A New Province for Law and Order

The Effects of Minimum Wage Laws on the Labour Markets

Peter R. Hartley*

  • Minimum wage laws are an example of a price control. Price controls limit the volume of transactions, and distort the quality of goods or services exchanged in the market place. In the case of a minimum wage, the costs are thought mainly to take the form of reduced employment and output, while the gains accrue mainly to those who keep their jobs at a higher wage rate.
  • Most economists believe that the aggregate losses accompanying price controls, including minimum wage laws, exceed the aggregate gains. Nevertheless, most democracies are characterised by political or quasi-judicial intervention into labour markets.

As with tariffs and many other policies, the political process might weigh the gains more heavily than the losses because the gains are more concentrated on individuals who may also be better organised as a political entity. Minimum wages reduce the demand for unskilled or inexperienced workers and raise the demand for substitute resources including, more than likely, skilled workers. If skilled workers are in limited supply, for example because a union controls entry to the trade, then their wages will increase as the demand for their services expands.

The subset of unskilled workers who keep their jobs at the higher wage might also gain from a minimum wage.l They could form another relatively concentrated vested interest in favour of the policy.

A diffuse and poorly organised group of unskilled workers who lose their jobs, or new entrants to the labour force who do not get jobs, seem to bear most of the costs. These individuals may not be aware of the source of their difficulties. Even if they are aware, their concern is mollified by an extensive system of government welfare benefits. Taxpayers or beneficiaries of other government expenditure then, perhaps unwittingly, bear some of the costs of the minimum wage as taxes are increased, or other expenditure is cut, to fund the higher welfare payments.

The support for intervention into labour markets appears, however, to be more widespread among voters than this theory predicts. Many voters appear to believe that legislated wages are an inexpensive alternative to higher taxes and welfare payments or wage subsidies as a policy to protect the disadvantaged, unlucky, or less able members of society.

We shall argue that it may be very easy to under-estimate the costs of minimum wages since many of them are hidden. Even the usual estimates provided by economists, which concentrate on the effects of wage distortions on employment and unemployment, may seriously understate the losses.

Our argument is based on the idea that, just as other price controls distort the quality of market goods and services,2 minimum wages distort the "quality" of labour services exchanged in the market place. The distortion in quality following the imposition of a price control lessens its adverse effect on the quantity of trade. Furthermore, the losses imposed by the distortion in quality are more difficult to measure than is any fall in the quantity of trade.

We shall identify the "quality" of labour services with the amount of "effort", or the net output per hour of labour input. Many firms can pay legally prescribed wages without reducing employment by adjusting their operations to increase the amount of effort per hour of labour input.

For example, consider a firm operating an assembly line. When a minimum wage that exceeds the current productivity of workers is imposed, the firm may be able to afford the wage by making the assembly line run faster. This will make the workers worse off, and may also raise costs by, for example, increasing wear on the equipment or the proportion of defective products. Yet it may enable the firm to stay in business without having to lay off workers or see them resign to find more attractive alternative jobs.

Other changes in working conditions might also affect output. For example, output might be increased if less of the labour time of employees is used to maintain the cleanliness or safety of the work place.

As another example, a firm might be able to increase current production by reducing on-the-job training. This will, however, reduce productivity growth and therefore future wages and profits.

Nevertheless, the ability of many firms to adjust to higher wages without reducing employment may encourage the belief that intervention into labour markets is not very costly. Furthermore, evidence of the apparent "arbitrariness" of wages might encourage the belief that economics cannot explain labour market outcomes. This sentiment can be exploited to argue that the legal framework applicable to contracting and trade in other markets is inappropriate for labour markets. Measures aimed at limiting competition and free exchange in labour markets might meet little resistance despite the efficiency losses they engender.

Several observations are consistent with our alternative view of the effects of minimum wages, but are quite difficult to explain using the standard economic approach. The standard approach cannot explain why we find a "clustering" of employees earning the minimum wage, or, in the Australian system, earning the various award wages. Moreover, these peaks in the distribution of wages shift with changes in the legally prescribed wage levels.

In addition, work practices and other conditions of employment appear to be a stronger issue of dispute between employers and employees in a regime characterised by binding minimum or award wages. This is a natural consequence of our model, since work practices are key determinants of net output per hour of labour input.

Finally, award wages might produce decreases in on-the-job training, and, as part of a more general concern on the part of employees to limit changes in work practices, opposition to new technology. This could explain some of the relatively low labour productivity growth that seems to be a feature of award wage regimes.


The standard analysis

We can illustrate the standard analysis using a simple supply and demand model of the labour market.

The demand for labour depends negatively on the real wage. Following an increase in the real wage, employers may alter their production processes to use less labour. If they cannot find less labour-intensive production techniques, their costs will rise and the demand for their output will decline. In either case, an increase in real wages paid to workers reduces the demand for their services.

The supply of labour depends positively on the real wage. As wage rates increase, workers are attracted to enter the workforce rather than continue education and training, work at home, work in their own businesses, or survive on the lower amounts of market goods and services they can buy using public or family "welfare" assistance.

Existing workers might also be willing to supply additional hours per week, or additional weeks of work per year, as the wage rate rises. For simplicity, the following discussion ignores any adjustment in hours worked in response to a minimum wage. The technical appendix discusses the complete model with variable hours of work.

The intersection of the supply and demand curves determines an equilibrium real wage and equilibrium level of total hours of employment. If the prescribed legal minimum real wage is above the equilibrium market clearing level, the minimum is said to be binding. A minimum that is below the equilibrium market clearing level is non-binding and has no effect on the market equilibrium.

Figure 1 illustrates the effect of a binding minimum wage in a competitive labour market.3 The high minimum wage reduces the demand for labour. The reduction in employment raises the marginal product to equal the new higher real wage.

Until workers become discouraged from their inability to find employment at the high minimum wage, the legally prescribed minimum also increases the supply of individuals willing to work.4 The queue of individuals searching for a job is measured as increased unemployment.

