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This is a section to explain fair wage-effort hypothesis in the behavioral economics

Introduction
Have you ever thought of fairness as to wage? What is a fair wage for you? If you feel like you receive a unfair wage for your work, what are you going to you. Here is a story to introduce the concept of fair wage-effort hypothesis. Bill and Hu who are close friends work in the different factories, but they are responsible for the same kind of work. One day, they occasionally talked about how much they made. It shocked Hu due to the wage differential. Hu thought it was unfair to receive less wage for the same amount of work. As a result, he decided to work less hard. However, it is not the only case. This story reflects part of fair-wage hypothesis. Basically, if someone feels he does not receive wage he think it is fair, he will proportionately diminish his effort on work. This is the main idea of fair wage-effort hypothesis. It can be translated to e = min (w/w*, 1), where e equals effort a worker contributes to his work, w equals the actual wage, and w* equals the fair wage, and 1 is maximum and normal effort corresponding to the market-clear wage. So how to interpret e = min (w/w*, 1)? A worker will exert the lower number that represents effort in the function.

Motivation
Through looking at 9 motivations for the fair wage effort hypothesis, you will have a better understanding of it. All these 9 motivations are credited to George A. Akerlof and Janet L. Yellen's and from the academic journal The Fair Wage-Effort Hypothesis and Unemployment.


 * 1) Equity Theory: Adams [1963] assumed that the exchange between the perceived value labor input and the perceived value of remuneration should be equal. There is an economic formula to interpret it: e = w/w*, where w is the perceived value of remuneration, w* is the perceived value of a unit of effective labor, and e is the number of units of effective labor input. Akerlof and Yellen further explained that workers may change their actual effort or their perceived effort e if they think they do not receive a fair wage for their effort e = 1 based on psychologists' finding. They used a realistic study conducted by Lawler and O'gara [1967] to support this statement. In the study, Lawler and O'gara compared the performance of workers who were received 25 cents per interview with the performance of workers were intensely underpaid at 10 cents per interview. They found that the lower paid interviewers conducted much poorer quality of interviews.
 * 2) Relative Deprivation Theory: Relative deprivation theory indicates that how people think of fairness are grounded on comparisons with salient others.
 * 3) Social Exchange Theory: Akerlof and Yellen used Blau's models of exchange [1955] and Homans' [1961] social exchange theory to explain the fair wage-effort hypothesis. Blau's model hypothesizes that equivalent rewards will be achieved on both sides of an exchange after the costs are deducted. In Blau's empirical study [1955] motivating him to propose this hypothesis, the agents who was in charge of investigative work could consult with other agents as to difficult problems. He found that the average agents tended to consult more with the agents with the average expertise. The consultation between the average and the experts were not frequent due to less reciprocation based on Blau's explanation. Homans [1961] has a similar theory that assumes people will get angry if they don't get what they think they deserve. This theory provides a simple proposition to Akerlof and Yellen's model. If workers think they receive a unfair wage, they will be angry. The anger probably reduce workers of labor input.
 * 4) Empirical Observation of Work Restriction in the Workplace: Two examples are applied to explain the idea of empirical observation of work restriction in the workplace. Sociologist Mathewson [1969] as a participant observer recorded 223 instances of restriction in 105 establishments in 47 different locations from his work. He concluded, "occasionally workers have an idea that they are worth than management is willing to pay them. When they are not receiving the wage they think fair, they adjust their production to the pay received." It underlies the fair wage-effort hypothesis. Another sociologist, Donald Roy, observed an interesting phenomenon from his own experience that heavy papers would be suddenly tore and stuck to the machine's rollers during the work due to the machine crew who was not satisfied with his wage put excessive stress on the machine when he operated it.
 * 5) Literature, Jealousy, and Retribution: Generally speaking, literature provides a lot of good examples about jealousy and retribution, the relation between equity and performance. The story as an example is about how Joseph is treated by his jealous brothers(Bible Genesis, 37-50).
 * 6) Personnel Management Texts: Textbooks on personnel management value the equitable treatment of workers as an extremely important factor in the labor market. Akerlof and Yellen used an quotation from Kochan and Barocci to illuminate it. The quotation was that "there is no single factor in the whole field of labor relations that does more to break down morale, create individual dissatisfaction, encourage absenteeism, increase labor turnover and hamper production than obviously unjust inequalities in the wage rates paid to different individuals in the same labor group within the same plant" (Kochan and Barocci, 1985,p.249).
 * 7) Wage-Salary Secrecy: It is not usual to openly discuss wages and salaries with other employees. Also, organizations in most cases don't allow their employees to disclose wages and salaries.
 * 8) Wage Patterns: One wage pattern given by Dickens and Katz is that if industries have high wages for one occupation, they tend to have high wages for other occupations. Also, the fair wage-effort hypothesis provides better explanations for wage compression and the behavior of union-nonunion wage differentials.
 * 9) Patterns of Unemployment: The fair wage-effort hypothesis provides a potential explanations for correlations, such as unemployment-skill correlations.

