Compensatory wage difference. Occupation choice and compensating wage differences. The concept of reserve salary
The hedonistic theory of wages suggests that the worker seeks to increase his utility by choosing workplace. This utility depends both on the amount of wages and on various other characteristics of the workplace (positive and negative), in relation to which the worker has preferences.
Differences in wages, compensating for "non-salary" differences in the characteristics of jobs, are called compensatory.
The compensatory wage differential model is based on the following assumptions:
when choosing a workplace, the employee maximizes his utility from employment in this workplace, taking into account all its characteristics, and not just income (in this, the model of compensatory differences is based on the hedonic theory of wages);
the employee has or can obtain in the process of work information about all the characteristics of the workplace, and the costs of obtaining information are low;
workers are mobile and can move freely from one workplace to another.
Worker preferences are described by a utility function
U = u (W, X i),
where W -- wages; Xi - "non-salary" characteristics of the workplace.
Consider the case negative characteristics on the example of injury risk and occupational diseases R.
Then the employee's utility function U = u (W, R) and u" (W)> 0, u"(R)<0.
Worker preferences are described by a family of indifference curves (Figure 5.3a). The concavity of the curves reflects the decreasing marginal rate of wage substitution for risk.
Rice. 5.3. Indifference curves of employee and employer iso-profits reflecting their preferences for wages and risk of injury
Since risk reduction requires the employer to increase costs, employer preferences can be described by a family of iso-profit curves whose convexity reflects the diminishing marginal revenue as risk decreases. Competition in the market will drive the firm to zero economic profit and to the isoprofit curve corresponding to zero profit (Fig. 5.3b).
The employee, in accordance with his preferences, can choose various jobs offered to him by firms, while maximizing his utility function. So, in fig. 5.4 employees are equally satisfied with the workplace in the company BUT, and the workplace in firm B. In the first case, the combination of wages - the degree of risk W 1 , R 1 , in the second case -- W 2 , R 2. An increase in the degree of risk by ( R 2 -- R 1) is accompanied by an increase in wages by the amount ( W 2 -- W 1), which in this case will constitute a compensating difference.
Rice. 5.4. Compensatory differences in wages for varying degrees of risk
In the market as a whole, the intersection of all possible combinations of jobs offered will form a market supply curve, wages, a degree of risk, which will be positively sloped and flatter than the iso-profit curves of individual firms.
Rice. 5.5. Market supply curve of combinations wages -- risk of injury
The points of contact with the curve formed by the intersection of all possible preferences of workers form a set of decisions wages - the degree of risk (Fig. 5.5).
Congressmen and non-economists often argue that any environment must be made secure, no matter the cost. “The safety of human life is not a question of economists at all,” they argue. But their claims that costs should not play a role in security issues do not withstand even the most simple scrutiny. It suffices to analyze some of the conclusions that follow from the statement made.
Consider safety in relation to the field of operation of cars. At any given moment, there is some possibility of brake failure while any vehicle is moving. The consequences of this event are dire. The chance of dying in a car accident is drastically reduced if every day an experienced mechanic performs a thorough check of the brakes. However, probably no motorist checks the brakes of his car so often, since the costs here are quite large compared to the possible benefits. Most people check their cars 1-2 times a year, and there is no good reason to believe that this procedure needs to be changed.
Security is an advantage that many people value. To ensure it, it is necessary to spend real resources. Just as with any other resource use problem, the optimal level of security is determined by comparing the associated costs and benefits.
Security costs and benefits are likely to be assessed differently by different people. People who are afraid of a lightning strike, for example, will experience more peace of mind from installing a lightning rod than those who do not experience fear of a thunderstorm. The optimal set of security controls will be higher for the former than for the latter.
Approximately the same questions arise when making decisions related to safety in the workplace. Many industrial activities involve health and safety risks. This risk can usually be mitigated through the use of safety tools and measures. All of them are associated with additional costs and, in many cases, they still do not completely eliminate the risk. Should these activities be carried out, and if they should, how much does it depend on the ratio of their value to costs?
To make our discussion more concrete, consider a situation in a coal mine where filters are being considered to keep coal dust out of the lungs with the air. The cost of installing and operating these filters is $50 per miner per week. With filters, the life expectancy of miners will be the same as office workers, without filters, 10 years less. The question of whether filters should be installed morphs into a narrower question: "Is the increase in the life expectancy of a miner valued at more than $50 a week?" If yes, filters must be installed, otherwise these devices will not be installed. Let's say the miners valued an extra 10 years of their lives at only $40 a week. At the same time, the mine manager who installed the filters must cut the wages of the workers by $50 a week to cover his additional costs (assuming that coal buyers do not intend to pay the additional costs of this mine). It is assumed, however, that miners would rather have $50 a week than the protection that filters provide.
Of course, many miners will prefer to install filters, but not all. Suppose, for example, that 30% of miners value filters at $60 per week, and the remaining 70% at $40. These 30% of miners would support the proposal to install filters, while the remaining 70% would prefer to do without them. The mines that install the filters will pay $50 less per week than others. Miners priced at $60 a week for filters would prefer to work in pits with filters, while other miners would prefer to work in pits without filters.
Usually, there are several options to choose from. Line B in the figure means the continuity of the technically feasible combination "wage - security". The horizontal axis represents the level of safety as an annual probability of survival in the workplace. (A job where this probability is equal to 1 is considered completely safe). The vertical axis represents the hourly wage rate. Line B has a negative slope because resources must be spent to improve safety. The shape of line B is convex because we install the cheapest and most effective safety devices first and only then use the more expensive ones. Aspiring to 1 line B never reaches it; this indicates that no matter how much money is spent on safety, we cannot guarantee the absence of accidents.
Rice. Combination "salary - safety"
Risk-averse people (those with low marginal rates of substitution of wages for survival) will choose higher-paying, riskier jobs (point A). Risk averse people will choose safer jobs with lower wages (point C).
