilibrium levels to the new ones.
  • However, many labor markets cannot adjust so quickly.
  • Two assumptions of the cobweb model:
    1. It takes time to produce skilled workers.
      • implies the short-run labor supply curve is perfectly inelastic.
    2. Persons are myopic: they decide to become skilled workers by looking at conditions in the labor market at the time they enter school.


Noncompetitive Labor Markets: Monopsony

  • Monopsony market exists when a firm is the only buyer of labor.

  • A monopsonist must increase wages to attract more workers, as different workers have different reservation wages.

  • A monopsonist faces upward-sloping market labor supply curve.

The Hiring Decision of a Perfectly Discriminating Monopsonist


Nondiscriminating Monopsonist

  • It must pay all workers the same wage, regardless of each worker’s reservation wage.

  • It must raise the wage of all workers when attempting to attract more workers.


The Impact of the Minimum Wage on a Nondiscriminating Monopsonist


Chapter 5: Compensating Wage Differentials

The Market for Risky Jobs

\(Utility = f(wage, risk\ of\ injury).\)


The Demand Curve for Risky Jobs

  • Firm must decide whether to provide a risky or a safe work environment to its workers. The firm’s choice will depend on what is more profitable.

  • To offer a safe work environment,

    • the production is: \(q_0=\alpha_0E^*\)
    • the profit is: \(\pi_0=p\alpha_0E^*-w_0E^*\)
  • To offer a risky work environment,

    • the production is: \(q_1=\alpha_1E^*\)
    • the profit is: \(\pi_1=p\alpha_1E^*-w_1E^*\)
  • Safety does not come for free. The firm has to allocate labor and capital to “produce” a safe environment.

  • This diversion of resources suggests that the marginal product of labor is higher in a risky environment, so that \(\alpha_1>\alpha_0\).

  • If \(\pi_1>\pi_0\), the firm will offer a risky environment.

Determining the Market Compensating Differential


Market Equilibrium When Some Workers Prefer Risky Jobs


Hedonic Wage Theory

  • Now suppose there are many types of jobs (firms), and the probability of injury in these types of jobs ranging from 0 to 1.

  • Hedonic wage functions reflect the relationship between wages and job characteristics.

  • Assume that workers:

    • Different workers dislike risk differently;
    • Maximize utility by choosing wage-risk combinations that offer them the greatest amount of utility.
  • Assume that firms:

    • Have different types and offer different job packages (wage, risk);
    • Operates in a competitive market with free entry and exit (zero profit in the end).

Indifference Curves for Three Types of Workers


  • The slope is the reservation price attached to moving to a riskier job.

Isoprofit Curves


Hedonic Wage Function


The Effects of Safety Regulation in a Perfectly Functioning Labor Market


Impact of OSHA Regulations When Workers Misperceive Risks


  • Mandated standards might reduce the utility of workers and the profits of firms.

  • As long as workers consistently underestimate the true risks, safety regulations can improve workers’ welfare.

Layoffs and Compensating Differentials


  • Evidence: The market indeed provides compensating differentials to workers at the risk of layoff.

Policy Application: Health Benefits and Compensating Differentials


Chapter 6: Human Capital

The Schooling Decision

  • Costs of human capital investment:

    • Out-of-pocket (direct) costs: tuitions, books, etc.
    • Foregone earnings: lost earnings during investment.
    • Psychic costs: mental stress.
  • Benefit of human capital investment:

    • Higher earnings, better jobs, respect, etc.
  • We assume workers acquire the education level that maximizes the present value of lifetime earnings.

    • The higher the discount rate, the less likely someone will invest in education (since they are less future oriented).


The Wage-Schooling Locus

  • Education increases a worker’s human capital (productivity), which in turn raises wages.


  • Properties of the wage-schooling locus:
    • Upward sloping.
    • The slope indicates the increase in earnings associated with an additional year of education.
    • Concave, reflecting diminishing returns to schooling.

Marginal rate of return to schooling: the percentage change in earnings resulting from an additional year of school.

A worker maximizes the present value of lifetime earnings by going to school until the MRR equals the rate of discount.

