Analysis of Approaches to Bargaining Models


This paper discusses the various types of methods to bargaining models, particularly indifference curves and iso-profit curves, monopoly union behavior and efficient deals. Then we go on to study the idea of efficiency pay in a unionised and a non-unionised environment and by making use of existing economic theories we develop a model and include the alternative wage rate. On completion of this newspaper, we are in a position to understand the affect of wage level, different wage rate and other factors on the career level, which would be very important to both organizations as well as the labourer's area while framing insurance policies.


Before starting with the paper, we have to know very well what efficiency salary are. It is the wage that is set by the organizations or the employers which is higher than the market clearing wage. There are certain implications behind this action. Doing this, it would encourage workers' loyalty on the employer; the companies would be able to attract higher number of talents and thereby improving the job seekers' pool, improve the morale of the employees and consequently the entire efficiency of the businesses increases. In various efficiency wage models, labour production has an optimistic marriage with the wage rate. Also worth mentioning, would be that the efficiency wage model can be an expansion from the Shapiro-Stiglitz style of efficiency wage. In this particular paper, we combine both microeconomics concept of labour union and the style of Shapiro-Stiglitz to derive the many propositions.

Moving forward, we discuss the essential two models of wage rate persistence for the unionised and non-unionised sector of the current economic climate. The first would be the monopoly model, as prescribed by Oswald in 1985, assumes that the labour union places the wage and the workplace chooses the income maximizing employment level. The next case also stated by Oswald in 1985, records that both the employer's area as well as the worker's side can take advantage of the monopoly results by jointly bargaining on the wages and career level.

Literature Review

  • Oswald, A. (1985): "The Economical Theory of Trade Unions: An Introductory Survey" Scandinavian Journal of Economics, volume 87.

Oswald assumed that the union sets the wage and the company chooses the profit maximising job level. He also stated that the successful bargaining model notes that both factors can improve on the monopoly end result by jointly bargaining over income and work.

  • Brown, J. and Ashenfelter, O (1986, June): "Testing the Efficiency of Career Deals" Journal of Political Current economic climate, quantity 94.

They used the significance of a way of measuring alternative wages within an job regression as proof for the useful bargaining model.

  • Stiglitz, J. (1987, March): "The Causes and Outcomes of the dependence of quality on price" Journal of Economic Literature, level 25.

In regards to the efficiency wages hypothesis, Stiglitz explained that, "one desire for this books is to make clear involuntary unemployment: In case the efficiency wage is framework is valid, then businesses might not lower wages even in the face of excess materials of labour.

  • Krueger, A. and Summers, L. (1988, March): "Efficiency wages and the inter-industry wage structure" Econometrica, volume level 56

Another additional determination of this books is the that the empirical observation that inter-firm or inter-industry wage differentials remain even after most possible economical determinants of these differentials have been governed.

  • Katz, L. and Summers, L. (1989): "Industry rents: Proof and Implications" Brookings Papers on Economic Activity, Microeconomics.

The wage differentials tend to lower quits and escalates the amount of queues of job seekers attempting to gain entrance. They explained the partnership between your existences of rents associated with efficiency pay.

Research Question

  • What is the effect of basic wage level and choice wage rate on the job level, when efficiency pay are paid both in a non-union as well as union setting?


The theory of income syndication is the analysis of the determination of the shares of the factors of production in the total output stated in the market over confirmed period of time. For simpleness, we suppose two factors of development, labour and capital, their shares are defined as follows:

Share of Labour = (w*L)/ X and show of capital = (r*K)/X

Where w= wage rate, r= lease of capital, L=quantity of labour hired, K=quantity of capital hired and X=value of productivity produced in current economic climate.