The choice of the optimal combination by each worker depends on his comparable assessment of risk and material well-being. Risk-averse people will have relatively steep indifference curves, reflecting their acceptance of lower wages in exchange for increased security (their choice is represented by point C).
On the other hand, people who are not afraid of risk will have a smoother indifference curve, reflecting their less willingness to give up wage income in exchange for additional security. The optimal choice of such a person is represented by point A.
The theory of compensatory wage differentials predicts that, all other things being equal, jobs that pay more are more dangerous. Cornell labor economist Robert Smith critically reviewed eight different empirical studies that examined the relationship between wage rates and job risk. These studies, each based on their own set of different data, found a positive relationship between wages and the likelihood of being killed on the job.
Compensatory wage differentials ranged from $20 to $300 per year for every 0.0001 increase in the annual probability of death at work. It is proposed in the future to take the probability of the annual death of steelworkers at the workplace as 0.0001, and the death of lumberjacks as 0.001. Assume that workers estimate a 0.0001 reduction in the probability of death per $100 per year. Then the compensatory wage gap for safety should be $900 per year higher for lumberjacks than for steelworkers (because the annual probability of dying is 0.0009 higher for lumberjacks). Of course, the overall wage difference between any two occupations depends on many factors besides the risk of death or injury, so the wage difference between steelworkers and lumberjacks can be either more or less than $900 a year. The theory suggests that if logging could somehow become as safe as working in a steel mill, lumberjacks' wages would have to drop by $900 a year.
I once attended a conference where an economist was discussing the concept of security-related compensatory wage differentials. The sociologist in the audience reacted angrily to his every word. He solemnly declared that "the theory is completely wrong, since everyone knows that the most dangerous and non-prestigious jobs are always done by the lowest paid workers." It is true that the most dangerous jobs are usually performed by low-income workers, but this does not invalidate the theory. The claim of the theory that wages will be higher in less safe areas of work has the caveat "ceteris paribus". When considering a large sample of American workers, many factors, in particular the level of education, mental development, experience and enterprise, vary significantly, and with it the ability to earn income from the sale of their labor in the market. From the plausible assumption that safety is a common good, it follows that high-capacity workers will choose jobs with high wages and security levels, and lower-productivity workers will choose jobs with lower levels of security and wages. But at the same time, their wages turn out to be higher than what they would receive if they chose a safer job (because of their low productivity, the salary in this job could not be high).
The above reasoning is easy to represent on the graph of choosing the optimal ratio between wages and security. The line in the following figure characterizes the set of technically feasible combinations between wages and security for a highly skilled worker.
Rice. Influence of qualification on the optimal choice of safety level
The budget constraint for highly skilled workers (B1) represents a more favorable set of options than for less skilled workers (B2). If safety is a common good, then most skilled workers will choose higher-wage, safer jobs (A) than jobs chosen by less skilled workers (C). But for any given skill level, there is also a trade-off between wages and security.
Line B2 means the appropriate set for a low-skilled worker. In the analysis, B1 and B2 play the role of budget constraints and, for a highly skilled worker, are located farther from the origin. If two workers have the same indifference curves and security is a common good, then a highly skilled worker (A) is optimally employed at a higher wage and higher probability of survival than a less skilled worker (C).
Many economists have argued that the existence of compensatory wage differentials associated with the presence or absence of security makes it unnecessary to regulate security in competitive labor markets. To illustrate this argument, consider again the example of logging and steelmaking. Imagine that there are measures (purchasing safer equipment, introducing stricter safety regulations, etc.) that reduce the annual probability of death during logging to 0.0001, i.e., to the level that exists now in steel plants. Let's say that the workers estimated at $100 a year for every 0.0001 reduction in the probability of death. This means that workers must agree to a $900 per year pay cut to allow for the implementation of all additional safety measures. Profit maximizing logging companies have an incentive to implement these measures if their costs are less than $900 per year per worker. If the costs are higher than $900, then neither the company nor the workers will be able to change the situation. It is clear that actions should be taken to make the logging process safer, but at a cost that the loggers themselves consider appropriate and not too high.
The Occupational Safety and Health Act (OSHA), passed by Congress in 1970, sets strict standards for workplace safety. Its stated purpose is to "guarantee a high degree of protection for the health and safety of the worker". Economists have often criticized OSHA, arguing that the security many people are forced to work in exceeds the security they would prefer to pay for it. For example, a worker would choose to work at point A, but OSHA requires the minimum job safety to be rc. As a consequence, the worker is forced to give up work at point A and do work at point C. But work at point C, although safer, tends to establish a lower indifference curve for that worker. At point C, the amount of money that he is willing to lose to increase security is less than the cost required for this increase. In evaluating the alternative from the point of view of the worker, we must recognize that the requirements of security put him in a difficult position.
Rice. Security requirements that reduce utility
The self-decision worker chooses to work at point A on the graph. However, minimum security requirements (rc) force him to choose work at point C, which tends to establish a lower indifference curve for him than work at point A.
Proponents of OSH regulation sometimes argue that economists' criticism of OSHA would only be justified in the presence of a fully informed, highly competitive labor market. However, this condition is rarely, if ever, satisfied in practice. With regard to health care in general and exposure to toxic substances in particular, workers are often completely uninformed and therefore unable to make an informed choice between different compensation programs. For this reason, workers empower government officials to act as expert advisors on their behalf to protect them from a risk they find too difficult to assess the consequences of.
This line of reasoning from OSH regulators seems sufficient to justify intervening in these processes in many cases. But it is not sufficient to explain many other examples. Consider again the problem of choosing between mines with polluted and clean air. In fact, every miner is aware that the likely consequence of working in a polluted mine is pneumoconiosis (dusty lungs) - an occupational disease of miners that greatly depletes the body and often leads to death. Since every miner probably knows a few people in his immediate circle who suffer from this "black lung" disease, it seems implausible that he would oppose the requirement to install filters.
But if the criticism of OSHA by economists is justified, then it must be admitted that workers will oppose the requirements and rules that this law establishes. At the same time, workers are often supported by the owners of enterprises who are not interested in observing safety regulations. This begs the question: why don't profit-maximizing mine owners simply install filters in their mines and bring in those miners who are interested in it (and who are willing to take a pay cut sufficient to pay for the filters)?