The costs of the policy include both the net value of the lost employment opportunities and the net value of the lost output from firms. There may also be losses associated with the increased unemployment as individuals spend more time and other resources searching for the limited jobs available at the legal minimum wage.

Losses in current employment may also have future costs as individuals who are denied valuable work experience suffer a reduction in future productivity. Time out of the work force can also produce a deterioration in previously acquired work skills.

Young people who are unable to find satisfaction through legitimate employment and consumption of market goods and services might turn to crime and drugs. This would also lead to future as well as current losses.

Brozen (1962) notes that minimum wages invariably do not cover all sectors of the economy, and that some individuals displaced from the covered sectors take jobs in uncovered sectors at a reduced wage rate. The opportunity to find work in occupations that aren't covered by the minimum wage lessens the adverse impact of the law on overall levels of employment.

Some of the effects of the minimum wage are, however, spread from the covered to the uncovered sectors as workers in the latter sectors suffer declines in their real wages. In addition, since the marginal product of labour is higher in the covered than the uncovered sectors, the value of output could be increased by transferring labour back to the covered sectors. Some of the efficiency costs of the minimum wage will therefore take the form of an inefficient allocation of labour across the different sectors of the economy.

Individuals priced out of the labour market by the minimum wage may also start their own businesses, or set themselves up as independent contractors. This may also lessen some of the costs of a minimum wage.

These workers decide to become entrepreneurs, however, only after the minimum wage is imposted. It is likely, therefore, that the expected benefits of starting their own businesses are less than the expected returns from remaining employed at the wages that prevailed before the minimum was imposed.

The standard analysis may explain the jump in youth unemployment that usually accompanies the imposition of a minimum wage. For example, youth unemployment in Australia jumped at the end of the Whitlam government's term of office when there was a large increase in youth wages. High minimum wages are particularly damaging for young workers. Many new workplace entrants need to invest in on-the-job training and general "work skills", such as how to co-operate with supervisors and fellow-workers, before they become sufficiently productive to justify high "adult" wages. Employers cannot compel employees to stay with the firm once training has been completed. Thus, if a minimum wage prevents the cost of on-the-job training from being recovered through lower "training wages" the demand for young workers will be adversely affected.5

There may be an offsetting increase in off-the-job training by young people in an attempt to raise their productivity and make themselves employable at the new minimum. However, since these training opportunities were available, but were not chosen, before the minimum wage was imposed they are likely to be less effective than on-the-job training.

Australia has also seen a rapid growth in self-employment and contracting out in the last fifteen years or so.6 Some of this could be related to increasingly binding award wages. It could also be related to increases in the fixed costs of employment, such as increased leave loadings, provision for long service, sick and parental leave, additional hiring and dismissal costs resulting from anti-discrimination statutes and so on. Self-employed individuals also have much greater opportunities to minimise their tax liability. Thus, increases in marginal tax rates on ordinary wage and salary earners during the 1980's may also have increased the relative attractiveness of self-employment.7

The standard analysis can also explain why trade unions whose members are paid significantly more than the legally prescribed minimum support a minimum wage.8 A high minimum reduces the demand for unskilled or inexperienced workers and raises the demand for, typically unionised, skilled workers as employers switch technologies.

Unions representing unskilled workers may also favour the policy. While some of their members will lose their jobs, those who remain in employment will earn a higher wage. Even those workers who lose their jobs might initially favour the policy if there is some uncertainty as to who will be laid off. The attraction of the policy to unskilled workers will also be greater if those workers who lose their jobs receive generous welfare payments.

On this view, the beneficiaries of minimum wage laws, but not necessarily more extensive intervention such as occurs with the Australian award wage system, are a concentrated vested interest. They are also currently organised as a political entity. The losers are a diffuse group. Each member of this group is probably unaware of the source of his problems, and is probably not in a strong position to lobby for change even if he is aware.

While the standard analysis can explain some of the effects of minimum wage laws, other consequences are more difficult to rationalize. In particular, the standard analysis cannot explain why so many employers appear to be able to pay the legally prescribed minimum wage without greatly reducing employment. In the standard analysis, it is only through a reduction in employment that the marginal product of workers can be increased to equal the legally prescribed minimum real wage.

We can imagine a "labour market" as consisting of a range of related supply and demand curves as illustrated in figure 2. There would be one pair of curves for each level of ability, experience and training ("skill") of the employees.

As we define skill levels more narrowly, the demand curve becomes more elastic (flatter) than the demand curve in figure 1. Any given skill category has close substitutes in the form of nearby categories. The demand for any one category therefore is likely to decline substantially following an increase in the wage rate paid to just that category. Indeed, one of the reasons for the downward sloping demand curve in figure 1 is that employers switch to demanding more unskilled workers as the real wage declines.

The distributions of experience, training, abilities and so forth across workers should be relatively smooth, particularly at the low wage levels where we would find most workers.9 We would also expect that the marginal product of employees should vary reasonably smoothly with the level of ability, experience and training of the employees. Firms use different technologies, and have different opportunities for substituting between technologies, as a function of the relative wages of different types of employees, the cost of capital equipment and so on. There would seem to be little reason for marginal products to jump discontinuously at a particular level of ability, experience or training.

The equilibrium wages and number of employees in each of the "markets" in figure 2 would therefore also vary smoothly as the relevant demand and supply curves shift in response to the distribution of characteristics in the population of workers and the distribution of job opportunities in the population of firms. In practice, real wages in a deregulated labour market tend to have a log-normal distribution as illustrated in figure 3.10

Figure 4 illustrates the distribution of wages following the imposition and enforcement of a minimum wage.11 Any individual whose marginal product after the minimum is imposed is less than the minimum would lose his job. The application of figure 1 to figure 2 implies that some individuals with a marginal product less than the legal minimum wage before the minimum is imposed will keep their jobs and be paid the minimum. As we noted above, however, we would expect the demand curves for a narrowly defined skill category of labour to be quite elastic. A legal minimum real wage of w0 would therefore eliminate most jobs with a marginal product less than w0 before the imposition of the minimum wage.

