The Employment Relationship

Henry Ford's Decision:

In 1914, Henry Ford decided to simultaneously decrease the hours worked per day and double the hourly wage paid to his employees. At the time, nobody fully understood his reasoning. The Walrasian model held that employees' wages were uniquely determined by the labor supply. Thus, Ford, who at the time faced an ample supply of labor, was expected to pay his employees a wage equal to their next best alternative.

Yet, the year following Ford's change, not only did employment grow but also both the number of employees that quit dropped nearly 90% and the number of employees that were fired fell nearly 99%.

The Walrasian model cannot adequately explain this phenomena. It seems there must be other factors at play...

A Company's Production Function:

To start, we can assume the employer has the production function:

y=y(he)+ε

• Assumptions:
  1. y' > 0
  2. y'' < 0
  3. h = # of hours worked (assuming 1 hour per worker)
  4. e ∈ [0,1] (Simply, e is the "effort" term and is equal to the amount per hour that a worker actually works)
  5. ε is an error term with μ=0

• Note that e, the effort exerted by the worker, is a function of the wage (w), the level of monitoring (m), and an exogenously determined
  "next best alternative" we'll call z. Thus, e(w,m;z).

The Game:

The Employer Starts:

• The employer seeks to maximize profit knowing that for a given wage rate (w), the employee will exert an associated effort (e).
• At the beginning of the game the employer selects:

1. The wage (w) to be payed to the employee
2. The level of monitoring (m)
3. A termination probability defined by t ∈ [0,1] with t_e < 0 and t_m >0
   • The termination probability is simply the probability that, at the end of a given period, the worker will be fired for inadequate work. This probability is thus obviously a function of both the worker's effort and the employer's level of monitoring.

The Worker Responds:

• The worker seeks to maximize his utility given the wage rate.

1. The worker's utility for a given period is a function of both wage and effort.
   • u=u(w,e) with u_w ≥ 0 and u_e ≤ 0
   • u_e ≤ 0 does not imply that the worker prefers to not work at all. Rather, it simply implies that the derivative of utility with respect to effort is not positive because this would mean that the employee would always choose to work more in order to maximize his utility.

• The worker decides upon an e in order to maximize the present value of his utility package (v) according to a discount rate (i) given w:

1. • v=(u(w,e)+(1-t(e))v+t(e)z)/(1+i)

Note that if the employee is fired the game ends and the employee receives z

• Rearranging terms we get: v=(u(w,e)-(i*z))/(i+t(e))+z

The employee simply chooses the appropriate e in order to maximize v.

1. v_e=0

This requires u_e=t_e(v-z)

Thus, the worker will choose to work at the level e that equates his marginals.

A Graph of the Relationship

The Employer's Profit Maximization:

The employer's profit function:
π=y(he(w,m;z))-(w+m)h

This standard first order conditions for a maximum are:

1. π_h=y'e-(w+m)=0
   
2. π_w=y'he_w -h=0
   
3. π_m=y'he_m -h=0

These conditions can be easily manipulated to show that a profit max requires:

1. e_w=e/(w+m)=e_m
2. y'=(w+m)/e

Note:

• e_w is the maginal effect of a change in wage
• e_m is the maginal effect of a change in monitoring expense
• e/(w+m) is simply the effort per total labor expense
• Recall from above that the employer did not set h. These first order conditions explain why this was the case.

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Source:

Bowles, Samuel. Microeconomics: Behavior, Institutions, and Evolution. New Jersey: Princeton University Press, 2004.