The answer to this and other specific questions about labor contracts is that in reality labor markets are often not competitive. Those who hold this belief claim that workers lack the freedom of movement, migration needed to have a wide range of job options that suit them, and are therefore vulnerable to exploitation by their employers.
To properly analyze this argument, we must digress a bit and examine the forces that affect wages and employment in a labor market where only one firm acts as an employer of labor.
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1. Reasons for wage differences
Wage is the price of labor services.
The wage rate is the price of labor services per unit of time worked.
Nominal wages -- wages in monetary terms.
Real wages are nominal wages divided by the price level.
Earnings - the wage rate multiplied by the number of hours worked.
Total remuneration is earnings plus bonuses plus non-monetary remuneration and deferred earnings benefits.
If we consider a model of the labor market with perfect competition, then the action of market forces in such a market should lead all workers to the same equilibrium wage (at least for a certain type of labor). But this does not happen, wages are different even for workers of the same type of work. The reasons for the differences in wages are that (Fig. 5.1):
workers are heterogeneous, they differ from each other in knowledge, skills, experience, have a different amount of human capital and, accordingly, different productivity;
jobs are heterogeneous, they differ from each other in “non-salary” characteristics (conditions, location, types of social benefits and benefits, status, etc.);
the conditions of perfect competition are not met (there are restrictions on the mobility of the labor force, the information is imperfect and its obtaining is associated with costs, there are discrimination effects in the labor market).
2. Heterogeneity of workers
Variable amount acquired (education, experience) or present from birth (ability) human capital in workers leads to the fact that they differ from each other. One of the consequences is that at any given time the labor force consists of a number of non-competitive groups that unite workers of a certain profession and qualification. There is no effective competition between these groups in the labor market, they act as imperfect substitutes for each other. As a rule, even within a group consisting of workers of any kind of activity, there is not always perfect substitution. The differences between such non-competitive groups lie in the abilities and the type, quantity and quality of workers' education. In the short term, this heterogeneity of human capital generates wage differentiation associated with different productivity of workers. In the long run, people can and do move from one non-competitive group to another by investing in human capital. But the ability for such mobility is limited by differences in investment opportunities and differences in the ability to perceive and apply the knowledge gained. To the extent that these differences persist, so will wage differences.
In addition to the fact that education contributes to the formation of non-competitive groups and segmentation of the labor market, workers can also differ within educational groups in terms of their degree of preference for education. Figure 5.2 shows indifference curves for two types of workers ( BUT and AT) and isoprofit curves for two different firms (1 and 2). Since acquiring human capital is costly, workers need incentives to invest in education in the form of higher wages after graduation. Employee BUT has a stronger preference for education, which reflects a flatter indifference curve U A its utility functions. Employee AT more wage growth is needed to get an extra "education unit". Preference for education will be influenced by a person's ability and ability to access financial resources for education. Firms also differ in their assessment of the benefits of educating workers. More educated workers in Firm 1 are valued more than in Firm 2, which is reflected in a larger increase in the earnings of educated workers per "unit of education" in Firm 1 than in Firm 2.
Rice. 5.2. Education and wage differencespland those
If a I 1 and I 2 - iso-profit curves of firms corresponding to zero profit in a situation of competitive equilibrium, then the outer line formed at the intersection of iso-profit curves is the employers' supply curve, showing the maximum wage that can be paid at different levels of education. For given firms and workers, equilibrium is reached at the points E A and E B. As a result, employees who have a greater propensity to invest and, accordingly, make significant investments in human capital, receive wages that are higher by the amount of compensatory differences. This value depends both on the preferences for education (from the capabilities and abilities) of different types of workers, and on the market opportunities of firms and the technologies they use.
3. Hedonistic Wage Theory and Compensatory Wage Differences
The hedonic theory of wages suggests that a worker seeks to increase his utility by choosing a job. This utility depends both on the amount of wages and on various other characteristics of the workplace (positive and negative), in relation to which the worker has preferences.
Differences in wages that compensate for "non-wage" differences in the characteristics of jobs are called compensatory.
The compensatory wage differential model is based on the following assumptions:
when choosing a workplace, the employee maximizes his utility from employment in this workplace, taking into account all its characteristics, and not just income (in this, the model of compensatory differences is based on the hedonic theory of wages);
the employee has or can obtain in the process of work information about all the characteristics of the workplace, and the costs of obtaining information are low;
workers are mobile and can move freely from one workplace to another.
Worker preferences are described by a utility function
U = u (W, X i),
where W-- wage; X i- "non-salary" characteristics of the workplace.
Consider the case of negative characteristics on the example of the risk of injury and occupational diseases R.
Then the employee's utility function U = u (W, R) and u" (W)> 0, u"(R)<0.
Worker preferences are described by a family of indifference curves (Figure 5.3a). The concavity of the curves reflects the decreasing marginal rate of wage substitution for risk.
Rice. 5.3. Indifference curves of employee and employer iso-profits reflecting their preferences for wages and risk of injury
Since risk reduction requires the employer to increase costs, employer preferences can be described by a family of iso-profit curves whose convexity reflects the diminishing marginal revenue as risk decreases. Competition in the market will lead the firm to zero economic profit and to an iso-profit curve corresponding to zero profit (Fig. 5.3b).
The employee, in accordance with his preferences, can choose various jobs offered to him by firms, while maximizing his utility function. So, in fig. 5.4 employees are equally satisfied with the workplace in the company BUT, and the workplace in firm B. In the first case, the combination of wages - the degree of risk W 1 , R 1 , in the second case -- W 2 , R 2. An increase in the degree of risk by ( R 2 -- R 1) is accompanied by an increase in wages by the amount ( W 2 -- W 1), which in this case will constitute a compensating difference.
Rice. 5.4. Compensatory differences in wages with different degree of risk
In the market as a whole, the intersection of all possible combinations of jobs offered will form a market supply curve, wages, a degree of risk, which will be positively sloped and flatter than the iso-profit curves of individual firms.