The reduction in employment following the imposition of a minimum wage generally raises the marginal products of labour and shifts the wage distribution to the right, particularly for low wages where most of the employment changes are concentrated. Thus, the post-minimum distribution in figure 4 is not merely a truncated version of the distribution in figure 3. Nevertheless, we would expect the post-minimum distribution to be a truncated version of some "smooth" distribution.

In practice, the imposition and effective enforcement of a minimum wage leads to a large number of workers receiving the minimum as illustrated in figure 5. Furthermore, a change in the minimum wage shifts the mass of workers receiving the minimum.

Similarly, the distribution of wages in Australia has noticeable peaks at various award wage levels. Many workers in different industries, or parts of the country, receive exactly the same wage. As with the simple minimum, however, the award wage is non-binding in some cases and the firms make over-award payments.

In a deregulated labour market, the wages paid for similar jobs in different industries or different locations would be related since the employers are drawing on a common labour pool. However, the marginal products of workers in a particular job classification are likely to vary from one industry to the next. Even in the same industry, different employers use different technologies, so the marginal products of workers nominally doing the same job are likely to differ. Finally, similarly classified jobs in different industries or locations are likely to have different non-pecuniary characteristics. This would also lead to wage variations as workers and firms competed on the attractiveness of the overall employment opportunity and not just wage rates.

In summary, in a free and competitive labour market we would expect to see a smooth distribution of wages within a particular job category rather than the high degree of uniformity characteristic of the Australian wage distribution.

These effects of minimum and award wages on the distribution of wages have several other important implications. The apparent ability of wages to adjust to legally prescribed levels might lead some to conclude that, without government intervention or monopolisation of the labour market through trade union action, all wages would be set at "starvation levels". Others might not go so far as this, but still might conclude that there is a considerable element of "convention" or "arbitrariness" in the determination of real wages and that neoclassical economic theory has little relevance to explaining wages.

In addition, the loss in employment, and increased unemployment, resulting from legally prescribed wages is less than standard economic theory would seem to imply. Workers whose value of marginal product is not far below the legal minimum keep their jobs and are paid the legal minimum. The policy appears to impose fewer costs than economists predict.

Finally, since minimum wages do not lead to as much unemployment as economists might expect, they could appear to be an attractive alternative to higher taxes and higher welfare payments as a means of protecting the less fortunate or less able members of society.12 It might not be surprising to find many middle class voters believing that minimum wages can be imposed at low cost.


An alternative model

Employees are interested in the remuneration per hour whereas employers are interested in the remuneration per unit of labour services. The productive services of employees can be varied in the intensity with which they are supplied per hour. For want of a better term, we can talk of the "effort per hour" supplied by the worker. Our key innovation is to allow employee effort to be part of the market exchange between employers and employees.

The so-called "efficiency wage theory" has also proposed models where employees can vary effort.13 This theory usually assumes that, while the employer cannot observe the level of effort, he believes that by increasing wages he will encourage his workers to supply greater effort.

We also focus on the relationship between wages and the level of effort supplied by workers. Contrary to the efficiency wage theory, however, we assume that the employer can to some extent observe and control the effort (net output per hour of labour input) of his employees. For example, the employer can increase supervision, decrease the number or length of work breaks, reduce the amount of socialising on the job, cut "fringe benefits", control losses from breakage or pilfering, or change the assembly line to force workers to produce more output per hour, or produce fewer defective items.14

Such modifications to technology or work practices may require additional maintenance, additional supervisory staff, extra equipment, or other expenditures by the employer. Employees also are likely to bear some costs. The work environment may become less pleasant and rewarding, or employees may be forced to expend more energy per hour of work.

Employees also can change their productivity in subtle ways that are not easily observed or controlled by the employer. For example, they can alter the care they take with their job, or the number or quality of suggestions they make for improvements to the production process. Employees who have worked for the same employer for some time acquire skills and abilities that are particularly useful to that employer but are of limited value in alternative jobs. The costs of acquiring such firm specific skills, along with significant search costs, make it expensive for employees to change jobs. Search and training costs also make it expensive for firms to hire new employees.

Firms and workers who have formed a productive match thus have a "surplus" to share between them. An employee is better off in his current job than he would be in the next best alternative. The firm is better off with its existing employees than it would be with the next best alternative employees.

If an employee believes he is being "cheated", in that he is not getting a "fair share" of the surplus arising from a productive match, he can reduce his "effort". To encourage greater productivity, an employer therefore needs to share some of the "rents" with employees.15

The employer thus has both a "carrot" and a "stick" to influence the effort level of employees. The net result is that employee productivity depends on both the real wage offered to the employee and the effort level enforced by the employer.

So that we can represent the analysis with simple diagrams, we assume the hours of work of each employee is fixed. This assumption might also be realistic, since the employer often has limited flexibility to vary the hours of any one employee.16 The algebraic model in the appendix allows for variable hours of work and numbers of employees. Except for an important aspect that we discuss later in more detail, the arguments presented in the paper also pertain to the more general model.

For a given number of labour hours, increases in effort enable the employer to pay a higher wage while maintaining profits. This gives an "iso-profit locus" in figure 6 where combinations of w and e keep profits constant.

As effort increases, the marginal product of effort decreases and the marginal cost of enforcing even higher effort levels increases. Hence, as w increases, larger increases in effort are required to compensate for equal increases in w. Beyond some level of effort, ê, further increases in e reduce the level of w the firm can pay. The locus in figure 6 therefore becomes negatively sloped for e > ê.

We also assume workers are worse off when they are forced to supply more effort but are better off with a higher real wage.17 This leads to a set of "indifference curves" as in figure 6. These trace out all combinations of w and c yielding a particular level of satisfaction of the employee.

Since the employee dislikes being forced to supply effort, he must be compensated by higher wages if he is to remain equally satisfied as e increases. Hence, the indifference curves are positively sloped in (w,e) space. The concavity of these indifference curves follows from the assumption of decreasing marginal utility of wages and increasing marginal disutility of effort. As increases, larger increases in w are required to compensate for a given increase in e.

