Wage Bargaining and the Wage Equation

An unfilled vacancy implies a lower expected net present value of profits than a job, even though with some probability, a job may disappear. Unemployment implies a lower permanent income for those who experience it than for employed workers, even though the workers who are employed may, with some probability, lose their jobs and become unemployed.

A firm with a vacancy will hire an unemployed job seeker if the job creation condition is satisfied (i.e., if the real wage is lower than or equal to productivity minus the marginal hiring cost). An unemployed job seeker will accept a job offer if the real wage is higher than the unemployment benefit.

The real wage for a particular job is determined by a negotiation between a prospective employer (a firm with a vacancy) and a prospective employee (an unemployed job seeker). Because all jobs are equally productive and all unemployed receive the same unemployment benefit, the real wage that is determined by an individual negotiation will be the same as the real wage that prevails in the rest of the economy.

From the assumptions that we have made about productivity and aggregate disturbances, any one employer and any one worker, when they come together through the matching process, will certainly agree to an employment contract and create a job. Otherwise, they must continue searching, with additional costs for both sides.

An employment contract between an employer and an employee is defined by a real wage and the provision that employment will be terminated if there is a disturbance that makes the job untenable.

For a real wage w_i, the expected return for a prospective employer and a prospective employee are given by

Equation (18.26), does not make use of the assumption that competition has reduced the expected present value of a vacancy V to zero.

The real wage is determined by a (generalized) Nash bargain that maximizes the weighted product of the surplus of the prospective employer and the prospective employee from the agreement to create a job. An agreement means that the prospective employer gets a surplus J_i − V, and the prospective employee a surplus W_i − U. Thus, the real wage satisfies

where 0 ≤ β ≤ 1 is a measure of the relative bargaining power of the prospective employee, over and above what results from the “threat” points U and V.⁶

The first-order condition for the maximization of (18.28) implies that

Thus, in this model, β turns out to be the share of the prospective employee in the total surplus generated by the creation of a new job.

Using (18.23) and (18.24), and imposing the condition V = 0, we get

From (18.30), the employee receives a real wage that exceeds the permanent income of an unemployed worker by a multiple β of the difference of productivity and the permanent income of an unemployed worker. From (18.30), it is obvious that real wages will be the same for all workers, as the right-hand side does not depend on i.

From (18.29) and (18.16), for V = 0, we can drop i:

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From (18.21) and (18.31), we have

Using (18.32) to substitute for rU in the wage function (18.30) yields

Equation (18.33) is the most convenient and easily interpretable form of the wage determination function in this model.

Higher labor market tightness θ results in a higher real wage, as this increases the average recruitment cost per unemployed person, thereby increasing the threat point of prospective employees versus prospective employers and weakening the effective bargaining position of prospective employers.

The job creation condition (18.12) plays a role analogous to that of a labor demand function in competitive labor market models without hiring costs, the wage function (18.33) plays the role of a labor supply function. Both are needed to determine real wages and labor market tightness.

18.6