Rice. 5.5. Market supply curve of combinations wages -- risk of injury
The points of contact with the curve formed by the intersection of all possible preferences of workers form a set of decisions wages - the degree of risk (Fig. 5.5).
4. The impact of labor safety standards on the labor market
The theory of compensatory differences in wages makes it possible to analyze the impact of labor safety standards on the labor market.
On fig. 5.6 presents a situation where labor safety standards are established with full awareness of employees about the degree of risk. In this case, two options are possible. The first (Figure 5.6a): when setting a standard R* will transfer the worker from the point A (W 0 , R 0) to the point AT ( W* 1 , R* 1) with a lower degree of risk and with a lower wage corresponding to a lower level of utility. Second (Fig. 5.66): when setting the standard R* will move the employer to the higher iso-profit curve corresponding to lower profits, the employee will also move from the point BUT exactly With (W* 2 , R) with a lower wage, but corresponding to the level of utility at which he was.
Rice. 5.6. The impact of labor safety regulations with complete information about the degree of risk
With incomplete awareness of the degree of risk (Fig. 5.7), the employee, accepting wages W 0 counts it to be at a point To co
Rice. 5.7. The impact of labor safety standards with incomplete information about the degree of risk
degree of risk R", in fact it is at the point F, corresponding to a lower level of utility and degree of risk R 0 . Setting a standard R* will move the worker to the point D (W*, R*), corresponding to an even lower level of utility, but the establishment of a labor safety standard in the range from R"" before R 0 would allow the worker to improve his situation and/or move to a higher level of utility compared to where he is ( R"" < R < R 0), or at least, remaining at the same level of utility, reduce the degree of risk ( R = R"").
5. Compensatory differences and non-monetary rewards
Compensatory differences in wages are also possible in the case of positive characteristics of the workplace: allowances, benefits, various types of non-monetary remuneration. In this case, the employee's utility function U = u (W, AT) and u"(W) > 0, u" (AT) > 0, the traditional graphic representation of which will be a family of indifference curves. The convexity of the curves means diminishing utility when wages are replaced by benefits. The employer's behavior is described as a function of its possible cost to the total remuneration, including wages and all benefits, and corresponding to zero economic profit C 0 = W + zB, which is similar to a budget cap and means that benefits can only be increased by lowering wages. If | z| = 1, then an increase in the cost of the benefit leads to an equivalent cost reduction in wages. If | z| > 1, then an increase in the cost of the benefit leads to a larger reduction in wages. If | z | < 1, то увеличение стоимости пособия приводит к меньшему сокращению заработной платы.
There are several reasons that increase the likelihood that | z | < 1. Во-первых, многие виды пособий и неденежного вознаграждения не облагаются налогом. Во-вторых, многие пособия (например, страхование) обходятся работодателю дешевле, чем если бы они покупались работником индивидуально, так как возникает экономия на масштабе и административных издержках. В-третьих, пособия могут использоваться как средство скрытого отбора и дополнительного поощрения предпочтительной рабочей силы (заработная плата для этого не может использоваться из-за явной дискриминационности подобной практики), в этом случае соответствующим образом выбранная структура пособий будет способствовать самоотбору работников более высокой производительности. Эти же причины делают пособия привлекательными для работников несмотря на то, что при прочих равных условиях вознаграждение в денежной форме обеспечивает работнику большую полезность из-за возможности его гибкого использования.
On fig. 5.8 line AC shows the employee's budget constraints in the wage-benefit space, provided that the benefits corresponding to benefits and non-monetary remuneration are acquired by the employee on their own and the cost of a unit of benefits is equivalent to a unit of wages. Then the worker chooses AT 1 good and will be at the utility level U one . If an employer offers a remuneration structure that includes AT* benefits, then it would be unprofitable for the employee, since his utility will be U 0 , but benefits are cheaper for the employer (its isocost AD), so in reality the worker will move to the level of utility U". In addition, the employer may apply a flexible benefit plan and in-kind compensation (so-called diner-style benefit plan) by determining that AT* -- This is only the maximum value of the package of benefits and benefits in kind within which an employee can determine an individual package. Then the employee will choose benefits in the amount AT 2 and maximizes utility up to U 2 .
Rice. 5.8. Choice of remuneration structure and determination of benefit amount
salary remuneration difference
Rice. 5.9. Market supply curve of aggregate remuneration structures
The market supply curve of various aggregate remuneration structures is formed in a similar way to the case of compensatory wage differences with the possibility of injury risk. It is a combination of the cost curves of individual firms (Fig. 5.9). The points of contact with the curve formed by the intersection of all possible employee preferences form the set of wage-benefit solutions.
6. Compensatory differencesandworkplace status
One of the characteristics of the workplace is the status. The Compensatory Differences for Job Status Model (or Frank Model) assumes that status is a special good for which the worker is willing to pay.
An illustration of the model is shown in fig. 5.10. On fig. 5.10a shows the dependence of the productivity of workers and their wages. The marginal product of the worker F- the largest and he receives the highest wages, from workers D and E marginal product is lower and their wages are lower, workers B and C are even lower
Rice. 5.10. Compensation differences and job status
scale step marginal product and wages, etc. The model assumes that the employee is interested in both more high level income and status positions, which depend on participation in the distribution of income, but workers differ in status preferences. Let's assume that the workers BUT, With and E have weak status preferences, and workers AT, D and F -- strong preference. Then local status markets can form. Employee AT can satisfy his demand for high status by finding another worker (or workers) in the firm who are willing to fill a low-status position. Status is thus a relative concept and can only exist within a group of workers.
