New Classical Macroeconomics: Cahuc’s adjustment costs

The static theory of labour demand does not specify how, or how long adjustments between production factors take. It is therefore necessary to consider the notion of adjustment costs, such as costs incurred by a company to change the number of factors.

We will follow the lines followed in the model of adjustment costs seen in “Le marché du travail”, 2001, by Pierre Cahuc. These adjustments involve production costs that do not correspond to the activity itself. There are two kinds of adjustment costs:

-Internal adjustment costs: those caused by the loss of efficiency due to reorganization within the company (for example, training for use of new machinery, training of new employees to existing machinery, etc.).

-External adjustment costs: those who can be differentiated from production variations (for example, hiring experts to implement the changes, layoff payments, etc.).

As Cahuc explains, previous studies on the labour markets in the United States and France allow us to compare the situation of two types of markets:

-Recruitment costs are higher than firing costs in the U.S.;

-Firing costs are higher than recruitment costs in France;

-Recruitment costs in the U.S. are higher than in France;

-Firing costs are higher in France than in the U.S.

Furthermore, these studies conclude that these costs increase with the level of wage and/or training.

Employment protection by the public sector is less rigorous in the U.S., Canada or the U.K. than in France, Germany and southern Europe. Furthermore, these studies conclude that much of the higher cost of firing in Europe is due to administrative or regulatory costs (due to the legislation of each country).

LINEAR FORMULATION:

In most jobs, costs are represented by a symmetric convex function (usually quadratic). However, this does not explain asymmetrical adjustments and discontinuous employment. Thus, we see the linear formulation, which is commonly used nowadays.

This representation will show us how companies sometimes hire or fire employees, or remain as they are.

c_h and c_f represent hiring costs (h) and firing costs (f). Adjustment of employment will therefore be asymmetricif c_h ≠ c_f.

EMPLOYMENT ADJUSTMENT:

It is possible to differentiate the effects of c_h and c_f when adopting a linear function. Furthermore, the linearity will see how the adjustment in the levels of labour can be immediate.

We define the adjustment cost function as:

The producer’s problem is choosing the level of labour that maximises its profits: 

(r=is the rate at which future profits are actualised to present value)

The employment level is given by the equation:

which translates into the following conditions:

In all other cases, the producer maintains its level of staff. As we assume w, r, c_h and c_f constant, we can define employment levels L_h and L_f  as:

The company adjusts its level of workers L_h (respectively L_f) if this is higher (respectively lower) than the initial level of employment L₀. If not, it means that L₀ is maintained between L_h and L_f, its optimal level:

GRAPHICAL ANALYSIS:

The curves in the lower half of the adjacent figure represent the relationship between initial employment and final employment levels. The conclusions we can derive from this model are:

-↑c_f: An increase in firing costs (U.S. spending levels to levels of FR.) Prevents staff adjustment downwards, and no incentive to hire;

-↑c_h: Increased recruitment costs (FR. spending levels to U.S. levels) prevents new hires;

-↓c_h: A lower recruitment cost always has positive effects on employment because it increases the optimal level of employment L_h;

Therefore, this model explains:

· higher unemployment in France (for little flexibility when firing);

· when wages are equal in both economies, U.S. production levels will be higher;

· in recessions, the situation is worse in France because it’s hard to fire employees;

· in times of expansion, the situation is worse in the U.S. because it’s hard to hire.

The main conclusion that can be derived from this model is that proper management of the costs of hiring and firing ensures greater stability in the demand for labour.