In a free market equilibrium, the chosen wage and effort levels will maximise the worker's utility for a given level of firm profits as at (w*, e*) in figure 6. The algebraic model in the appendix provides a more explicit justification for the equilibrium as drawn in figure 6. Firm profits and worker utility at the equilibrium depend on the trade-off between enforced effort and worker surplus as alternative means of increasing productivity.

Now suppose the firm and the worker are forced to negotiate in the context of a minimum wage law specifying that the worker must be paid a (real) wage w0 per hour. The appendix presents an algebraic analysis of the effect of the law. It can be represented as in figure 7.

The firm can pay the higher minimum wage by increasing the amount of effort of the employee, but the deal between the employer and employee is no longer efficient. It does not make either the firm or the worker as well off as they could be given the technology.18

If the exogenously imposed minimum is too high, there may be no level of e that would enable the employer to pay w0 and earn a profit. The minimum wage would then produce unemployment as in the standard analysis.19 Alternatively, the employer might have to increase e so much that the worker is worse off than his "reservation level" of utility, U0. Unemployment would again increase as workers leave their current job to search for an alternative they believe will yield higher utility. For some unskilled workers, the relevant alternative might be long term unemployment and the dole.

The indifference curve corresponding to utility level U0 intersects the zero profit locus for the firm at wmax. Any exogenously imposed real wage between w* and wmax would not lead to unemployment, or efficiency losses as usually measured.

Since many employers can adjust to the minimum wage, however, many employees would receive the minimum. Furthermore, as the minimum adjusts, the mass of workers on the minimum would adjust along with it. In contrast to the standard analysis, our model can explain the effect of minimum wages on the wage distribution.

An observer looking only at wages and employment might conclude that intervention is able to increase real wages with few adverse consequences. One might be tempted to conclude, mistakenly, that wages are a matter of "convention" and cannot be explained by economic theory.

Our model can also explain why minimum wages are more likely to reduce the employment of younger workers.20 These workers have accumulated fewer firm-specific skills and therefore are probably earning fewer "rents" from their current job than more established workers. There would be less of a difference between the maximised utility level and U0 for these workers. Wages could not be increased as much above w* before utility declined below U0.

Even where the minimum wage does not reduce employment it probably will reduce both firm profits and the employee's surplus in his current job. Thus, a minimum wage that has little effect on employment nevertheless can impose considerable costs. Reduced worker satisfaction with jobs could be a large, even if disguised, component of these costs.

The implication that those unskilled workers who keep their jobs are likely to be made worse off by a minimum wage contrasts starkly with the usual result that such workers necessarily gain. The analysis in the appendix shows, however, that unskilled workers who keep their jobs could be made better off, especially when we allow hours and employment to vary.21 In particular, suppose most of the adjustment to a minimum wage takes the form of a decrease in the number of employees. If the hours worked by each employee fall, or do not rise greatly, then total hours worked (hours per employee times the number of employees) will fall and the marginal product of labour will rise. The firm may then be able to afford the minimum wage without having to increase e. The increase in the real wage, perhaps combined with a change in hours worked by each employee, could then increase the utility of those unskilled workers who keep their jobs.22 In this circumstance, even unions representing unskilled workers might favour a minimum wage, particularly if there is a welfare system to assist those who are priced out of employment. In any case, unions representing skilled workers would be in favour of the policy as in the standard analysis.


Some further implications of the model

Our analysis can explain the concern of trade unions with conditions of work and work practices. At the distorted position following the imposition of a minimum or award wage, the workers are not at a utility maximising position. In the new distorted equilibrium, workers are happy that their real wage is higher, but unhappy that the level of effort required of them is too high. There will be agitation to reduce the level of effort.

Unions may oppose the introduction of new technology in an attempt to avoid changes in work practices that increase worker effort. Many of the productivity gains from technological progress can only be realised, however, by introducing new capital equipment and new work practices. Opposition to change engendered by exogenously imposed wages might therefore explain the relatively slow productivity growth that seems to be a feature of labour markets, such as those in Australia, that are characterised by extensive intervention.

A more direct adverse effect of award wages on productivity growth has recently been discussed by Boot (1992). He observes that high minimum wages prevent employers from providing extensive on-the-job training in general work skills. Employers can only recover the cost of investing in these skills by paying their employees a low "training wage."23 A reduction in training in turn reduces future productivity, and future real wages. In the context of our model, the reduction in current training can be viewed as another way of increasing effort. While the effects of award wages identified by Boot are another example of the type of distortions identified in this paper, they are worthy of a separate, explicitly intertemporal, analysis.

While high minimum and award wages are likely to reduce productivity growth, the current level of productivity is another matter. In so far as employers successfully raise the effort of their employees in response to high minimum or award wages the productivity of workers is likely to increase. As we have seen, however, these increases in effort levels are likely to make both the employees and the owners of the firm worse off.

For example, suppose an employer ran an assembly line at a speed that was at the limit of the physical endurance of his employees. Productivity could be extremely high, in the sense that net output per hour of labour input could be extremely high, but the operation would not be efficient. Both the employees and the owners of the firm could be better off if the speed of the assembly line were slower. The employees would be willing to "pay" quite a bit in terms of reduced wages to be able to work at a less hectic pace. The saving in wages from reducing the speed of the line could therefore more than compensate the employer for the fall in output.

Our analysis suggests, therefore, that we should be wary of associating productivity levels with "welfare". While there is a relationship between productivity growth and growth in living standards, we are ultimately concerned about individual welfare. Productivity increases are valuable not for their own sake but only when they are a reliable indicator of individual welfare.


Concluding remarks

The standard economic analysis of labour markets has difficulty explaining the effect of minimum wages, and other legally prescribed wage awards, on the distribution of wages. This has probably contributed to the belief that labour markets do not behave like other markets. In turn, the belief that politicians or tribunals can set wages without regard to the usual laws of economics has encouraged voters, who are wary of new taxes, to view minimum wage laws as a "free lunch" method of protecting disadvantaged members of society.

We have argued that when "effort", or labour services per hour of work time, are explicitly recognised as part of the trade between employers and employees, economics can explain many of the "stylised facts" about the effects of minimum and award wages on labour markets. The modified model implies that the costs of exogenously imposed wages are likely to be much greater than even many economists expect.