Employee AT cannot acquire a higher status by exchanging it for a share of income with an employee With, even if the employee With lower status preference. Then With there will be both a higher income and a higher status dependent on income. Employee AT can only pay for a low-status position to an employee BUT, in this case he can compensate for his low status and at the same time have an income that provides him with the highest earnings in group 1, consisting of workers BUT and AT. The price paid by one who strives for a higher status is a wage less than his marginal product of labor. Compensation for someone who occupies a position of lower status is a wage above his marginal product of labor. The result of the exchange of status positions is shown in fig. 5.10b, which shows that three groups with relative statuses have formed, and the wages of workers BUT, AT, With, D, E and F as a result, differ from the marginal product of labor. Thus, firms offer workers a set of combinations of wages and status, and the worker chooses the set he prefers.
7. Market imperfections and wage differences
Deviation from the conditions of a perfectly competitive labor market in terms of the impact on the distribution of wages occurs in two directions. First, information on the market is imperfect and obtaining it can be costly. Second, labor mobility is not absolute; there are limitations to mobility, including those associated with the costs of mobility.
In the course of the labor market, changes in the demand for labor occur, causing changes in wages, resulting in a set of offered wages instead of one. The imperfection of information leads to the fact that the offer is slow to adjust and wage differences persist. The protracted adjustment over time can also be caused by the inelasticity of labor supply in short term, as happens in the case of the web-like model of the market for highly skilled labor (Fig. 5.11), when wages fluctuate around the equilibrium We.
Rice. 5.11. Adjustment of wages over time
As a result of the time span of adjustment, at a given point in time, there is not one but many wages for the same type of work in the labor market, reflecting transient differences in wages.
But even over time, the process of wage adjustment may not necessarily lead to the establishment of a uniform wage. Obtaining complete information on all existing wage rates can be costly and there may be a situation where the marginal cost of obtaining information is higher than the gain from wage increases. Then the differences in wages caused by the imperfection of information will not be temporary, but permanent. In more detail, the process of choosing an acceptable wage for an employee is analyzed in the theory of job search.
There are two types of mobility restrictions: geographical and institutional.
Labor markets are not concentrated at one point, they have a spatial, territorial extent. Territorial movements of labor (migration) are associated with the costs of overcoming the distance and changing the place of application of labor and, possibly, the place of residence. In addition, geographical restrictions can be combined with institutional, legislative restrictions on territorial mobility. The costs and limitations of mobility are explored in more detail in the analysis of migration, inter-firm mobility, and labor market segmentation.
Institutional constraints arise as a result of the existence of formal and informal rules and procedures in society that impede mobility. Formal restrictions may arise as a result of the activities of the state and trade unions. Informal restrictions are the result of unwritten rules and norms established in society. An example of the operation of such norms is discrimination in the labor market.
8. Distribution of earnings
All kinds of differences in wages lead to the fact that at a certain point in time there are many observable values of earnings, or the distribution of wages. The static distribution of earnings has a so-called logonormal distribution (Figure 5.12), which is shifted to the left of the normal distribution, or it has a large right-sided concavity. For a normal distribution, the average and median wages are the same; for a lognormal distribution, the average wage is greater than the median. This kind of observed distribution of earnings is stable and characteristic of many economies in different periods of time.
The effect of this distribution of earnings can be shown using Pen's model called the "parade of gnomes and giants" (Figure 5.13). It assumes that a person's height is proportional to his income, and all people, lined up in height from the smallest to the largest, parade for one hour. When in the first minutes we see the tiniest people, then more, but until the 50th minute people below the average height will pass in front of us. Then giants will appear whose growth will grow rapidly so that we will not see the faces of the latter, their heads will be behind the clouds.
Pareto was derived the law of distribution of earnings (income) (Fig. 5.14).
If a Y income, N more income than income Y then N = AY, or log N = log A log Y, where BUT, options.
Rice. 5.12. Logonormal distribution of earnings
Rice. 5.13. Parade of gnomes and giants
Log Y
Rice. 5.14. Pareto distribution law
Rice. 5.15. Lorenz Curve and Gini Coefficient
This law corresponds to the right-hand concave section of the income distribution curve, called the "Pareto tail" and reflects the earnings of high-income workers, and poorly describes the distribution of income among low-income groups.
The traditional ways of representing inequality in the distribution of income or earnings are the Lorenz curve and the Gini coefficient (Fig. 5.15).
The Lorenz curve shows the ratio of the cumulative percentage of employees and the cumulative percentage of earnings. Uniform distribution, when each increase in the cumulative percentage of workers per unit corresponds to a unit increase in cumulative earnings, shows a straight line emerging from the origin at an angle of 45 °. The more the Lorentz curve deviates to the right of the diagonal line, the greater the inequality in the distribution of earnings.
The degree of inequality visually shown by the Lorenz curve expresses the Gini coefficient. It corresponds to the ratio of the area of the figure between the Lorentz curve and the diagonal line to the area of the triangle under the diagonal line.
Bibliographic list
1. Zhiznin S.Z., Krupnov V.I. How to become a businessman. - Minsk: Entrepreneur, 2010. - 64 p.
2. Zotov V. V. On the role of the concept of "economic man" in posing the problem of motivation // Motivation of economic activity: [Coll. Art.]. M.: VNIISI, 2009. Issue. 7. S. 72-79.
3. Kalacheva L.L. Working conditions. - Novosibirsk: Nauka, 2009. - 386 p.
4. Kalacheva L.L. Working conditions: Methodological issues of a comprehensive study. Novosibirsk: Nauka., 2008. - 286 p.
5. Qualification directory of positions of managers, specialists and employees. Regulatory production. edition // Goskomtruda USSR, All-Union Central Council of Trade Unions. - M.: Economics, 2010. - 272 p.
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2.1 Introduction
The main questions related to the analysis of supply in the labor market relate to the factors influencing
- by the share of the economically active population
- on the number of hours of work (per day, per year, throughout life) and the change in this number (for example, with age)
- on the offer of labor to a particular firm, the choice of form of employment
- on the quality of the services offered (associated with investment in human capital)
The labor supply is formed on the basis of decisions:
- whether to work at all, and if so, how much (full or part-time, how much for wages (employed) and how much in the household)
- if you work, then what type of work to choose, in which industry, region, company, etc.
