Compensating Wage Differentials

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Compensating Wage Differentials - Massey University

• An isoprofit curvegives all the risk-wage combinations that yield the same level of profits to a firm • Isoprofit curves are upward sloping because production of safety is costly • Wage-risk combinations on higher isoprofit curves yield lower profits A wage cut shifts the isoprofit curve down

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1Chapter 6

Compensating

Wage Differentials

Labor Economics, 4th

edition6 - 2Introduction •The labour market is not characterised by a single wage:

Workers differ and jobs differ.

•Adam Smith proposed the idea that job characteristics influence labour market equilibrium. •Compensating wage differentialsarise to compensate workers for nonwage characteristics of the job (i.e. how 'pleasant' or 'unpleasant' a job is). -If a job is unpleasant, the firm must probably offer a higher wage to attract workers and vice versa. •Workers have different preferences and firms have different working conditions. 2 6 - 3

6.1 The Market for Risky Jobs

•Simple model: Assume only two types of jobs in the labour market (safe jobs versus risky jobs). -Safe jobs have probability of zero that worker gets injured. Risky jobs have probability of 1! Workers know this. •Workers care about whether their jobs are safe or risky. •A worker's utility function: Utility = f (w, risk of injury) •Indifference curves reveal the trade-offs that a worker prefers between wages and degree of risk (risk assumed to be a 'bad'): To provide the same utility, risky jobs must pay higher wages than safe jobs. 6 - 4

Figure 6.1: Indifference Curves Relating the

Wage and the Probability of Injury on Job

w 1 1 ˆw U 1 Wage 1

0Probability of

Injury

w 0 Q PU 0 w U 1

The worker earns a wage of w

0 dollars and gets U 0 utils if she chooses the safe job. She would prefer the safe job if the risky job paid a wage of w' 1 dollars, but would prefer the risky job if that job paid a wage of w'' 1 dollars.

The worker is indifferent

between the two jobs if the risky job pays w^ 1 . The worker's reservation priceis then given by ǻw^= w^ 1 -w 0 3 6 - 5

Indifference Curves Relating the Wage and

the Probability of Injury on Job ctd. •The greater the worker's dislike for risk, the greater the bribe required for switching from a safe to a risky job, and the greater the reservation price (case of step indifference curves). •Firms have to choose which type of job to offer. Which is more profitable? -Firms may have a risky work environment because it is less expensive to pay higher wages than to make the environment safe. -As the wage firms have to offer for risky jobs increases, fewer firms will offer risky jobs (resulting in a downward sloping demand curve for such jobs, see Figure 6.2). •Reason: It becomes more profitable for firms to make jobs save than to pay the higher wage. 6 - 6

Figure 6.2: Determining the Market

Compensating Differential

The supply curve slopes up

because as the wage gap between the risky job and the safe job increases, more and more workers are willing to work in the risky job.

The market compensation

differential equates supply and demand, and gives the bribe required to attract the last worker hired by risky firms.

Number of

Workers in

Risky JobE

S P Dw 1 -w 0 (w 1 -w 0 4 6 - 7

Determining the Market Compensating

Differential ctd.

•Note the features of the equilibriumin Figure 6.2:

1.The wage differential is positive. Risky jobs pay more

than save jobs.

2.The equilibrium wage differential is that of the last worker

hired (the marginal worker). It is not a measure of the average dislike for risk among workers in the labour market.

3.Therefore, all but the marginal worker are

overcompensated by the market! 6 - 8

Can the Compensating Wage Differential go

the "Wrong" Way? •What about workers that like risk and get utility from it (e.g. racing car drivers, test pilots, explorers, undercover agents)? •Their reservation price is negative! They would pay to get a risky job even if it paid less than other jobs. •If demand for workers in risky jobs is small there could be a negative compensating wage differential for such workers (see

Figure 6.3).

•Firms might get away with paying a lower wage for risky jobs! 5 6 - 9

Figure 6.3: Market Equilibrium when Some

Workers Prefer to Work in Risky Jobs

w 1 -w 0 (w 1 -w 0 0E P

Number of

Workers in Risky

JobS D N w MIN

If some workers like to

work in risky jobs (they are willing to pay for the right to be injured) and if the demand for such workers is small, the market compensating differential is negative. At point P, where supply equals demand, workers employed in risky jobs earn less than workers employed in safe jobs.

6 - 10

6.2 Hedonic Wage Theory

•Assume there are many types of firms (instead of just those offering safe or risky jobs). The probability of injury can take any value between 0 and 1. •Workers maximise utility by choosing wage-risk combinations that offer them the greatest amount of utility. Assume workers dislike risk, but to different degrees, i.e. they have different optimal wage-risk combinations. •Firms are on their isoprofit curves that give the risk-wage combinations that provide zero (economic) profit. They differ between firms. •A hedonic wage function reflect the relationship between wages and job characteristics. It matches workers with different risk preferences with firms that can provide jobs that match these different risk preferences. 6

6 - 11

Figure 6.4: Indifference Curves for Three

Types of Workers

U C U BU A Wage

Probability of Injury

Different workers have

different preferences for risk. Worker Ais very risk- averse. Worker Cdoes not mind risk as much.

The slope of an

indifference curve is the reservation price a worker attaches to moving to a slightly riskier job.

6 - 12

Isoprofit Curves for Different

Wage-Risk Job Packages

•An isoprofit curvegives all the risk-wage combinations that yield the same level of profits to a firm. •Isoprofit curves are upward sloping because production of safety is costly. •Wage-risk combinations on higher isoprofit curves yield lower profits

A wage cut shifts the isoprofit curve down.

•Isoprofit curves are concave because production of safety is subject to the law of diminishing returns. Reducing risk of job injury is at first relatively cheap, but becomes more expensive the further risk is reduced. •Assume a competitive market , i.e. all firms will have zero (economic) profit. All wage-risk combinations of the different firms will lie on their "zero-profit" isoprofit curves 7

[PDF] Compensating Wage Differentials - Massey University

1Chapter 6

Compensating

Wage Differentials

Labor Economics, 4th

Workers differ and jobs differ.

6.1 The Market for Risky Jobs

Figure 6.1: Indifference Curves Relating the

Wage and the Probability of Injury on Job

0Probability of

Injury

The worker earns a wage of w

The worker is indifferent

Indifference Curves Relating the Wage and

Figure 6.2: Determining the Market

Compensating Differential

The supply curve slopes up

The market compensation

Number of

Workers in

Risky JobE

Determining the Market Compensating

Differential ctd.

1.The wage differential is positive. Risky jobs pay more

2.The equilibrium wage differential is that of the last worker

3.Therefore, all but the marginal worker are

Can the Compensating Wage Differential go

Figure 6.3).

Figure 6.3: Market Equilibrium when Some

Workers Prefer to Work in Risky Jobs

Number of

Workers in Risky

If some workers like to

6 - 10

6.2 Hedonic Wage Theory

6 - 11

Figure 6.4: Indifference Curves for Three

Types of Workers

Probability of Injury

Different workers have

The slope of an

6 - 12

Isoprofit Curves for Different

Wage-Risk Job Packages

A wage cut shifts the isoprofit curve down.

6 - 13

Figure 6.5: Isoprofit Curves

Probability of Injury