Bestiary of Behavioral Economics/Efficiency Wages
- An efficiency wage, also commonly referred to as a fair wage, is a theory in behavioral economics suggesting that a wage which exceeds the market clearing wage for a given occupation will illicit greater effort and productivity, ensuring that workers avoid shirking. Generally, there are five sub-types of efficiency wage model. They are the Shirking Model, the Gift-Exchange Model, the Fair Wage-effort Model, the Adverse Selection Model and the Turnover Model.
Labor as a Commodity 
Labor is a commodity because it is provided to satisfy wants. Like other tangible goods and services, there is a market clearing price for which the labor demand and supply will be in equilibrium.  This is the price for which a worker is just willing to trade his labor for income, meaning that only the minimal amount of effort will be exerted. In this situation, a worker may shirk responsibilities that are felt to be unwarranted at the market clearing price or wage.
The theory of efficiency wages suggests that there is a positive relationship between wages which exceed the market clearing wage and the level of effort that a worker reciprocates to their employer. In turn, it is postulated that the effort and therefore productivity of a worker will increase along with their wages.
Basic Mathematical Model 
The basic concept of efficiency wages can be explained mathematically using the formula below. In order for a wage to increase the efficiency of a worker, it must satisfy the following:
θ(α-β) > G
- θ represents the likelihood that a worker will be caught and punished for unsatisfactory labor
- α represents the efficiency wage
- β represents the going market clearing wage
- G represents the value a worker places on providing only the minimum necessary effort
A worker will choose the benefit, G, of supplying the minimum level of effort his occupation requires in the case that their employer fails to provide a wage α large enough to render the risk of release, θ(α-β), greater than or equal to the benefit of slacking on the job. The efficiency wage α must exceed the market clearing wage β so that the cost associated with losing one's job is greater than the benefit of supplying minimum effort. If the wage α does not exceed β, a worker can simply move to a different firm within the industry and maintain a constant level of utility while enjoying the benefits of minimal effort.
Efficiency Wages and Employment 
In an economy which features full employment, the efficiency wage concept will be ineffectual due to the reasons explained above however, the very nature of the efficiency wage guarantees that an economy will not operate at full employment levels. The wages - paid by firms to induce increased effort - exceed those that would clear the labor market, resulting in a decreased level of overall employment. This is necessary to ensure that the mechanisms at work within the efficiency wage theory function properly. As the mathematical model indicates: a worker will choose to forgo limited effort if and only if the potential losses incurred by termination exceed the benefit of shirking. The resulting marketplace conditions do not guarantee that laborers will be able to find work after termination, and will therefore take measures to avoid such a fate.
Furthermore, shirking and unemployment are inversely related. Simply put, lower levels of unemployment will result in greater shirking as the perceived difficulty of obtaining a job in the case termination decreases, while higher levels of unemployment have the reverse effect.
Other Effects 
- Without the self-regulation that stems from the implementation of efficiency wages, ensuring efficient labor from workers would require that firms increase monitoring levels. However, increased monitoring paired with low wages will result in a labor force that feels more disconnected from their sense of duty to the firm, compounding the problem of inefficient labor. Increasing wages can help ignite a workers sense of duty, leading them to feel more closely associated with the goals of the firm. As a result, they will put forth more effort in their occupations.
- In spite of this, empirical evidence suggests that the benefits of increased wages are short lived. In an experiment organized by Uri Gneezy and John List, two mutually exclusive groups of individuals, say A and B, were asked to digitize a library's catalog. Both A and B were promised a wage of $12 an hour for six hours of labor. Upon arrival, however, group A was instead offered a wage of $20 an hour, 167% of group B's wage. Initially, the generosity of the wage was reciprocated by the individual laborers of group A- information processed by A exceeded that of B by nearly 25%, suggesting greater effort. After ninety minutes time, productivity slipped to levels which were indistinguishable from that of group B.
- In is uncertain if these results would be reflected in extended time periods, where factors other than wage may effect one's effort and productivity.