The case for free trade is based on the presumption that the parties to an exchange can best look after their own interests. Outside intervention aimed at limiting the range of bargains that individuals are free to negotiate can only reduce the gains from trade. While such intervention can alter the distribution of the benefits from trade, there are more efficient methods of redistributing income to protect the interests of the unlucky, and less able members of society.

We have argued that when "effort", or labour services per hour of work time, are explicitly recognised as part of the trade between employers and employees, economics can explain many of the "stylised facts" about the effects of minimum and award wages on labour markets. The modified model implies that the costs of exogenously imposed wages are likely to be much greater than even many economists expect.

The case for free trade is based on the presumption that the parties to an exchange can best look after their own interests. Outside intervention aimed at limiting the range of bargains that individuals are free to negotiate can only reduce the gains from trade. While such intervention can alter the distribution of the benefits from trade, there are more efficient methods of redistributing income to protect the interests of the unlucky, and less able members of society.


Technical appendix

Let w be the real wage per hour, H0 the (fixed) number of hours and assume output is an increasing function, f, f > 0, f" < 0, of "effective" labour services. Let effective labour services per hour worked be given by a function.

(I) G(c, U(wH0e)), with Gl > 0, G2 > 0, U1 > 0, U2 < 0, U11 < 0, U22 < O

where e is the level of enforced effort (the "stick") and the second argument in G represents the encouragement offered to the worker by the surplus attached to his current job (the "carrot"). We assume G 0 if both e 0 and U(wH0,e) U0, where U0 is the utility the worker can obtain in the next best job. Furthermore, we assume G2 0 as U(wH0,e) U0. That is, "encouragement effect" disappears as the "surplus" attached to the current job vanishes. At the other extreme, G is bounded above, so that Gl 0 as e and G2 0 as U(wHo,e) .

We assume the worker likes higher real wages because they enable him to afford additional consumption, but he experiences diminishing marginal utility from wage increases. The worker also dislikes enforced effort, and experiences increasing marginal disutility from increases in e.

Finally, we assume that the per employee cost to the firm of enforcing effort level e is

(2) c(e), with c(e) > 0, c(e) > 0.

Increases in e require increased expenditure by the firm. Furthermore, since the easiest methods of rising e are likely to be exploited first, the marginal cost of raising e increases as e increases.

The firm then chooses e and w to maximise:

(3) max f[G(e,U(wHo,e))Ho] - wHo - c(e)

e,w

The first order conditions for a maximum are

(4) f[G1+ G2U2]H0- c(e) = 0

(5) fG2U1H20- H0 = 0

From the second equation, we find

(6)

and, since G2 0 as _U = U(wH0,e) - U0 0, the worker will receive positive surplus from his job. From equations (6) and (4), we obtain

(7)

The left hand side of (7) represents the marginal trade-off for the worker from increases in effort versus increases in real income, or the slope of an indifference curve. Specifically, along a given indifference curve, U(wH0,e) = U*, the slope ids given by

(8)

A marginal increase in e, holding U fixed, increases profits by fG1H0- c(e) and therefore allows the firm to increase the real wage it pays by

(9)

while maintaining profits unchanged. Equating (8) and (9) we arrive at equation (7). Equation (7) therefore implies that the maximum will occur where the slope of an indifference curve matches the slope of a wage-effort iso-profit locus for the firm as illustrated in figure 6. The particular indifference curve and iso-profit locus are determined by the solutions w* and e* to (6) and (7).

Imposition of a minimum wage

Now suppose a minimum wage, w0 is imposed. Since w w0, the maximisation changes to

(10) max f[G(e,U(wH0,e))H0] - w0H0 - c(e) + l (w - w0)

e,w

with first order conditions

(11) fG2U1H2o - H0 + l(w-w0) = 0, l 0, w w0

If the minimum wage is binding, then w = w0 _ w* and l _ 0. Hence,

(13) fG2U1H0 - 1 _ 0.

a condition that can be explained as follows. At the maximising value for w in the absence of the minimum wage, w*, the first derivative of the objective function with respect to w is zero and second derivative is negative. Then for w0_ w*, the first derivative of the objective function with respect to w, evaluated at w0, must be negative.

We can use (13) to show that the slope of the indifference curve at the constrained equilibrium is flatter than the slope of the iso-profit locus, as illustrated in figure 7. The distorted equilibrium generally will involve a lower level of utility for the worker and lower firm profits. Some of the "surplus" associated with the superiority of the match between the firm and the worker will be dissipated in satisfying an arbitrary exogenous wage level that neither of them would voluntarily choose were they left to bargain in freedom.

If f(G(e, U(woHo,e))Ho) < woH + c(e) or U(w0,e) < U0 at the maximising value for e then the minimum wage is set so high that the firm will choose not to employ the worker, or the worker will choose to quit and accept the "reservation level" of utility, U0. The minimum wage will then have adverse effects on output and employment as in the standard analysis. In terms of figure 7, these correspond to situations where w0 exceeds the level wmax given by the intersection of the zero profits locus and the indifference curve corresponding to utility level U0.

Variable hours and number of employees

In principle, it is easy to generalise the analysis to the case where the hours of work, L, and the number of employees, N, are variable. The firm can then increase the marginal product of labour to match the higher wage rate by reducing employment and hours rather than by increasing e.24

In addition to increasing with consumption and therefore real income, wL, and decreasing with e, worker utility now decreases with hours of work L (holding real income constant). We also introduce a fixed cost of employment v in addition to an hourly wage w. In the unconstrained case, the maximisation problem for the firm changes to25

(14) max f[G(e,U(wL,e,L))LN] - wLN - c(e)N - vN

e,w,L,N

with first order conditions now given by

(15) f[G1 + G2U2]LN - c(e)N = 0

(16) fG2U1L2N - LN = 0

(17) f[G2U1wLN + G2U3LN + GN] - wN =0

(18) fGL - wL - c(e) - v + 0

These four equations are solved for e, w, L and N. The equations (15) - (18) can be simplified to

(19) G1 + G2U2 - c(e)G2U1 = 0

(20) fG2U1L = 1

(21) G2U3L + G = 0

(22) G = G2U1[wL + c(e) + v]

Equations (19), (21) and (22) can be solved for e, w, and L independently of the level of employment N. Using these solutions for e, w and L equation (20) can be solved for N.