With this backdrop, we proceed to the model where we consider firms and labours point of view, in both unionised and non-unionised labour setting. Initially, labour drive is unionised. Being a union, three of the most commonly pursued goals are: maximization of career, maximization of total wage invoice and maximization of total increases to the union all together. The general conclusions produced from this microeconomic thought are first of all, if the firm buyers have no monopsonistic vitality, labour unions can possibly attain a rise in the wage rate at the expense of a lower level of unemployment. Second of all, if the organization purchasers have monopsonistic electricity, the unions actions can eliminate one area of the monopsonistic exploitation and thirdly, if the firm buyers have monopsonistic electric power, trade unions can improve the total wage charge in almost all of the circumstances, by either increasing career or the wage rate or both.

Considering, the idea of efficiency wage hypothesis and combining the alternative wage rate as utilized by Shapiro and Stiglitz we incorporate this macroeconomic phenomenon with the microeconomic idea of labour union. Looking at the employment level, substitute wage rate, normal wage rate we can run a regression examination on the occupation level with many other factors and determine the importance of these and produce propositions under different cases.

Bargaining Models

In the framework of labour unions, there will vary types of bargaining that can take place between a company and a labour union. These procedures are also appropriate in a great many other aspects apart from labour unions.

  • Indifference Curves and Iso-profit Curves

Here, we look at the union's preferences as the preference for an individual worker. We can formulate the power of the employee as a function of ingestion, C and leisure, L, i. e. U (C, L). Representing, the electricity function in conditions of wage rate, w and labour provided, h, we can write it as follows:

U (h, w) = U (w*h, 1-h)where C = w*h and considering time constraint L= 1 - h. An indifference curve in (h, w) space is defined by setting up u as (constant) and we specify w implicitly as a function of h, w (h). Therefore, we can write it the following:

U (h, w (h)) = U (w (h)*h, 1-h) =

Differentiating, these equality regarding h and therefore acquiring the slope of the indifference curve.

This means that across the labour supply curve, where MRS = w the indifference curve will have zero slope. To the left of the labour supply curve, personnel work more and so MRS < w and the indifference curve is downward sloping. Symmetrically, to the right MRS > w and the indifference curve is upwards sloping. We can reinterpret the first order condition for finding labour supply as the staff member locating the highest indifference curve in (w, h) at the mercy of the constraint that w equals the offered wage, leading to the tangency shown below.

Looking at the firm's area, its preferences are produced using the iso-cost curve. The firm's profit function can be written as follows:

О  (E, w) = f (E) - w*E

We set the price to unity and along an iso-profit curve, we established the profit equal to some regular, which signifies an implicit romance between w and E. Therefore, we can write it as f (E) - w (E)*E =.

Differentiating, these formula implicitly, we find the slope of the iso-profit curvealong the demand curve MPE = w, implying that iso-profit curves are flat when they mix the labour demand curve. Remaining of the demand curve, means MPE > w hence iso-profit curve is upwards sloping, and right of the labour demand curve, means MPE < w hence iso-profit curve is downward sloping.

  • Monopoly union Bargaining

In this model, the labour union sets the wage rate, w and the organization chooses the job level, E. Since, the firm's target is to increase profits, it'll set the job level at the stage where VMPE = w. Presuming the union operates like a single specific so that h = E, its problem is then

Max U (w*E, 1- E)subject to MPE = w

Maximizing with respect to E, and using the first order conditions we get, f' (E) = w.

The above expression implies that the indifference curve will have a negative slope as the iso-profit curve has a no slope also to interpret the cross of both curves it would mean inefficiency. Individuals would be ready to work more at a slightly lower wage and businesses would make earnings selecting them. However even if unions do function this way, that does not mean they are always bad - personnel are made better off, but these gains are smaller than the losses to organizations and consumers. If the worthiness of the redistribution to workers is known as more important than the loss to the other functions then your union may be a "good" thing. Nonetheless it would be better for everyone if the union and organization could find a far more efficient way of bargaining.

  • Efficient Contracts

This is another model of unions which assumes that the labour union and firm will bargain so that it brings about an efficient results. Now, any Pareto reliable end result will be reached between two people by guaranteeing some degree of income to the company, and making the most of the union's utility.