Schooling and Earnings When Workers Have Different Rates of Discount


Schooling and Earnings When Workers Have Different Abilities


An Alternative Explanation: Schooling as a Signal

  • The signaling model:

    • Productivity is determined by immutable (unchanging) innate ability.
    • Education has no effect on an individual’s productivity.
    • Education level is “sheepskin” which signals a worker’s ability and qualifications.
  • Asymmetric information: A worker knows his own productivity, but it takes many years for the employer to learn that.

If Education Is Treated as a Signal

  • Suppose a firm chooses the following rule for allocating workers to the two types of jobs.

    • If a worker has at least \(\bar{y}\) years of college: treats as high-productivity worker and pays $300,000;
    • Low-productivity worker otherwise and pays $200,000.
  • Assumption: obtaining academic credits is more costly for less-able workers.

    • Less-able: more time, pay for tutors, etc.
    • It costs $20,000 per year for high-productivity workers;
    • It costs $25,001 per year for low-productivity workers.


There could be a “separating equilibrium.

  • Low-productivity workers choose not to obtain X years of education, voluntarily signaling their low productivity.

  • High-productivity workers choose to get at least X years of schooling and signal their high productivity.

Human Capital vs. Signaling Model

  • Both models can explain why earnings and education are positively correlated.

  • Although education may incorporate a signaling aspect, it is well-accepted that education is more than a signal. Education is at least partially an investment in human capital.

  • Investment in education

    • Human capital model: It may be rewarding both privately and socially.
    • Signaling model: It may be rewarding privately, but less rewarding, if not wasteful, socially.

Private vs. Social Returns to Education

  • Private rate of returns to education: By how much an individual’s earnings increase resulting from an additional year of schooling.

  • Social rate of returns to education: By how much the national income increases resulting from an additional year of schooling.

  • Non-monetary returns may exist.

    • Private: better social skills, better health, etc.
    • Social: lower crime rates, higher voter participation rates, technological advance, etc.

Post-School Human Capital Investments

Three important properties of age-earnings profiles:

  • Highly educated workers earn more than less educated workers.

  • Earnings rise over time, but at a decreasing rate.

  • The age-earnings profiles of different education groups diverge over time.

    • Earnings increase faster for more educated workers.
    • Highly educated workers may invest the most in human capital during the post-school period.

On-the-job Training (OJT)*

  • Most workers augment their human capital stock through on-the-job training (OJT) after completing education investments.


  • Firms only provide general training if they do not pay the costs (e.g., MBA program).

  • In order for the firm to willingly pay some of the costs of specific training, the firm must share the returns to specific training.

  • Neither workers nor firms that have invested in specific training want to terminate the employment contract.

  • Workers who have specific training are effectively granted a type of tenure or lifetime contract in the firm.

  • Other implications of specific training:

    • “Last hired, first fired” during an economic downturn.
    • Temporary layoffs of specifically trained workers in many labor markets.
    • The probability of job separation declines with job seniority.

Policy Application: Evaluating Government Training Programs

  • Aimed at exposing disadvantaged and low-income workers to training programs and improving their incomes.

  • Self-selection problem:

    • Participants are not randomly selected.
    • The most committed to “self-improvement” participate.

Chapter 7: The Wage Structure (Inequality)

The Earnings Distribution

  • There is a lot of wage dispersion.

  • The wage distribution is positively skewed.

    • A long right tail.
    • A few workers get a very large share of the rewards for work.

Explanation for the Earnings Distribution: Human Capital Model

  • Wage differentials exist due to:
    • Human capital investments that vary from worker to worker.
    • Age differences. (Young workers are still accumulating human capital, while older workers are collecting returns from earlier investments.)

Income Distribution When Workers Differ in Ability but Have the Same Discount Rate


Measuring Inequality: The Lorenz Curve and the Gini Coefficient


The Gini coefficient:

  • Increases as inequality increases.

  • Summarizes the entire income distribution with a single number between 0 (perfect equality) and 1 (perfect inequality).