General principles
A convenient model for the analysis of individual supply in the labor market is a graphical illustration of the "work-leisure" choice problem, the main elements of which include:
- description of possible "lifestyles" of a person in the coordinates "time - consumption of material goods"
- description of agent preferences
- choice based on possible "lifestyles" and preferences
Since employment and employment in the household are two ways to get the same result, at first you can not distinguish between them and consider any work activity as paid work. Then we can characterize the decision to hire as a choice between leisure and paid work.
2.2 Possible "lifestyles"
When considering the problem of choosing "work - leisure", a graphic description of the lifestyle is illustrated by the position of the point M on the following graph:
If a line is drawn on the graph through point M, the slope of which at each point is equal to the hourly wage, it will illustrate the possibilities of exchanging time for goods (with a given lifestyle).
It should be borne in mind that there is always a certain physiological minimum of leisure and consumed goods necessary to maintain life. That. the time allotted for labor cannot be more than some Hmax.
2.3 Preferences
Indifference curves u(C, L) = const can be plotted on the same graph, for each of which the slope of the curve at any point shows how many benefits (minimum) you need to get in order to agree to work one more hour after h hours of work (i.e. the marginal rate of substitution of leisure for material goods).
- if the derivative of the utility function dU/dL is large, then leisure time is highly valued, and vice versa
- if the derivative of the utility function dU/dL is negative, then leisure is evil
- usually considered an area where leisure is a blessing, i.e. derivative dU/dL is positive
2.4 Choice of possible "lifestyles"
The choice occurs as a result of a comparison of possible lifestyles and preferences:
Formally, the point M is determined from the solution of the problem:
max u(C, L)
under conditions:
pC = WнH + v
H+L=T
which boil down to:
pC + WнL = WнT + v
those. the sum of the price of consumer goods and the price of leisure is equal to total income
Solving this problem, we get
-dC / dL \u003d u "L / u" C \u003d Wn / p
Here -dC/dL is the marginal rate of substitution of leisure for goods,
Wн/p - market marginal value of time
2.5 Decision to work: entry into the economically active category
Data on the share of economically active population for 1990-1995
(in percentages)
| countries | (1) EAN share |
(2) change EAN |
change population in working order age (NRV) |
(3) EAN change due to change in the share of EAN |
|
| 1990 | 1995 | ||||
| Belarus | 76 | 68 | -12.2 | -1.4 | -10.9 |
| Russia | 76 | 74 | -3.8 | -0.8 | -3.0 |
| Ukraine | 74 | 70 | -5.8 | -1.3 | -4.5 |
| Poland | 69 | 69 | 2.5 | 2.7 | -0.2 |
| Czech Republic | 79 | 74 | -4.1 | 3.0 | -7.0 |
(1) EAN share = EAN / NRT
(3) ((NRW)1995 (EAP share)1990 - (EAP)1995) / (NRW)1995 (EAP share)1990
- NRV - the number of working-age population (from 15 to 64 years)
- EAN = employed + unemployed
The concept of reserve salary
Reserve salary wR: Marginal subjective estimate of time when offering zero hours of work.
if w< wR =>H=0
the value of wR depends on the opportunity costs associated with the use of time (for example, payment for Kindergarten or nursery)
for v = 0 wR = 0
If the indifference curve is described by the Cobb-Douglas function
U = C a L b , a + b = 1, then w R can be expressed in terms of v:
U " L \u003d b C a L b-1,
U " C \u003d a C a-1 L b,
U"L/U"C=b C/a L=w/p,
Assuming T = 1 and taking into account that pC = wH + v, we get:
L = (1 - a) (1 + v/w), H = a + (a - 1) v / w,
whence for H = 0 we get w R = (1-a) v / a.
For a -> 1 w R -> 0 (u ~= c),
as a -> 0 w R -> + (u ~= L).
In a situation where, for example, the place of work changes from close to far from home, the amount of the reserve salary increases:
In the West in recent times there is a strong influx of female labor force. The condition for the decision to work is w > wR, therefore, apparently, for women, wR has decreased, and w has increased, and we need to look for the reasons for this (for example, the availability of a nursery, household appliances etc.).
A possible reason is also the opening of jobs in the service sector. For example, in France now 2/3 of all workers are employed in the service sector, and 50 years ago only 1/3 were employed. At the same time, with the opening of 100 places in the service sector, the number of unemployed may decrease by only 50, because. some of those who have already worked before will go to new places.
The value of wR also changes depending on the number and age of children (because the shape of preference curves changes, i.e. leisure is valued more or less).
2.6 Individual labor supply
How does the individual labor supply in hours change depending on the hourly wage?
As the graph shows, during the first two decades, as the average hourly wage increased, the average number of hours worked per week increased, and then began to gradually fall.
replacement effect - increases H
income effect - reduces H
Slutsky equation
As a rule, at high H, the income effect dominates. For low-skilled workers, the substitution effect dominates; for highly skilled and highly paid workers, the income effect dominates.
Individual labor supply curve
For most workers, this curve looks like this. Although the case of a "workaholic" is possible, who will not reduce the supply of labor, since work for him is an independent value (a valuable good).
The market supply curve is the result of summing the individual supply curves:
ε s/w = (w/s) ds/dw ≥ 0
Unlike individual ones, the market curve does not have a section with a negative slope, since as wages rise, more and more new workers enter the market with a high level of W R .
2.7 Sentence L and actual hours worked
Desired number of working hours (individual offer)
If the worker chose freely - his choice is (H*, C*) (max u(C, L)).
In practice, such a situation arises when an employee who prefers to work a part-time week (working day) chooses a full-time job, since the alternative - not to work at all - is less profitable for him.
An interesting situation is when the number of working hours offered by the employer is lower than desired. For example H3< H*. Тогда работник, соглашаясь на это предложение (u1 >u0) is looking for a second job (or even a third one) if the first job does not have the opportunity to work overtime. The goal is to reach the equilibrium point H*.
