The Equivalence of Agents in Time
Ioana Ramniceanu, Ph.D Candidate, The Bucharest Academy of Economic Studies
Email: [email protected]
Daniela Marinescu, Ph.D, The Bucharest Academy of Economic Studies
Email: [email protected]
Dumitru Marin, Ph.D, The Bucharest Academy of Economic Studies
Email: [email protected]
Abstract
In this paper we will analize what happens when an agent has to choose between two or more jobs and he knows
that after a period of time the wages will be the same. So, we could say that between the two agents there is no
difference. But still there is a great one: if we will consider a small increase of time, then the utility of the new
amount is different for the two agents.
The same anayze will be made for the exerted effort (having in mind that the function of the effort cost is increasing
and convex). We know that the higher the reference standard from the previous period ( wt 1 ) is, the higher the effort
level is to obtain a greater utility.
Next we will define the equivalence of the agents in time using the non-neutrality measure.
We will find that to do the best choice the employer should know first the effort function for the two agents.
Keywords: Job satisfaction, Non-neutrality measure, Cost function.
JEL Classification: M51, D86, D84
Echivalenţa Agenţilor în Timp
Ioana Ramniceanu, Ph.D Candidate, Academia De Studii Economice, Bucureşti
Daniela Marinescu, Ph.D, Academia De Studii Economice, Bucureşti
Dumitru Marin, Ph.D, Academia De Studii Economice, Bucureşti
Rezumat
În această lucrare se va analiza ce se întâmplă în cazul în care agentul trebuie să aleagă între două sau mai multe
locuri de muncă şi ştie că după o perioadă de timp salariul va fi acelaşi. Astfel, putem spune că între cele două locuri
de muncă nu este nicio diferenţă. Dar totuşi, există o diferenţă foarte mare: dacă es consideră o creştere foarte mică a
timpului, atunci utilitatea obţinută în cazul celor două locuri de muncă este diferită.
Aceeaşi analiza se va face şi pentru efortul depus (ţinând cont de faptul că funcţia efortului este crescătoare şi
convexă). Cu cât nivelul salarial de referinţă este mai mare în perioada anterioară ( wt 1 ), cu atât va fi mai mare
nivelul efortului exercitat pentru a obţine un nivel superior al utilităţii.
În continuare se va defini echivalenţa locurilor de muncă şi a agenţilor în timp folosind măsura de ne-neutralitate.
Din analiza făcută va rezulta că pentru a putea face cea mai bună alegere, agentul va trebui să cunoască funcţia
efortului pentru cele două locuri de muncă.
Cuvinte cheie: Satisfacţia obţinută la locul de muncă, măsura de ne-neutralitate, funcţia de cost.
Clasificare JEL: M51, D86, D84
1. Introduction
The principal hypothesis is that the agent increases his job satisfaction in every period of time
and this depends on the current and previous wage level.
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Easterlin (2001) has shown empirically that some people do not anticipate that the aspiration
level increases with the income. Grund and Slivka (2005) have proved that the job satisfaction
depends not only on the absolute level of the wage, but also on the wage increases, and the wage
level from the previous period was considered a reference point. It was proved that in time people
become less and less satisfied by their jobs, meaning that the job satisfaction is decreasing in
time.
2. The evolution of the wage and effort
We will consider that the function of the effort cost is increasing and convex (the agent will need
to exert a higher effort to obtain a greater wage) and the wage function is increasing and concave.
In this case the agent will obtain satisfaction at his job until the two function are equal. It is very
interesting to study what happens at this moment.
Figure 1: The evolution of the wage and effort
As we can see the agent starts to work at t 0 , and his wage is w0 . This wage level is influenced
only by the level of the qualification. The higher this level is, the higher the effort is.
It is known that the wages and the effort are increasing over time. So by the time t1 the agent has
no reason to look for a new job because his satisfaction is strictly positive.
At time t1 the agent has to choose between finding a new job and keeping his one.
- If he keeps his job then the level of the exerted effort will be too big in
comparison with the wage increasing. The function of the wage increasing is
decreasing over time (see Grund and Slivka, 2005). In this case the agent has
no motivation to exert such an effort.
- If he chooses to change his job then the new reference level of the wage will
become the last wage level from his previous job ( w1 ). In this case the
functions of the wage and effort level will change. But the agent will be
satisfied with his new job until the two functions are equal.
How should the employers react in the reference points?
The employers should analyse the activity of the agent. If they want to keep the agent then they
should promote him offering a new wage and tasks. In this moment for the agent will be the same
if he keeps his job or not.
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Another solution of this problem is job rotation (see Campion, Cheraskin and Stevens, 1994)
3. Job Rotation or Specialization
We will suppose that the agents prefer to deal with a variety of tasks that specialize. To
generalize this affirmation we can say that the agents’ preferences depend on the attributes of
their work, wages and taking part at the decisional process.