With an exogenously imposed binding minimum wage, w0, we lose the first order condition (16) for w and solve equations (15), (17) and (18) for e, L and N as functions of w0. Again, the equations can be simplified to a pair of equations to be solved for e and L:

(23) (G1 + G2U2)[wL + c(e) + v] - c(e)G

(24) (G2,U1wL + G2U3L + G)[wL + c(e) + v] - wLG = 0

with N then obtained from equation (18).

The additional freedom the firm has to vary hours of work and the number of employees should enable it to adjust to an even larger range of exogenously imposed real wages without going out of business. In so far as the firm reduces N, however, a change in the minimum wage will produce a fall in employment. We might identify this fall in employment with "layoffs" rather than "quits" (when U falls to U0) or "bankruptcies" (when firm profits fall to zero).

The key difference between this more general model and the simple model with fixed employment and hours, however, is that a reduction in total hours worked, LN, is now an alternative to an increase in e as a method of raising the marginal product of labour to equal w0. If the increase in the real wage together with the change in hours worked by each employee raises utility, and if e does not increase too much, then the utility of those individuals who keep their jobs, U(w0L,e,L), can rise. We can restore the proposition from the standard analysis that the imposition of the minimum wage may be favoured by a union representing unskilled workers when it raises the utility of those who keep their jobs. This is only likely to happen, however, in those cases where the minimum wage reduces total hours worked, and therefore imposes high efficiency losses as conventionally measured.

Since the minimum typically is specified in nominal terms, it may become less binding over time. The firm would then wish to replace some of the employees it laid off when the minimum was first imposed. If the minimum is expected to be binding for only a short period of time, and there are high costs of searching for, and training, new employees, employment might be unaffected by the imposition of a minimum wage. The case where employment is held fixed is also of interest since it represents the outcome when the employment consequences of a minimum wage, emphasised by the standard analysis, are absent. Finally, we can return to the simple model, with both L and N fixed, by solving (15) for e given values for w0, L and N.

A numerical example

To illustrate the model, we calculated the effect of a minimum wage for the following example. Employee utility was taken to be additively separable between consumption and the remaining arguments, effort and hours of work:

(25) U(wL,e,L) = (wL)g - b (H - L)-d(e* - e)-Y

The marginal disutility of working depends on the level of effort required per hour and as L H, or e e*, U - . Additional consumption raises utility, but at a diminishing rate when g < . The "productivity" of each hour of work was normalised to lie between zero and one with increases in e and U both raising effective labour input per hour of working time:

(26)

In this expression, Uo is the utility level in the next best alternative use of the employee's time with U U0 being a necessary condition for the employee choosing to remain in his current job. Also, e 0 and k, 0 k 1, represents the relative weighting of the "stick" and the "carrot" as means of stimulating worker productivity. The two components of G for U0 = 0.2 are graphed in figure 8.

Clearly, for the given functional form, small increases in enforced effort e above zero are less effective than small increases in U above U0 in raising worker productivity. The squared functional forms were chosen to ensure the partial derivatives of G with respect to e and U each tend to zero as e 0 and U U0 respectively.

We used the simple Cobb-Douglas production function with output a function of total "effective" labour input

(27) Q + (GLN)a, 0 < a < 1.

Finally, the cost of enforcing effort was taken to be proportional to the square of e:

(28) c(e) = le2

The values of the parameters used for the illustrative calculations are set out in table 1.


Table 1

Parameter Base Dk Dg Db De* Dd DU0
g 0.75 0.75 0.9 0.75 0.75 0.75 0.75
b 10.0 10.0 10.0 5.0 10.0 10.0 10.0
d 1.05 1.05 1.05 1.05 1.05 1.0 1.05
Y 0.75 0.75 0.75 0.75 0.75 0.75 0.75
H 75.0 75.0 75.0 75.0 75.0 75.0 75.0
e* 1.0 1.0 1.0 1.0 1.25 1.0 1.0
k 0.75 0.25 0.75 0.75 0.75 0.75 0.75
U0 0.2 0.2 0.2 0.2 0.2 0.2 0.25
a 0.75 0.75 0.75 0.75 0.75 0.75 0.75
l 0.005 0.005 0.005 0.005 0.005 0.005 0.005
v 0.025 0.025 0.025 0.025 0.025 0.025 0.025

The results for the base case are given in Table 2. The effect of a minimum wage was simulated by imposing w0 = 1.05w, where w is the solution to the unrestricted model.

The imposition of a minimum wage raises e, and reduces worker utility and firm profits. As the firm is given less flexibility to respond to the minimum wage (with N and then N and L fixed) firm profits are adversely affected to a greater extent. When hours are free to vary but N is fixed, the imposition of a minimum wage leads the firm to reduce working hours. Worker utility is then less adversely affected since the reduction in working hours partially compensates the workers for the increase in e. Finally, it is interesting to note that when N, and both N and L, are fixed the imposition of a minimum wage raises output and worker productivity even though it makes both the firm and the workers worse off.


Table 2

Restricted Minimum Wage Percent Change Fixed Employment Percent Change Fixed

Employment & Hours

Percent Change
w 0.0167 0.0175 5.0 0.0175 5.00 0.0175 5.00
e 0.6411 0.6690 4.36 0.6690 4.36 0.6690 4.36
L 38.8843 38.5819 -0.78 38.3814 -1.29 38.8843 0.00
N 144.0445 136.9885 -4.90 144.0445 0.00 144.0445 0.00
U 0.2230 0.2189 -1.85 0.2191 -1.78 0.2187 -1.95
h 32.4042 32.0628 -1.05 32.0348 -1.14 32.0149 -1.20
G 0.1171 0.1224 4.49 0.1224 4.51 0.1223 4.45
Q 129.6169 128.2514 -1.05 132.6724 2.36 133.9197 3.32

Table 3 presents selected results for the parameter variations given in Table 1 In table 3, a subscript 0 refers to the solution under a minimum wage, a subscript 1 refers to the solution with employment N fixed at its initial value and a subscript 2 refers to the solution with both N and L fixed at their initial values. A caret (Ù) over a variable signifies a percentage change.