Measuring Inequality: Wage Gap

Examples of Wage Gaps:

  • The 90-10 Wage Gap is the difference in the 90th and 10th percentiles as a percent of the 10th percentile wage, or (w90 – w10)/w10

    • A measure of the range of the income distribution.
  • The 50-10 Wage Gap is the difference in the 50th and 10th percentiles as a percent of the 10th percentile wage, or (w50 – w10)/w10

    • A measure of inequality between “middle class” and low-income workers.

Changes in the Wage Structure from Shifts in Supply and Demand


Why Did Wage Inequality Increase?

International trade.

  • Increased the demand for skilled labor.

  • Reduced the demand for unskilled labor.

Skill-biased technological change.

  • Substitutes for unskilled workers and complements for skilled workers.

  • Lower the demand for unskilled labor.

Institutional changes in the U.S. labor market.

  • Less protection for the low-skill workers.
    • Decline in unions.
    • Drop in the real minimum wage.

The Earnings of Superstars

  • Superstar phenomenon: a few persons in some professions earn very high salaries and seem to dominate the field.

  • Superstar phenomenon does not occur in every occupation.

    • For example: university professors, doctors.

Superstar Phenomenon: Explanation

Only a few sellers have the exceptional ability to produce the quality goods that we demand.

  • e.g., Lionel Messi, Taylor Swift

The technology of mass production allows the very talented to reach very large markets.

  • Pop star vs. heart surgeon

The cost of distributing the product does not increase in proportion to the size of the market.

Inequality across Generations

Social mobility: whether wage inequality in a particular generation is transmitted to the next generation.

There is a positive correlation between the skills (incomes) of parents and their children.

  • High-income parents typically invest more in the education of their children.

  • Innate ability.

  • Social capital: quality of the environment where a child grows up.

The Intergenerational Link in Skills (Incomes)


Chapter 8: Labor Mobility

Family Migration

Tied Movers and Tied Stayers


The Decision to Immigrate

The decision ultimately depends on individual skills and the returns to those skills in the source and destination countries.


The Self-Selection of the Immigrant Flow


Roy model: The relative payoff for skills across countries determines the skill composition of the immigrant flow.

The Economic Benefits from Immigration


  • Immigrants also can make an important contribution to the receiving country.

  • The immigration surplus is a measure of the increase in national income that occurs as a result of immigration. (The surplus accrues to natives.)

  • Immigrants raise national income by more than it costs to employ them.

Job Turnover: Stylized Facts

  • Newly hired workers tend to leave their jobs within 24 months of being hired, while workers with more seniority rarely leave their jobs.

  • There is a strong negative correlation between a worker’s age and the probability of job separation.

    • This fits with the hypothesis that labor turnover can be an investment in human capital.
    • Older workers have a smaller payoff period. Thus, they are less likely to search (or move).
  • Long jobs have been the norm rather than the exception.

    • Especially for men over the age of 35.
  • The rate of job loss is highest among the least educated workers.

The Job Match

  • Each particular pairing of a worker and a firm has its own unique value.

  • Both firms and workers are ill-informed about the true value of the match at the time the job begins.

  • Workers and firms might improve their situation by shopping for a better job match.

  • Efficient turnover is the mechanism by which workers and firms correct matching errors and obtain a better and more efficient allocation of resources.

Specific Training and Turnover

  • When a worker receives specific training, his productivity improves only at the current firm.

  • This implies there should be a negative correlation between the probability of job separation and job seniority.

    • As age increases, the probability of job separation decreases.

Impact of Job Mobility on the Age-Earnings Profile


Chapter 9: Labor Market Discrimination

Race and Gender in the Labor Market

  • Men earn more than women, and whites usually earn more than nonwhites.

  • Differences in educational attainment between whites and nonwhites account for a portion of the wage differential.

  • Wage dispersion in competitive labor markets arise due to:

    • differences in job characteristics.
    • differences in workers’ human capital.
  • Differences in earnings and employment opportunities may arise even among equally skilled workers due to discrimination.

  • Discrimination occurs when the marketplace takes into account such factors as race and gender when making economic exchanges.

Economic Theories of Discrimination

  • The economics of discrimination: how perceptions of characteristics such as race and gender alter the costs and benefits of an economic exchange.