Those who work in several places are called moonlighters - night owls. The scale of this phenomenon is often difficult to assess, since secondary employment often takes place in the shadow economy (or in the secondary market), where contracts are not concluded and cash is accepted. However, there are some estimates - for the UK, for example, 3.5% of men and 2.5% of women have a second job.
In Russia, there are twice as many "night owls" among those who regularly face salary delays.
salary delays
On section AB, where W 1 = 0, it is profitable not to work, but, bearing in mind future payments, the employee actually faces a budget constraint in the form of a broken line ABC.
u 1 > u 0 , therefore point C is preferred to point A.
2.8 General theory of time distribution
Enriching the concept of lifestyles(Becker, 1965)
u = u(z 1 ,...,z N)
z i \u003d f i (x i , t i)
z i - consumer activity in area i:
- nutrition
- entertainment
- trips
- clothes
- ......
x i = (x i 1 ,...,x i n) - consumed goods or services
t i = (t i 1 ,...,t i k) - the corresponding consumption time
(here t i j is the time required to consume the good j within the consumer activity i)
Households maximize the function U given in this way under the constraints:
Example: Consider a simple production function:
Xi = aizi, ti = bizi,
where a and b are parameters
| p i a i z i + |
wb i z i = wT + V |
| (a i p i + b i w) z i = wT + V |
pi = a ipi + biw - full price of "unit" of activity i => Max u(z)
under the restriction pz = wT + V
First order maximization conditions: u "i / u" j = pi / pj
Of two goods that are different in intensity in the use of time, good 1 is more intensive if
b1w / (a1 p1 + b1 w) > b2w / (a2 p2 + b2w)
How will the offer of opening hours be affected by changes in
1. unearned income?
2. wages?
3. the market price of the goods?
- 1. As V grows, both z 1 and z 2 will grow, more time will be used for consumption => less for work, this is a net income effect.
The use of the more time intensive good (inferior) will increase to a greater extent.
- 2. Compensated effect of wage increase.
- 3. If there is an increase in the market price p1:
If there is a general proportional increase in p1 and p2: => decrease in consumption z2 ("good-intensive" activity).
2.9 Compensatory wage gap theory
The offer of labor for certain places of workplace of work A: w A x A
Job B: w B x B
x A, x B - non-financial characteristics of the work. For example: risk, ecology (noise, vibration), operating modes, vacation duration, etc.
Job A is selected if u i (w A , x A) > u i (w B , x B), even if w A<
w B .
Compensatory wage for worker i - w A *i is the wage that makes the choice between A and B indifferent:
u i (w A *i , x A) = u i (w B , x B)
D w i = (w B - w A *i) - compensatory wage difference
(w A *i - w B) / w B = k i , w A *i / w B = 1 + k i
k i< 0 - работник предпочитает
неденежные аспекты работы A
k i > 0 - the employee prefers non-monetary aspects of work B
What is the market difference between salaries in places A and B?
When the demand curve shifts to the left, those who "like A" less will leave.
Economic rent is something that can be taken away, and a person will not leave yet.
2.10 Supply quality and investment in human capital.
2.10.1 Harry Becker's theoryInvestments in human capital:
- education spending
- health care costs
- mobility (moves, migrations)
- retraining of personnel
costs - now
benefits - later
Expenses for initial education at the end of "compulsory" school
Empirical fact:
Here you need to compare:
for II - A and B: A - total costs of individual II for the period of study, B - benefits II (compared to I)
for III - C and D: C - the total costs of the individual III for the period of study, D - the benefits of III (compared to II)
If we take into account the interest rate r, then over a long period of T years, the present income (salary) of the one who spent a year on education (B) and the one who did not do this (A):
VA A = W A / (1+r) + W A / (1+r) 2 + ... + W A / (1+r) T =
W A / (1+r) =
= W A [(1+r) / r] / (1+r) = W A / r
VA B = W B / (1+r) 2 + ... + W B / (1+r) T =
= W B / (1+r) 2 =
= W B / (r(1+r))
VA A = W A / r<
W B / (r(1+r)) = VA B
if W B > W A (1+r)
W B > W A + r W A
ρ = (W B - W A) / W A > r
ρ - internal (marginal) rate of return
ρ is the interest rate that equalizes these two flows:
VA A = VA B
ρ > i, i - interest in the capital market
if ρ exceeds i - it makes sense to invest
(W B * - W A) / W A = i DW * = i W A
Δ W * - minimum salary supplement required to select profile B
W A - opportunity costs, but if there are direct costs, then
Δ W * = iC, where C - total costs
The difference in ability will affect the amount of cost required to reach a certain level - for more talented, the cost is less.
D W * n > D W * t
Difference in social status (wealth) - for the richer, the interest rate is less:
i poor > i rich => D W * poor > D W * rich
2.10.2 Ben Porat model
Quality of supply and investment in human capital. The Ben Porat Model The Life Cycle of Education and Training: The Ben Porat Model (1967)
Generalization: a person constantly makes a decision - should he invest in his human capital or not?
The answer depends on the relative benefits and costs of investment, but the situation is special in that investment is the result of using one's own time in the production of human capital.
Q t = (S t K t) b , 1 ≥ b ≥ 0
Q t is the number of units of human capital produced in year t
S t - share of human capital invested in "production" (0 ≤ S t ≤ 1)
K t - human capital at the beginning of period t
b - parameter of human abilities (0 ≤ b ≤ 1)
Quality of supply and investment in human capital. Ben Porat Model
C t = w S t K t - opportunity costs, S t K t = Q t 1/b
costs C t = w Q t 1/b dC t /dQ t = (w/b) Q t (1-b) / b
benefits: B t = PV(w,i) Q t = (w/i) (1 - 1 / [(1+i) 65-t ]) Q t
What is approximately = (w/i) Q t if t is small (youth)
or approximately = 0 if t -> 65 (older generation)
2.10.3 Minser's equation
Empirical confirmation of the theory and verification of the Mincer equation (Mincer) - a standard way to test the return on investment in human capital
r 1 - return on investment for 1 year
Y o - the income of someone who is not trained at all
Y n - income in year n (including investments made)
Quality of supply and investment in human capital. Minser's equation
r 1 \u003d (Y 1 - Y o) / Y o
Y 1 \u003d Y o (1 + r 1) r 2 \u003d (Y 2 - Y 1) / Y 1
<=>Y 2 \u003d Y o (1 + r 1) (1 + r 2)
. . . . .