Table 3

Base Dk Dg Db De* Dd DU0
w 0.0167 0.0160 0.0186 0.0139 0.0188 0.0192 0.0189
e 0.6411 0.6406 0.6689 0.6450 0.7515 0.6312 0.6509
L 38.8843 38.4437 41.2981 46.7518 43.8202 38.7594 39.9755
N 144.0445 5.9020 101.9944 856.1539 425.5522 77.0982 93.3079
U 0.2230 0.2019 0.2170 0.3987 0.4112 0.2193 0.2856
h 34.4042 1.2624 26.9862 193.3849 121.1065 19.8547 24.4006
ê0 4.36 3.75 4.14 1.31 1.74 4.15 4.79
0 -0.78 -0.46 -0.65 0.52 0.55 -0.62 -1.09
0 -4.90 -5.05 -5.06 -5.45 -5.56 -4.98 -4.77
0 -1.85 -0.11 -1.39 5.26 5.59 -1.39 -2.68
0 -1.05 -0.91 -1.09 -0.41 -0.46 -0.97 -1.20
ê1 4.36 3.77 4.14 1.47 1.91 4.15 4.78
1 -1.29 -1.00 -1.17 0.09 0.05 -1.16 -1.58
1 -1.78 -0.11 -1.34 5.10 5.40 -1.34 -2.59
1 -1.14 -1.01 -1.18 -0.53 -0.58 -1.06 -1.29
ê2 4.36 3.74 4.13 1.50 1.93 4.15 4.81
2 -1.95 -0.12 -1.45 5.06 5.38 -1.45 -2.87
2 -1.20 -1.04 -1.23 -0.53 -0.58 -1.11 -1.38

When enforced effort e becomes a less significant determinant of G (the second column of table 3), the equilibrium levels of e and U decline. The imposition of a minimum wage now increases e and reduces U to a lesser extent, while the percentage effect on employment is greater. The equilibrium level of employment before the imposition of the minimum is, however, greatly reduced by the reduction in k. The marginal effect of e on G depends positively on k and, from (20), a reduction in G2 requires a higher marginal product of labour and thus a lower level of employment.

An increase in g (the third column of table 3) increases the importance of consumption, and therefore income, in worker utility while reducing the extent of decreasing marginal utility of consumption. Equilibrium real wages, hours and enforced effort are higher, while the level of employment is lower. The imposition of a minimum wage has less of an effect on hours, e and U and a more adverse effect on employment and profits than in the base case.

A reduction in b also increases the relative weight of consumption in worker utility, but without altering the marginal utility of consumption at any given level of consumption. As b 0, the indifference curves in figures 6 and 7 become vertical. Thus, for small values of b, the maximising level of e is closer to the level that maximises wages. Thus, e doesn't change much with the imposition of a minimum wage. At the parameter values in table 1, those workers who keep their jobs are made better off by the imposition of a minimum wage. The adverse employment effects of the minimum wage are, however, larger in percentage and absolute terms than we found in the first three columns of table 3. Furthermore, those workers who lose their job suffer a greater loss in utility since the equilibrium value of U exceeds U0 by a greater margin.

An increase in e* also reduces the adverse consequences for workers of increases in enforced effort levels. The consequences for the equilibrium values of w, e L and N and the effects of a minimum wage are similar to the case of a reduced value for b.

A decrease in d on the other hand raises the marginal disutility of increases in e for a given level of e and L. The equilibrium value of e in the undistorted equilibrium therefore is relatively low and the imposition of a minimum wage again reduces worker utility.

Finally, an increase in the reservation level of utility raises the equilibrium level of worker utility by a greater percentage but also increases the adverse consequences of a minimum wage.


Notes

* I thank Robert Albon, Matt Benge, Ray Evans, Mark Harrison and Frank Vella for valuable comments on previous versions of this paper.

I Unskilled workers who keep their jobs do not necessarily gain since, as we shall see, there could be other adjustments in their working conditions or hours of work that make them worse off.

2 For example, rent controls often lead to a deterioration in the quality of housing services through reduced maintenance and refurbishing. Albon (1980) contains a discussion of the effects of rent controls in Australia and several overseas countries. Albon and Stafford (1990) model the effects of rent control on housing maintenance and discuss how different types of rent control can affect maintenance decisions by landlords.

3 As noted by Stigler (1946), the minimum wage will increase employment in sectors affected by the minimum wage if the labour market in the covered sector is monopsonistic. Brozen (1962) observes that since many categories of employment in the published statistics consist of both covered and uncovered employees, it is easier to test for monopsony in the covered sector by looking at employment in an uncovered sector. If the covered sector is monopsonistic then employment should fall in uncovered sectors, such as domestic service, following the imposition of the minimum wage. On the other hand, if the covered sector is competitive, employment should rise in the uncovered sector. Using data on the volume of employment in domestic service in the US, Brozen concludes that the sectors covered by the minimum wage in the US are competitive.

4 Mincer (1976) presented evidence that higher minimum wage rates in the US eventually lead to reduced labour force participation rates as job-seekers become discouraged and cease to look for a job.

5 If the skills are specific to the firm, when the worker has completed his training his marginal product working for his current employer would be higher than his marginal product working for other employers. The employer can recover some of the costs of training by paying the worker less than his marginal product in the post-training period. If the employer is to recoup his training costs, however, then a high minimum wage in the training period would require a larger gap between the post-training wage and marginal product. This would in turn make the post-training wage closer to wages the employee could receive from other employers. The employee would be on the margin of quitting and this would place the employer's investment in training at risk. Minimum wages might therefore penalise on-the-job training in firm-specific skills in addition to general skills. Hashimoto (1982) presents evidence that minimum wages have reduced on-the-job training in the US.