To highlight the importance of the preferences we will suppose that the utility function depend
not only on the wage, but also on the level of the job satisfaction.
For the simplicity we will suppose that the utility function is additive separable, as following:
U I , A1 , A2 ,..., An   V  u A1 , A2 ,..., An 
where V represents the income utility, but we will consider it equal with income level and
Ai , i  1,..., n are the attributes of the job.
We will consider two periods of time. For the first period we will suppose that the agent utility is
equal with the income, and for the second one the agent will win a utility premium u if the jobs
rotate. If V 1 is the income at t1 , then U 2  V 1  Vs2 if the agent choose to specialize and
U 2  V 1  Vr2  u if the jobs rotate. Of course, Vs2  Vr2 because the output is greater if the agent
choose to specialize. The utility at t 2 will be greater if the jobs rotate only if the utility premium
satisfies the inequality: u  Vs2  Vr2 . If u *  Vs2  Vr2 then for the agent will be the same if the
jobs rotate or he chooses to specialize.
4. The equivalence of agents in time
Next we will see what happens if the employer has to choose between two agents when he knows
that after a period of time the wage level will be the same. (See figure 2)
Figure 2
We will consider that at the moment 0 the agent’s wage level can be only w0 , this level being
determined only by the level of qualification. We will denote with M and N the two agents. If the
employer chooses the agent M, then his wage function will be wM t  , and if he chooses the agent
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N, then his wage function will be wN t  . Next, we will suppose that at the moment 1 we will
have wM t1   wN t1  .
From wM t1   wN t1  we should say that there is no difference between the two agents at t 0 . But
there is still a great difference between the two agents: we will suppose a small increase of the
time from t 0 to t0  tx and we will analyze what happens with the utility for every agent. We can
note that the wages increase for both agents but for the agent M the increase is greater than for N.
We will find that it is true:
dwM t0   w'M t0 tx
dwN t0   w' N t0 tx
Because
w'M t0   w' N t0 
we will have
dwM t0   dwN t0 
Although the wages are the same for both agents at t 0 , the behaviour is different.
The analyse is the same for the exert effort (the function of the effort cost is increasing and
convex). We know that the higher the reference standard from the previous period ( wt 1 ) is, the
higher the effort level is to obtain a greater utility (see figure 3).
Figure 3
Now we can define the equivalence of two agents in time using the non-neutrality measure (see
Ramniceanu I., Marinescu D., Marin D., 2007), as follows:
„two agents M and N are equivalent in time if:
w'M t0   w' N t0 
”

e'M t0   e' N t0 
But to test the equivalence of agents in time the employer should know a priori the wage and
effort functions for both agents to find the moment when they would promote.
The same analyse can be made to find the equivalence of jobs in time. If we denote with A and B
the two jobs then we can define the equivalence of jobs in time (see Ramniceanu I., Marinescu
D., Marin D., 2008 a, b), as follows:
„two jobs A and B are equivalent in time if:
w' A t 0   w' B t 0 
”

e' A t 0   e' B t 0 
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If an agent has to choose between two jobs, to do the best choice, he should know first not only
how his wage raises (in order to estimate his wage function) but also the specific tasks (to
estimate the cost of the effort).
5. Conclusions
Taking into account that the job satisfaction depends not only on absolut wage level, but also on
wage increases and the previous wage level was considered a reference point to keep the agent
the employer should promote the employe (who should specialize) or should propose to him a job
rotation. The employees would rather preffer a various tasks than specialize and their satisfaction
increases if they take part at decizional process. But if u *  Vs2  Vr2 , then the agent would be
indifferent if the jobs rotate or if he specializes.
There are a lot of cases when the agent should choose between two or more jobs. To do the best
choice, he should know first not only how his wage raises (in order to estimate his wage function)
but also the specific tasks (to estimate the cost of the effort). So, we have defined the equivalence
of jobs in time.
Also there are cases when the employer should choose between two or more agents. To test the
equivalence of agents in time the employer should know a priori the wage and effort functions for
both agents to find the moment when they would promote.
6. References
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Grund C., Sliwka D., The Impact of Wage Increase on Job Satisfaction – Empirical Evidence and
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Grund C., Sliwka D., Reference Dependent Preferences and the Impact of Wage Increases on Job
Satisfaction: Theory and Evidence, IZA DP, no. 1879, December, 2005;
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Ramniceanu I, Marinescu D, Marin D, “Measuring the Risk Aversion”, Economic Computation and
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Conference Economic Growth and E.U. Extension Process, Bucharest, may 2008;
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10. Râmniceanu I., Marinescu D., Marin D., A promotion Model in a Small Colectivity, Sixth International
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