Max U (w*E, 1- E)at the mercy of f (E) - w*E =

On fixing, we get w = (f (E) -) / E. The first order condition can be written as follows

Solving algebraically we get that the iso-profit curve and the indifference curves are tangent. It can't be solved as to which blend of (E, w) will be chosen as there are several things- the locus of all these points stand for the contract curve. Some information on profit and utility functions is necessary to determine whether the contract curve of the productive deals is downward or upward sloping, or vertical (the highly efficient circumstance).

The Model

General Assumptions:

  • All the personnel are identical.
  • The worker's choose their own level of work effort and this work work is checked by the company by using technology.
  • The monitoring process by the company is not the most effective or it is not perfect.
  • The monitoring process can be expressed in conditions of work work the following, q (e), >0, which implies that a worker will not be dismissed for an exogenously given level of work work.
  • All the staff have an identical electricity function given the following:

U (w, e) = w - e2(eqn. 1)

  • The workers are provided with unemployment insurance or they can obtain another or choice job with income rate.

Efficiency Wages in a non-union setting


Now, if the personnel are able to choose their level of work effort, which is not checked flawlessly by the firm, then the organization may pay wages above the market income rate to ensure a higher level of efficiency or work by the worker. The question is how would alternative wages type in a jobs regression in this case?

We have already assumed that the firm's monitoring process can be indicated as a function of, q (e), suggesting that the workers aren't dismissed for an exogenously given degree of work effort. The personnel can reduce their odds of getting dismissed, by the organization, by increasing their degree of work effort. Implication behind this affirmation suggests that, q' >0.

Let n be the elasticity of q regarding level of work. We can therefore show that the optimal work for the staff member is

e =(eqn. 2)

In order to model the organization, we make another assumption of an concave income function, f'' < 0. This income function depends on efficiency of labour or the effective labour, eL, where L is the amount of labour hired. Therefore, the income function of the organization can be written as

О  = f (e*L) - w*L(eqn. 3)

Using the optimization technique, the organization chooses the level of w and L, subject to the worker's selection of e.

From the equations 2 and 3, we find out that the perfect wage rate, w is twice that of the alternative income rate, .

Expressing f' as a logarithmic form as a linear combo of varied exogenous variables that have an effect on the revenue and effective models of labour, the perfect amount of labour for the non-union organization is

ln L = + ln - ln w + X + ln (w - )

And ln f' = О±0 + О±1X - О±2 ln(e*L)(eqn. 4)

X is the vector of non-labour factors impacting the marginal earnings product of labour.

Interpretation of equation 4, is that the alternative income rate, , depending on w and X, will be negatively correlated with the genuine or observed job.

Proposition: On owning a regression of career on income level and choice wage rate, it will yield a poor coefficient for the alternative wage if efficiency wages are paid even in the lack of successful bargaining.

Efficiency Wages in a Union setting

Here, we discuss the truth for efficiency wages in a unionised scenario and discover the resulting demand for labour under both (a) monopoly unions and (b) efficient bargaining methods.

  1. Monopoly Unions

Considering that the union comprises total of N volume of workers, who are used at the wage rate, 2. Using, the previous method mentioned we calculate the optimal worker effort, e*, where

e* =

Each worker encounters the probability of getting dismissed with a probability of q (e*). We also believe that the personnel getting dismissed by the businesses are changed immediately. Now, the union's purpose is to choose w, in order to maximize the expected energy, V, of unionised staff member. Let L be the job level at the new union wage, w. Then for each and every wage, w, we have,

V = [ q (w - e2 - ) ] + if L < N

And V = q (w - e2 - ) + if L ‰ҐN (eqn. 5)

Now, in the event for monopoly unions, as the union raises the wage levels, it generally lowers the total employment level, hence we have L < N. Although, at some wages below 2, a increasing w would lead to growing career because of increased work effort. The union balances the negative aftereffect of wages on career and results of wages on applied members' utility. Multiplying, equation 5 by N, the union chooses w to maximize

V = Lq ((w - e2 - ) (eqn. 6)

Subject to f'e = w

Using the search engine optimization techniques, we solve for the monopoly union income, w

w = (eqn. 7)

2 is the measure of the slope or the steepness of the marginal income product curve. Higher the elasticity, n, regarding effort, higher will be the union wage. In this particular model, the marginal income output condition for the monopoly model with efficiency wages is comparable to the condition for non-union firms, although in cases like this, the unions will raise the wages and lower the total employment. This contributes to the following proposition.