  • Taste discrimination (Becker)

    • A person has a taste for discrimination if he acts as if he is willing to pay some price to avoid being associated with a certain group of people.
    • Prejudice could be due to dislike or ignorance.
  • Statistical discrimination (Arrow & Phelps)

    • Due to imperfect information, an unprejudiced person judges a member of a certain group based on that group’s average performance.

Taste Discrimination

Prejudice is represented by the discrimination coefficient (d).

  • An employer:

    • With a taste for discrimination (d) against black workers
    • who pays black workers a wage of w
    • will act as if the wage of blacks is w(1+d), d > 0.
  • An employee:

    • with a taste for discrimination (d) against black co-workers
    • who is offered a wage w to work with black co-workers
    • will act as if the wage is w(1-d), d > 0.
  • A consumer

    • with a taste for discrimination (d) against black workers
    • who faces the price p
    • will act as if the price is p(1+d), d > 0.

Employer Discrimination

The Employment Decision of a Firm That Does Not Discriminate

  • image-20200808113450668

The Employment Decision of a Prejudiced Firm

  • image-20200808113635621

Profits and Discrimination


  • In competitive markets, free entry and exit ensure that firms are not earning excess profits.
  • Employers must pay for the right to discriminate.
  • Prejudiced firms will be driven out by unprejudiced firms.

Determination of Black–White Wage Ratio in the Labor Market


Employee Discrimination*

  • An employer must pay prejudiced whites more if he employs both blacks and whites.

  • Therefore, if blacks and whites are perfect substitutes, the firm hires either blacks or whites but not both.

  • Implications:

    • Firms are segregated by race.
    • There is no racial wage difference (\(w_W=w_B\)).
    • The profitability of firms is not affected (no advantage to being either a black or a white firm).

Customer Discrimination

  • Employer will try to segregate the workforce within a firm,

    • e.g., blacks in the back office, whites in the front office.
  • If firms are unable to “hide” black workers, then customer discrimination may have an adverse effect on black wages.

    • Firms employing black workers have to lower the price to compensate white customers for their disutility.
    • The wages of black workers will fall to compensate the employer for the loss in profits.

Statistical Discrimination

  • Statistical discrimination arises because the information gathered from the résumé and the interview does not predict perfectly the applicant’s true productivity.

  • The underlying uncertainty encourages the employer to use statistics about the average performance of the group to predict a particular applicant’s productivity.


  • Applicant’s expected productivity will be a weighted average: \(w=\alpha T+(1-\alpha)\bar{T}\)
    • \(T\) is personal score;
    • \(\bar{T}\) is the average test score of the group
  • a). If \(\bar{T}_W>\bar{T}_B\) and \(\alpha_W=\alpha_B\): white workers earn more than black workers with the same score.
  • b). \(\bar{T}_W=\bar{T}_B\) and \(\alpha_W>\alpha_B\): high-scoring whites earn more than high-scoring blacks, and low-scoring whites earn less than low-scoring blacks.

Measuring Discrimination

  • One possible measure of discrimination is the difference in mean wages.

  • A better measure would compare the wages of equally skilled workers.

  • Oaxaca decomposition: a technique that decomposes the raw wage differential into a portion related to a difference in skills and a portion attributable to labor market discrimination.

    • image-20200808123100886

Measuring the Impact of Gender Discrimination on the Wage


Policy Application: Determinants of the White-Black Wage Ratio

There has been an upward trend in the wages of blacks in recent years.

  • This has been attributed to increases in the quality and quantity of black schooling.

  • Government programs have positively affected black wages.

  • The least-skilled blacks are no longer working.

Policy Application: Determinants of the Female-Male Wage Ratio

  • Women usually drop out of labor market during their child-raising years (motherhood penalty).

    • Shorter payoff period, invest less in human capital;
    • Human capital depreciates during that period;
    • Interruption in on-the-job training;
    • Disruption in career advancement.
  • Occupational crowding has segregated women into particular occupations where the return to education is lower.

  • Other determinants? (Motivation, ambition, …)

Chapter 11: Incentive Pay

Incentive Pay

Incentive pay: a compensation package designed to elicit particular levels of effort from the worker.