Y n = Y o (1 + r 1)....(1 + r n)
r i ~ r for any i, Y n = Y o (1 + r) n
1 + r ~ e r Y n = Y o e rn
<=>Log(Y n) = Log(Y o) + rn
0.02 < r < 0.20 , т.е. r в пределах процентных ставок
Log(Y n) = A + α o S i + α 1 EXP i + α 2 EXP i 2 + β 1 TEN i + β 2 TEN i 2 + γ 1 SEX + γ 2 Z i + ε i
we assume that the random variable ε is normally distributed.
S i - number of years of study
EXP i - experience in the labor market
TEN i - work experience at the last enterprise
SEX - worker gender (dummy - variable)
Z i - vector of other individual characteristics (age, region, firm, etc.)
ε i - unaccounted factors
The length of service in the labor market is also the accumulation of human capital; at the last enterprise, the accumulation of specific human capital.
Approximately 60% of income differentiation can be explained by this equation (and 40% of the factors are apparently not taken into account here).
Let us proceed to a brief presentation of the main ideas of the theory of vector compensating fields or, as they are sometimes called, fields
Yang-Mills. The theory is based on the idea of dynamic implementation of the laws of conservation of isospin, baryon number and strangeness by analogy with the conservation of charge-current. Continuity equation
as is known, follows from the Maxwellian equations
The task is set: to establish the equations of new vector fields generated by the baryon charge density current, as well as by the strangeness and isospin currents. From these equations, the baryon charge conservation law should naturally follow,
And two other similar equations expressing the conservation of strangeness or hypercharge.
Since the quanta of new vector fields, apparently, must have nonvanishing rest masses, it is natural to write the Klein-Gordon equations for them taking into account the sources. For example, in the case of a baryon charge-current, we will have
with additional conditions
This system, as is easy to see, leads to the desired conservation law
On the other hand, the electromagnetic field is introduced not only as a vector field, but also as a compensating one, which makes it possible to ensure the invariance of the Lagrangian with respect to gauge (phase) transformations
where are the wave functions. For constant a, from this, as is known, follows, according to Noether's theorem, an expression for the current and the law of its conservation. Consider, however, a more general case, when the phase a is a function of the coordinates (i.e., when it is local),
Then in the relativistic field theory equations, which can all be written as first order equations,
where Г are some generalized matrices (Dirac matrices, Kemmer-Duffin matrices, etc.), there will be terms with phase derivatives that violate the invariance of the equation or, accordingly, the Lagrangian. To eliminate, or compensate, these terms, it is necessary to introduce some new, compensating (generally speaking, vector) field; in the case of a conventional charge-current, this will be a vector electromagnetic field, characterized by a vector potential, which must simultaneously be transformed in a gradient manner
In other words, we proceed to replace the usual derivative of the wave function with a compensating one
The deep idea of Yang-Mills, Lee, Sakurai, Uchiyama, whose works are translated in this collection (articles 1 - 4, 14), and a number of other authors is that the parameters of transformations in isospace, leading to the laws of conservation of isospin, baryon number or oddities are now assumed to be local, i.e., dependent on the coordinates of the usual Minkowski 4-space. Arguing similarly to the previous one, we then come to the need to introduce three types of compensating vector fields, associated with the corresponding laws of conservation of the baryon number, isospin, and hypercharge. The general theory of compensating fields was developed by Uchiyama, whose work, however, was not taken into account at first either, for example, by Sakurai or in our works (with Brodsky and Sokolik). Uchiyama obtained a general expression for the compensating derivative in the form
where is the operator of the corresponding group, and is the potential of the compensating field. Thus, we see that the "vectors" turned out to be "compensators"!
Generalizing these considerations, we can construct new fields by passing from constant parameters of certain groups of transformations to localized parameters that depend on coordinates. In this way, for example, the Toushek-Salam neutrino gauge group
leading to the conservation of "neutrino charge". We will dwell on the application of the general theory to gravitation in § 4.
The main empirical success of the compensation theory lies in the fact that the number of resonons, apparently, really corresponds to the predicted and partly independently discovered particles of this type. These include primarily and -reasons. Regardless of the theory of compensating fields, the search for these particles was previously prompted by the theory of electromagnetic form factors of the nucleon (Nambu, Frazer and Fulko, Chu, Stangelini, Fubini and others) 171, 82 ± 84]. Along with this, the compensation vector theory indicates that resonons or vectons will play an essential role in nuclear forces. A short-range repulsion is expected between two nucleons, as particles with the same baryon numbers and the same hypercharges, in full analogy with Coulomb's law. It is possible that here lies the explanation for the repulsive core of baryons, which was usually introduced purely phenomenologically.
On the other hand, it is possible that the strong attraction between nucleons and antinucleons, predicted by the present theory, just corresponds to the tendencies for the production of -mesons in the spirit of Fermi-Yang's ideas. At the same time, it should be recognized that the inclusion of the ordinary -meson Yukawa nuclear forces in the compensation theory encounters difficulties. From the new point of view, -mesons are secondary particles, and the Yukawa forces take on a somewhat phenomenological character in relation to the fundamental interactions carried by vectons (i.e., resonons or "compensons"). In this regard, we point out the interesting research of Babikov (Dubna), who builds a theory of the masses of nuclei, taking into account both ordinary meson and new resonant interactions.
Considering the connection of nucleons with vectons (resonogs) as primary, Sakurai naturally comes to the idea of the transformation of a nucleon-antinucleon into resonons, which in turn decay into -mesons, which directly leads to an explanation of the previously mysterious fact of the appearance of about five -mesons during annihilation . Further empirical implications and predictions of the new theory can be found in Sakurai's papers and other works translated in this collection.