6 The ratio of non-farm self-employed individuals to total non-farm employment rose from about 9% in the late 1960's to 10% in 1974, 12% in 1977, 12.5% in 1988 and over 13.5% in 1992.

7 Other industrialised countries have also experienced an increase in the number of small firms relative to large firms in recent decades. Reductions in transport, communications and data manipulation costs, and increasing demands for "customised" products with increasing levels of consumption might have favoured the growth of small relative to large firms.

8 For example, Hamermesh (1982) claimed that if a non-binding youth sub-minimum wage were introduced in the US, without any adjustment being made to adult wages, roughly one adult job would be lost for every four teenage jobs created. With no legally binding minimums applying to the adults, the loss of adult jobs would actually show up as a fall in adult wages. Kau and Rubin (1978) presented evidence that union support for minimum wage legislation in the US affected Congressional votes on the issue.

9 There will be few substitute workers for some specialist jobs so we might expect a more discontinuous distribution of equilibrium wages at the "high end" of the market.

10 Roy (1951) argued that if workers with normally distributed productivities self-select into jobs according to their marginal products the resulting distribution of real wages will be log-normal. The sorting process systematically biases the distribution toward large wage values relative to a random assignment of workers to jobs. The latter process would yield a normal distribution of wages in accordance with the distribution of productivities.

11 Since the minimum wage is not completely enforced, a survey of real wages will find some individuals being paid less than the legal minimum. Ashenfelter ant Smith (1979) present evidence suggesting that at least 30 percent of covered workers in the US are paid less than the minimum.

12 Since many low-wage earners are teenagers, however, they are often secondary earners in middle or upper income families. Even if the minimum wage could increase the wages of unskilled workers without reducing their employment opportunities, it would not necessarily be a very effective device for redistributing to low income families.

13 This literature originated with Calvo (1979), Salop (1979) and Solow (1979). The version closest to the model discussed in the text is Shapiro and Stiglitz (1984). Many of the basic articles in this literature are reprinted in Akerlof and Yellen (1986). The aim of these models is to explain why an excess supply of labour might not reduce (real) wages. While a reduction in wages would reduce costs, the productivity of the work force might fall so much that real profits decline when wages are lower. Akerlof and Yellen also reprint articles by Calvo and Wellisz (1979), Lazear and Moore (1984) and Malcomson (1984) that use the idea that employees can vary their level of effort, perhaps in a way that is only partially detectable by the firm, to explain the hierarchical structure of wages and age-earnings profiles within firms. Lazear ant Moore claim that the desire to provide employees with incentives not to shirk may be more important than on-the-job training as a source of increasing earnings with job tenure.

14 Our explanation is also related to the literature on "compensating differentials." These are variations in wage payments that "compensate" for variations in the non-pecuniary aspects of jobs. A compensating differential could, however, apply to variations in working conditions or living conditions that do not affect effort levels per hour of work. Examples could include wage variations between locations that compensate for differences in weather conditions, recreational and cultural amenities, the quality of schools, the quality of local public facilities or variations in the cost of living.

15 When used technically, "rents" refers to payments for the use of a resource that are strictly greater than the bare minimum required to retain the resource in its current use.

16 We implicitly assume that the firm can arrange a combination of wage and effort level for each of its employees. In fact, the production technology may require workers doing a given job to work under the same conditions. In that case, the preferences of the workers for effort level and real wages will have to be "aggregated" by some (political) mechanism. The necessity to make such "joint" trade-offs between wages ant "working conditions" (another example is safety) may rationalise trade unions (see, for example, Freeman ant Medoff (1979) or the survey article by Oswald (1985) for views on the economic role of trade unions).

17 The firm and the worker are actually interested in two different real wages. The firm is interested in the wage relative to its output price while the worker is interested in the wage relative to the cost of living. Changes in the relative price of the output of the firm will therefore shift one of the curves in figure 6. 18 A minimum or award wage that applies across a range of markets may also affect the reservation level of utility, U0. The minimum wage is likely to have similar effects on utility associated with the current job and the utility expected from an alternative job. In those cases where the next best alternative is unemployment, changes in unemployment benefit levels and eligibility conditions will affect U0 and therefore bargains between employers and employees.

19 In the short run, the firm only needs to cover its operating costs to remain in business. It may be willing to earn less than a competitive rate of return on its capital stock for a short period of time so long as it expects to be able to earn more than the competitive return on its capital at some time in the future. The firm may be reluctant to lay off employees to cover a temporary decline in profits when it has invested in a relationship with those employees.

20 An alternative explanation is that unions often negotiate a "last on first off" hiring policy that discriminates against younger workers. Such policies may be easy to negotiate, however, precisely because they are agreeable to the parties for the reason given in the text.

21 1 am indebted to Mark Harrison for making this point clear to me.

22 An increase in hours will further raise real income, but it will reduce non-work time. A decrease in hours will increase non-work time, but will tend to offset the positive effect of the increase in w upon real income.

23 As argued above, training in firm-specific skills is also likely to be affected, but to a lesser extent.

24 In the long run, the firm could also vary its capital stock in response to variations in profitability. Changes in capital would further alter labour productivity and the endogenous solutions for e, w, L and N.

25 In a long run equilibrium, we would have three additional equations to determine the capital stock of each firm K, the relative price of the firm's output, p, and the number of firms in the industry m. The three additional equations would be a first order condition for the firm's choice of K, a zero profits condition (so entry into, and exit from, the industry would occur until profits equalled the normal return on K) and a market equilibrium condition so that total supply from the industry equalled total demand. As usual, if the firm's technology displays constant returns to scale in K and total labour services, GLN, then the scale of each firm (K and N) and the number of firms in the industry, m, cannot be determined. We could make m and scale determinant by introducing fixed costs per firm and assuming decreasing returns to scale (for example because there are additional factors of production that are in fixed supply). As far as the long run effects of a minimum wage are concerned, competitive pressure that limits profits in the long run would restrict the range of wages that could be imposed on the firm without reducing employment.


References

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