Proposition: Under monopoly model and efficiency wages, if we run a regression of job on X, w and and a union shift term, the coefficient on the union move should be zero. However, in a regression which includes only the exogenous factors X and and a union change term, the coefficient should be negative.

  1. Efficient Bargaining

Here, we give attention to the truth where labour and the management jointly placed income rate, w and employment level, L.

According to Mc. Donald and Solow, 1981, to derive the group of efficient contracts, they may have suggested the necessary conditions for the deal curve.

Vw / VL = Пw / ПL

The subscripts signify the partial derivatives.

Using equations 3 and 6, and substituting in the above mentioned contract curve relation, we get,

(w - f'e) / (1 - f'ew) = (w -) > 0 (eqn. 8)

As long as the union boosts the wages above the non-union wage 1- f'ew > 0 therefore is w - f'e. Wages exceed the marginal earnings product of labour (as already advised by McDonald and Solow, 1981). Algebraically, dealing with the slope of deal curve is extremely hard and therefore is indeterminate which causes another proposition.

Proposition: Under productive bargaining method and efficiency wages, if we operate a regression of career on X, w and and a union move term, it will yield a positive coefficient for the union move term when compared with a zero coefficient under monopoly model. However, in a regression that includes only the exogenous parameters X and, the hallmark of the union shift coefficient is ambiguous, when compared with a negative coefficient in the monopoly model.


The results from the above mentioned classification of models suggests that traditional way of identifying wage costs, i. e. labour times the wage rate, by the labour union and the career level persistence by the firm side aren't really the only factors that have an impact on the decision making procedure for both the sides. Rather, the alternative income rate, which is one of the factors adopted by Shapiro and Stiglitz in their "efficiency income model", is also instrumental in affecting the career level. Another union change term designed while working the regression, we find that it's also one of the determinants of employment determination. So, the best conclusion that people can derive is that there are certain other factors as well in both wage and employment perseverance and these factors are statistically significant in different situations which again lead to various plan implications. Hence, modification of the theoretical microeconomic base and including certain other parameters will show us a greater and deeper knowledge of the employment determination and thereby many other plan prescriptions that both sides can take into account while framing one.


  • Stiglitz, J. (1976, July): "The Efficiency Wage Hypothesis, Surplus Labour and the Distribution of Income in L. D. C. s" Oxford Economics Documents, pp. 185-207.
  • Oswald, A. (1985): "The Financial Theory of Trade Unions: An Introductory Study" Scandinavian Journal of Economics, level 87.
  • Brown, J. and Ashenfelter, O (1986, June): "Testing the Efficiency of Career Agreements" Journal of Political Overall economy, amount 94.
  • Katz, L. and Summers, L. (1989): "Industry rents: Data and Implications" Brookings Paperwork on Economic Activity, Microeconomics.
  • Krueger, A. and Summers, L. (1988, March): "Efficiency wages and the inter-industry income framework" Econometrica, level 56
  • Stiglitz, J. (1987, March): "THE COMPLEXITIES and Effects of the dependence of quality on price" Journal of Economic Literature, size 25.
  • Cowell, F. A. (2004, December): "Microeconomics: Rules and Examination" STICERD and Section of Economics, London College of Economics.
  • Autor, D. H. (2003, November): "Lecture Take note: Efficiency Wages, Shapiro-Stiglitz Model" MIT and NBER.
  • Koutsoyiannis, A. (1979): "Modern Microeconomics" Macmillan.


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