The type of labor market contract matters because

  • Employers often do not know the workers’ true productivity;

  • Workers would like to get paid a high salary while putting in as little effort as possible.

Pay Systems: Piece Rates

  • A piece-rate system compensates the worker according to some measure of the worker’s output.

    • E.g., delivery service, hair cut, tea leaves collection.
  • Piece rates are used by firms when it is cheap to monitor the output of workers.

  • Piece-rate compensation systems attract the most able workers and elicit high levels of effort from the workers.

The Allocation of Work Effort by Piece-Rate Workers


Pay Systems: Time Rates

  • A worker is paid a time rate if she is paid a fixed amount per period of time she works, such as being paid an hourly wage.

  • Time rates are used by firms when it is costly or impossible to monitor the output of workers.

    • e.g., white-collar workers, school canteen workers
  • Suppose there is a minimum level of output, \(\bar{q}\), that can be easily monitored by the firm.

  • A time-rate worker will then produce \(\bar{q}\) units of output, and no more.

Effort and Ability of Workers in Piece-Rate and Time-Rate Jobs


Why Are Piece-rates Not Used More Often in the Labor Market?

  • The work incentives are of little use when the firm’s production depends on team effort.

  • It overemphasizes the quantity of output produced.

    • Worker will want to trade off quality for quantity.
  • Many workers dislike piece-rate systems because their salaries might fluctuate a lot over time.

  • Workers in piece-rate firms fear the well-known ratchet effect.

    • Managers may interpret the high level of production as evidence that the job was not that difficult and lower the piece rate the next period.

Bonuses, Profit-sharing, and Team Incentives

  • Many bonus programs are not tied to a particular worker’s performance, but to the firm’s performance.

  • We can interpret the income from these profit-sharing plans as a piece rate on the output of a group of workers.

  • Unlike piece-rate systems, profit-sharing programs may suffer from the incentive problems, particularly the free-riding problem.

  • Nevertheless, evidence suggests that profit-sharing plans increase productivity.


  • Some firms award promotions on the basis of the relative ranking of the workers.

  • A tournament (contest) might be used when it is cheaper to observe the relative ranking of a worker than the absolute level of the worker’s productivity.

  • The rewards are then distributed according to rank, with the winner receiving a sizable reward and the losers receiving much smaller payoffs.

The Allocation of Effort in a Tournament



  • Workers allocate more effort to the firm when the prize spread between winners and losers in the tournament is very large.

  • A large prize spread, however, also creates incentives for workers to damage the efforts of other players.

Constant Wage and Upward-Sloping Age-Earning Profile


Work Incentives and Delayed Compensation

  • Impact on work incentives:

    • Constant wage: If get fired, move to another job which pays the same wage.
    • Upward-sloping profile: If get fired, lose the “loan” forever.
  • An upward-sloping age-earnings profile (AC) discourages workers from shirking.

  • The firm will not want the employment relationship to continue beyond year N, as the firm has paid off the loan and the wage is higher than worker’s VMP.

  • A delayed-compensation contract implies that at some point in the future the contract must be terminated, which explains the existence of mandatory retirement.

Efficiency Wages

  • Some firms might want to pay wages above the competitive wage in order to motivate the work force to be more productive.

  • What is the “optimal” wage that the firm pays?

    • If wage too low: it cannot attract high-ability workers.
    • If wage too high: it cannot make profit.
  • Efficiency wage: the marginal cost of increasing the wage exactly equals the marginal gain in the workers’ productivity.

The Determination of the Efficiency Wage (Not a Strict Method)


Efficiency Wages–Implications

  • The efficiency wage maximizes the firm’s profits.

  • The efficiency wage will have to exceed the competitive wage, the firm has an oversupply of labor.

  • Efficiency wages create a pool of workers who are involuntarily unemployed.

  • Efficiency wages imply the possibility of dual (segmented) labor markets, where permanent wage differences arise due to differences in firms’ ability to monitor for shirking.

Why Is There a Link between Wages and Productivity?

  • A high wage makes it costly for workers to shirk (i.e., they lose the wage if caught).

  • People who are well-paid might work harder even if there is no threat of dismissal (view the high wage as a gift from employer).