Ford's $5 Work Day 
It is impossible to have a proper discussion of efficiency wages without bringing up Henry Ford's $5 work day. January 5th, 1914 became one of the most important events in the history labor economics. Harley Shaiken of the Economic Policy Institute wrote that as a result of his wages, Ford saw rising productivity which allowed for higher profitability, a suprise to his competitor firms.  Though, some economists have questioned whether Ford was paying his workers efficiency wages in the first place. Daniel M. G. Raff and Lawrence H. Summers, two prominant economists, concluded, in a very influential paper that is commonly cited in reference to efficiency wages, that Ford did in fact use efficiency wages. It is very hard to gain direct quantitative analysis on productivity of workers who would qualify as having effeciency wages. Different firms give wages of different quanitities skewing the analysis.  For all of these technical issues in setting up a quantitative methodology, they settled for a historical approach. A historical approach was made easy by the Ford example because each worker recieved an increase in wages from $2.34 to $5. This isolated and uniform incident allowed for appropriate analysis.  First, they found that Ford intended to pay wages to increase his profitability. Next, they analyzed the effects of the policy on the quality of workers, turnover, and other desired effects that should occur as a result of efficiency wages. The first effect of the wage increase was to see an enlargement of the supply of labor; so much so, that the factory had to repell them with water, the excess supply. The intent was not to gain higher quality workers necessarily but to reduce worker turnover and compensate for the crude working conditions. Turnover, by some estimates, dropped from 400% to 23%. Profits rose as productivity increased by 40 to 70%. This is due to increased output (15% more cars with 14% less workers) and a reduced ability of workers to collude to work less hard. Though, the author's concede that it is not possible to attribute all productivity gains in the Ford plant to efficiency wages. The Ford plant had the capability to monitor their workers for effort, new technology played an incalculable role, and the quality of the work was "menial" in the first place so turnover was not a very high cost to Ford's firm.
Relation to Fair Wage-effort Model 
Fair wage-effort hypothesis is a member of the family of the efficiency wage model. It is a sub-model with improvements on the efficiency model.
Introduction to Fair Wage-effort Hypothesis 
The concept of the fair wage-effort hypothesis can be described by a narrative. Bill and Hu who are close friends work in different factories, but they are responsible for the same kind of work. One day, they talked about how much they made. The differences in wages shocked Hu. He thought it was unfair to receive less wage for the same amount of work. As a result, he decided to work less hard. This is one of many possible narratives to identify the fair wage-effort hypothesis. Basically, if someone feels he does not receive a wage he think is fair, he will proportionately decrease his level of work effort. This is the main idea of the fair wage-effort hypothesis. It can be translated, mathematically to e = min (w/w*, 1), where e equals effort a worker contributes to his work, w equals actual wage, w* equals 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.
Important Motivations for Akerlof and Yellen to Construct Fair Wage-effort Hypothesis 
Through looking at 4 motivations for the fair wage-effort hypothesis, you will have a profound insight of it.
- Equity Theory: J. Stacy Adams  asserted 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 used a realistic study conducted by Edward E. Lawler and Paul W. O'gara  to support the fair wage-effort hypothesis. In the study, Lawler and O'gara compared the performance of workers who received 25 cents per interview contrasted to, the performance of workers who were intensely underpaid at 10 cents per interview.  They found that the underpaid interviewers conducted poorer quality interviews. 
- Relative Deprivation Theory: Relative deprivation theory indicates that how people think of fairness are grounded on comparisons with salient others. 
- Social Exchange Theory: Akerlof and Yellen used Peter M. Blau's model of exchange  and George C. Homans'  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  motivating him to propose this hypothesis, the agents who were 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  had a similar theory that provided a simple proposition to Akerlof and Yellen's model. If workers think they receive unfair wages, they will be angry. The anger probably reduce workers of labor input.
- Empirical Observation of Work Restriction in the Workplace: Sociologist Stanley B. Mathewson  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 putting excessive stress on the machine when he operated it. 