Advantages over the original efficiency wage model
In terms of labor market, the fair wage-effort provides better explanations for some phenomena, such as the existence of involuntary unemployment. Akerlof and Yellen thought a efficiency wage model based on fairness explained the leading efficiency wage model build on maximizing behavior failed to predict wage compression, negative correlation between unemployment and skill, and the strong positive correlation between industry profits and industry wage; in contrast, the efficiency wage model with respect to fairness better explained these difficulties. Also, the efficiency wage model with the feature of hedonism that workers hedonistically maximize utility merely subject to their pay and their effort lacks of worker motivation and seems simplistic.

A Rudimentary Model of Unemployment With the Fair Wage-effort Hypothesis
This model built on fair wage-effort hypothesis (e = min (w/w*, 1) is used to explain unemployment. And it is credited to Akerlof and Yellen. It is assumed that the fair wage, w*, is exogenously determined, there is a single class of labor, and it is perfectly competitive market. In addition to the function e = min (w/w*, 1), there is a production function: Q = αeL, Where: Also, there is a trick concerning with w*. W* is  not only fair wage, but it also can be a benchmark to the marginal cost of a unit of effective labor. In other words, the marginal cost of a unit of effective labor is at least as large as w*. W/e, the wage per unit of effort, is real marginal cost of effective labor. Finally, Akerlof and Yellen assume there is a fixed supply of labor, which is independent of the wage rate.
 * Q = out put
 * α = the marginal product of a unit of effective labor
 * e = average effort of laborers hired
 * L = the labor hired.

Analysis
In the model, the unemployment rate is either 100% or zero.
 * 1) In the case that α exceeds w* (firm will gain benefit from hiring one additional worker): At the beginning, Akerlof and Yellen assumes the aggregate supply of labor is great than the aggregate demand for labor so that there is unemployment and the firm is free to set any wage it wants due to this phenomenon of excessive supply of labor. As a result, a firm's goal is to choose a wage to minimizes w/e. If the firm chooses to pay workers any wage not exceeding w*, the marginal cost of effective labor will be w* instead of w/e. This is because w/e is less than w*/e and the prerequisite is that the marginal cost of a unit of effective labor is at least as large as w*. The following process will be like the marginal product of effective labor > the marginal cost of effective labor (α > w*) -> the firm hires an infinite amount of labor -> aggregate excess demand for labor -> w > w* (the firm increases the wage, under the competition). However, the demand for labor is still infinite when wage is between w* and α. It's because the marginal product of effective labor is still larger than the marginal cost of effective labor. In a word, if  α > w*, the unemployment is zero and all labor will be hired.
 * 2) In the case that w* exceeds α: the marginal cost of effective labor is greater than the marginal product of effective labor, a firm no longer hires any worker. As a result, the unemployment rate is 100%.

Different Approaches to the Fair Wage-effort hypothesis
Thomas I. Palley has a different view of the fair wage-effort hypothesis. There are two differences between his fair wage-effort model and Akerloff and Yellen's model. One is that Palley focused on wage-profit, which indicates worker-firm concerns, while Akerloff and Yellen emphasize on wage-wage, which reflects comparisons between workers. The other difference is that Palley's model does not have psychological consequences in contrast to A-Y's because someone argues that effort and more involvement in the work increase workers' happiness. Akerloff and Yellen's fair wage-effort hypothesis is based on the how workers value their treatment. If they psychologically think they does not receive fair wage, they will proportionally reduce their effort. However, this may be the case that feeling involvement in work enhances their happiness, workers will not reduce their effort proportionally even when they think they are not paid fairly.It's difficult to decide which is overweight.

Palley thinks treating labor as commodity misrepresent the nature of the labor exchange because people can intentionally react to the exchange, unlike the dead commodity. Also, he provides a new way to look at the relationship between fairness and effort. His idea is that effort depends on the relation of fairness-firm's non-labor surplus: e = Min [e(wL/(pq-rk)), e(1)], e'>0, e"<0, e(0)= 0, e= e(1) if pq -rk -wL<0, Where: The equation e = Min [e(wL/(pq-rk)), e(1)] specifies effort as a function of the level of non-labor surplus and makes a connection between the value they receive and the value they contribute. pq = the value of output, rk = the non-labor cost, wL = labor cost, and pq - rk = the value the labor create. If wL - (pq -rk) = 0, effort is e(1); if wL - (pq -rk) < 0, effort declines; if wL -(pq - rk) > 0, effort is e (1).
 * e = level of effort
 * w = nominal wage
 * L = level of labor input
 * p = price of output
 * r = cost of capital
 * k = level of capital stock

Relation to Fair Wage-Effort Model
Fair wage-effort hypothesis a member of the family of the efficiency wage models. It is a sub-model with improvements to the efficiency model.

Efficiency Wage Theory
Generally, there are five sub-types of efficiency wage models. They are Shirking Models, Gift-Exchange Model, Fair Wage-effort Model, Adverse Selection Model, and Turnover Model.
 * Shirking Model(Shapiro and Stiglitz): If workers receive a higher wage, the cost of losing their job becomes higher, and this acts an incentive for wokers not shirk and risk being fired.
 * Gift-Exchange Model (Akerlof): A higher wage is seen by workers as a gift from the firm, and workers will want to return this gift in the form of higher effort.

Sandbox
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