  • Efficiency wage reduces the quit rate, so it reduces turnover costs and minimizes the disruption.

  • A firm that pays efficiency wages attracts a more qualified pool of workers, increasing the productivity and profits of the firm.

Chapter 12: Unemployment

Types of Unemployment–Frictional Unemployment

  • Frictional unemployment arises when workers and firms need time to locate each other and to digest information about the potential job match.

  • Even a well-functioning competitive economy experiences frictional unemployment, since some workers will unavoidably be between jobs.

Types of Unemployment–Seasonal Unemployment

  • Workers in some industries are laid off regularly because new models are introduced with clockwork regularity, and firms shut down so that they can be retooled.

  • Spells of seasonal unemployment are usually very predictable.

  • Most of the unemployed workers will return to their former employer once the employment season starts.

Types of Unemployment–Structural Unemployment

  • Structural unemployment arises when there is

    • an imbalance between the supply of workers and the demand for workers;
    • or a mismatch between workers’ skills and the skills needed by firms.
  • Structural unemployment is the most concerning type of unemployment.

  • The displaced workers must retool their skills and the government needs to provide training programs.

Types of Unemployment–Cyclical Unemployment

  • If the economy has moved into a recession, firms require a smaller workforce and employers lay off many workers, generating cyclical unemployment.

  • To reduce this type of unemployment, the government may have to stimulate aggregate demand and reestablish market equilibrium.

Flows Between Employment and Unemployment: A Lake Model

Suppose a person is either working or unemployed.

At any point in time, some workers lose their jobs and some unemployed workers find jobs.

  • If the probability of losing a job equals \(l\), there are \(l\times E\) job losers.

  • If the probability of finding a job equals \(h\), there are \(h\times U\) job finders.

Steady State: \(l\times E=h\times U\)

Steady-state Rate of Unemployment \(=\frac{U}{LF}=\frac{l}{l+h}\)

  • The steady-state rate of unemployment depends on the transition probabilities between employment and unemployment.
  • The steady-state rate of unemployment is sometimes called the natural rate of unemployment.

Job Search

The worker’s economic trade-offs are clear:

  • The longer he searches, the more likely he will get a high wage offer;

  • The longer he searches, however, the more it costs to find that job.

Search costs

  • Direct costs: transportation, time, etc.

  • Opportunity cost: the job offer at hand was rejected.

Asking Wage


Determinants of the Asking Wage

  • A decrease in the benefits from search reduces the asking wage and shortens the duration of the unemployment spell.

  • A decrease in search costs increases the asking wage and lengthens the duration of the unemployment spell.

Discount Rates, Unemployment Insurance Benefits, and the Asking Wage


Unemployment Compensation

  • The level of unemployment benefits depends on previous earnings.

  • Unemployment insurance lengthens the duration of unemployment spells and increases the probability that workers are laid off temporarily.

The Intertemporal Substitution Hypothesis

Job search models provide an important explanation for the existence of frictional unemployment (voluntary).

The intertemporal substitution hypothesis:

  • People consume more leisure when it is cheap.

The large increase in unemployment observed during a severe recession might also have a voluntary component, because some workers may reallocate their time to enjoy more leisure when it’s cheap.

The Sectoral Shifts Hypothesis

Job search models do not explain the existence and persistence of long-term unemployment.

The sectoral shifts hypothesis: structural unemployment arises because the skills of workers cannot be easily transferred across sectors.

  • The skills of workers laid off from declining industries have to be retooled before they can find jobs in growing industries.

Efficiency Wages and Unemployment*

  • The above-market efficiency wage generates involuntary unemployment.

The Determination of the Efficiency Wage


The Impact of an Economic Contraction on the Efficiency Wage


Implicit Contracts and Temporary Layoffs

Implicit contract: often unspoken and unwritten

  • Fixed-employment contract

    • Substantial wage cuts during a recession;
  • Fixed-wage contract

    • Fewer working hours or temporary layoffs during a recession.

The typical implicit contract in the labor market is a fixed-wage contract—implying that the wage is sticky over the business cycle and that unemployment increases during a recession.

The Phillips Curve


The Short-Run and Long-Run Phillips Curves


作者: 公子小白



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