Advantages over the Original Efficiency Wage Model 
In terms of labor market, the fair wage-effort model provides better explanations for some phenomena, such as the existence of involuntary unemployment. Akerlof and Yellen thought the leading efficiency wage model built on maximizing behavior failed to predict wage compression, negative correlation between unemployment and skill, and the strong positive correlation between industry profits and industry wages; 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 maximized utility merely subject to their pay and their effort seemed simplistic and it lacked workers' motivation.
Models Based on the the Fair Wage-effort Hypothesis 
A Rudimentary Model of Unemployment with the Fair Wage-effort Hypothesis 
This model built on the 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:
- Q = out put
- α = the marginal product of a unit of effective labor
- e = average effort of laborers hired
- L = the labor hired.
Also, there is a trick concerning with w*. The variable,w*, is not only fair wage, but it also can be a benchmark to the marginal cost of a unit of effective labor. The marginal cost of a unit of effective labor is at least as large as w* under the fair wage-effort hypothesis. It's because an additional worker hired is paid, psychologically, a fair wage when a firm considers effort in relation to production. The wage per unit of effort,w/e, is the 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. 
In the model, the unemployment rate is either 100% or zero.
- In the case that α exceeds w* (firm will gain benefit from hiring one additional worker): At the beginning, Akerlof and Yellen assume the aggregate supply of labor is greater 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. 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.
- 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 focuses 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 thought treating labor as commodity misrepresent the nature of the labor exchange because people could intentionally react to the exchange, unlike the apathetic commodity. Also, he provided a new way to look at the relationship between fairness and effort. His idea was 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:
- 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
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).
- Blackwell, Andrew. "Efficiency Wage Theory" (PDF). http://www.blackwell.dk/writing/non-fiction/academic/economics/Efficiency%20Wages.pdf. Retrieved 4 November 2011.
- Harley Shaiken, “Unions, the Economy, and Employee Free Choice” Economic Policy Institute. February 22, 2007.
- Raff, D., and Summers, L. (1987), “Did Henry Ford pay efficiency wages?”, Journal of Labor Economics, Oct 1987 pg. S59
- Raff, D., and Summers, L. (1987), “Did Henry Ford pay efficiency wages?”, Journal of Labor Economics, Oct 1987 pg. S69
- Raff, D., and Summers, L. (1987), “Did Henry Ford pay efficiency wages?”, Journal of Labor Economics, Oct 1987 pg. S59
- Raff, D., and Summers, L. (1987), “Did Henry Ford pay efficiency wages?”, Journal of Labor Economics, Oct 1987 pg. S59-60
- Raff, D., and Summers, L. (1987), “Did Henry Ford pay efficiency wages?”, Journal of Labor Economics, Oct 1987 pg. S73
- Raff, D., and Summers, L. (1987), “Did Henry Ford pay efficiency wages?”, Journal of Labor Economics, Oct 1987 pg. S74
- Raff, D., and Summers, L. (1987), “Did Henry Ford pay efficiency wages?”, Journal of Labor Economics, Oct 1987 pg. S77
- Raff, D., and Summers, L. (1987), “Did Henry Ford pay efficiency wages?”, Journal of Labor Economics, Oct 1987 pg. S76
- Raff, D., and Summers, L. (1987), “Did Henry Ford pay efficiency wages?”, Journal of Labor Economics, Oct 1987 pg. S81
- Raff, D., and Summers, L. (1987), “Did Henry Ford pay efficiency wages?”, Journal of Labor Economics, Oct 1987 pg. S60
- Akerlof, George A.; Yellen, Janet L. (1990), "The Fair Wage-Effort Hypothesis and Unemployment", Quarterly Journal of Economics 105 (2): 255-283, http://www.jstor.org/stable/2937787
- Akerlof, George A.; Yellen, Janet L. (1988), "Fairness and Unemployment", The American Economic Review 78 (2): 44-49, http://www.jstor.org.ezproxy2.library.arizona.edu/stable/1818095
- Palley, Thomas I. (1994), "The Fair Wage-Effort Hypothesis:Implications for the Distribution of Income and Dual Labor Markets", Journal of Economic Behavior and Organization 24 (2): 195-205, http://www.sciencedirect.com/science/article/pii/0167268194900264