Interpretación de los esquemas eléctricos

Throughout the following, w will refer to a firm's wage offer (which will be assumed to be constant over time) and L will denote the total number of job slots or vacancies that a firm creates. L is the cut-off point of applicants accepted.

In the conventional static theory of the firm, output is

generally taken to be some smooth continuous function of capital and labour inputs. Here we shall assume capital fixed and consider

labour input as synonymous with the number of individuals employed ('hours' or 'effort' variables are ignored). Consider a firm that at time t has a labour force l (integer). Given a number of

stochastic influences operating in a labour market, it is reasonable to expect individuals to leave the firm. Leaving may take many forms, quitting in order to find a better job (possibly search for a better wage or other job characteristics), layoff, illness or

retirement. Here we assume that 'learning' is exogenous and therefore that the latter explanations are dominant. The exogenous leaving of individuals from a firm will be modelled by assuming a probability ufit that an individual leaves the firm in a time interval fit. For suitably small fit the probability of more than one individual

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leaving is of order (fit) and approximately zero. The advantage of working in continuous time is now clear. In continuous time we can concentrate attention on employment processes that change by a single increment rather than more general 'Markov' processes.

Once unemployed, individuals are assumed to search for new employment. It is of no consequence whether search is discrete, each contact taking exactly 1 week, say, to achieve or continuous, given a distribution of searchers over time, it will still be the case that the firm will be contacted periodically by job searchers. We will denote the probability of a contact to the firm (again relative to an interval fit) by y S t . Of course, if individuals

differ as to their reservation wages there will be a probability that the firm's wage offer w will be rejected. If we denote by g(r) the probability density function of job searchers' reservation wages, then the probability that a job searcher contacting the firm will accept an offer of w is simply G(w) where G(w) is the cumulative

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distribution function. We can therefore write the probability that the firm's employment increases by one unit of labour in time fit (call this Xfit) as,

(4.1) Xfit » yG(w)5t

In the simple framework just described, the firm's employment level is a random variable which evolves through time. Increases in employment have been made dependent (through G(w)) on the firm's wage offer whilst decreases in employment occur through exogenous

influences. The structure described above is perfectly capable of handling endogenous quitting. If for example search 'on the job' were possible, then one element determining the rate at which

employment declines would again be the firm's wage offer. By paying a high wage the firm would reduce the probability of employment losses. We will, however, remain with the framework described above which is consistent with 'intensive' search as described in the previous two chapters.

Starting from some employment level l at time t, the possible

employment outcomes at time t+5t can be shown via a simple probability tree (Fig.l).

l + 1 3 . P ( l + 1, t + fit) - Xfit l ---» p(£, t + 5t) ■ 1 - (X + p)fit l - 1 p(£ - i, t + fit) ■ yfit

Figure 1

The probability of finding a firm at some employment level at a given time will therefore in general depend upon the initial state, the time elapsed since the initial state was occupied, the parameters y, v> and the firm’s wage offer w. We shall have

distribution function. We can therefore write the probability that the firm's employment increases by one unit of labour in time fit

(call this Xfit) as, (4.1) Xfit « yG(w)6t

In the simple framework just described, the firm's employment level is a random variable which evolves through time. Increases in employment have been made dependent (through G(w)) on the firm's wage offer whilst decreases in employment occur through exogenous

influences. The structure described above is perfectly capable of handling endogenous quitting. If for example search 'on the job' were possible, then one element determining the rate at which

employment declines would again be the firm's wage offer. By paying a high wage the firm would reduce the probability of employment losses. We will, however, remain with the framework described above which is consistent with 'intensive' search as described in the previous two chapters.

Starting from some employment level i at time t, the possible

employment outcomes at time t+5t can be shown via a simple probability tree (Fig.l).

P(A + 1, t + fit) - Xfit

P U , t + fit) - l - (x + p)fit

p(i - l, t + fit) - pfit Figure 1

The probability of finding a firm at some employment level at a given time will therefore in general depend upon the initial state, the time elapsed since the initial state was occupied, the parameters y , y and the firm's wage offer w. We shall have

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cause to simplify analysis by considering only steady states of the employment process, in which case only the last two factors enter into the problem.

So far attention has been confined to describing the environment in which a firm operates. It is now time to consider the value to a firm of being in a particular employment state, and of transmitting through states over time.