BAILY WAGES AND EMPLOYMENT The unsubscripted expectations operator will be used to denote this expected value, i.e. when the state variables from 1, ., T(the prices Pi,..., Pr in the above case)are unknown The operator Er will denote the expected value of a variable when state variables up to period t are known. It is the conditional expectation defined in the usual way It is convenient to take the technology and capital equipment to be constant. It is doubtful if any essential features of the results depend upon this, but a number of awkward Assumption 2. The firms output in period t is x, and is given by x1=9(L)g′>0,g"<0, where L, is employment in period t 3 Let a worker's income in period t be The values (,., yr), which depend upon the wage and employment prospects of the worker, will in general be stochastic variables. Each worker's decision function is of the form given by Assumption 3. A worker making a decision in t-I which affects his path of income yu., yr will maximize Vt-1 given by U()(1+p) where U>0, U"<O and p is a constant The assumption implies all workers are alike in their preferences. This makes life much easier, as I shall comment later, but obviously is pretty strong. The firm and industry are assumed small relative to the rest of the economy. The overall price level is constant ects in the rest of the are given exogenously. There may, in fact, be many choices open to a worker who is not employed with the firm we are analysing. But just as one assumes an equilibrium wage prevailing in the economy in the standard textbook theory, I shall assume a given(possibly stochastic) path of income available elsewhere Assumption 4. The path of income available to a worker elsewhere in the economy is yi,..., yT. The y2 are stochastic and may be jointly distributed Consider a worker who does join the firm we are analysing. If he is employed in criod t his income is simply the firm wage wr. If there were no mobility or information costs in this economy the firm would have no real choice. It would pay w,= yo in each riod as a perfect competitor in the labour market. more realistically, however, although a firm may face a long-run horizontal supply of labour, this is not true period by period because of information and mobility costs The fact that mobility costs exist has been well recognized in the literature. - In ctual practice the cost of changing jobs may be quite different from one worker to another. Some workers may have many jobs open to them in the same location and have a general skill needed in many industries. There would seem to be many workers, however, for whom changing jobs would involve considerable costs. These might be moving expenses search expenses, income foregone and possible retraining. For almost all firms there are significant costs involved when a new worker joins the company. He may have to be fROTh us. E ( p) is t te the ite ral r Feo eh conditional density of Pr, defined as the ratio of the integral 3 The length of the period can be taken as the order of er Is as an analysis of very short-run fluctuations and overtime