BAILY WAGES AND EMPLOYMENT very simple and gives the favour of the more complex case where employment varies, which is handled subsequently. Consider the properties then of two specific strategies Strategy S,: the firm pays a constant wage w and employs a constant number of workers Any worker taken on is guaranteed employment up to time T. He may, of course quit if he wishes. Strategy S2: the firm employs a constant number of workers L but the path of wages is unknown at time zero, 1. e. w,= b, (Pi,., Pr, yi,.. . yi) so that w, is a stochastic In order for these strategies to be meaningful the level of wages set must be such that the firm actually can employ workers Definition. Strategies S, and S2 are said to be feasible if the firm has at least L worker To model the assumption of a long-run horizontal labour supply, assume that at time zero all workers search for firms to find the best expected utility offer A single firm can then ensure L workers at the beginning of period one by offering the same expected utility as that available elsewhere Assumption 7. If the labour supply condition(5)is satisfied by strategies S, and S2 then the firm will have L workers available at the beginning of period one v=E∑Uo1+p) =∑U()(1+p)forS1 U(w)(1+p) The simple form of Assumption 7 depends upon the fact that workers were to have identical preferences. If this assumption were changed the analysis would assumed a lot more complicated. It seems intuitively likely that if workers, on the average, are risk averse, then the risk -reducing strategy S, is going to turn out to be the cheapest way of attracting any given size of work-force. It might be tricky to prove, however. Once workers have chosen to come to this firm they can re-evaluate their positions at any time. If they decide to move they incur the mobility costs Cr. For S1, consider the 200+)+(-2E-1亿202-cx+p)+ If this inequality is satisfied for t= 2,..., T then a worker who leaves the firm operating S, will always be worse off. The firm will retain its workers and S will be feasible. To nterpret this condition consider a strategy S which satisfies the labour supply condition (5. It is clear that if the variations of yo are large relative to mobility costs then the constant wage strategy will not be feasible. A large sustained increase in yo will force the firm to adjust its own wage upwards The force of the inequality( 6) is therefore that the constant wage strategy, that satisfies the labour supply condition, will be feasible provided mobility costs are sufficiently large relative to the short-run fluctuations in yo (the wage income available elsewhere in the economy)
REVIEW OF ECONOMIC STUDIES costs relative to fluctuations in the wage income available elsewhere in the economy are large enough so that a strategy s, which satisfies(5) will satisfy the inequality(6) Strategy S2 is really the class of strategies with stochastic wage paths which the firm may wish to choose. The set of these which is feasible must also satisfy a feasibility con- straint as well as the labour supply condition. This is given by Er-12 U(w (1+p)+(e-112 the RHS of (6) The formulation has a slight musical chairs air to it, since everybody searches at and then joins a firm when period one starts. This feature results from the synchronization of everyone's actions, rather as the exact consumption loan model does. Let me try and relate the model a little more closely to reality as follows Workers enter the labour force or retire at random. Some workers quit to look for better conditions and some others come from other firms. What I am trying to capture in the labour supply condition is that, provided the firm offers an expected utility over a period equal to that available elsewhere in the economy, it will find that it can quits and retirements with new entrants and hiring. The feasibility condition is a of the amount of period by period freedom open to the firm resulting from the costs of the labour market The strategy S, is defined in terms of a constant wage. Constancy is stronger than certainty but it is the latter that is really the key feature of S,. This model has ignored such factors as capital accumulation and technical change. In a more general model or in thinking about the relevance of the results, one might plausibly generalize by allowing ing fluctuations around the trend. I have commented(and will comment) on uncertain or stochastic strategies compared with pre-announced, non-stochastic wage strategies in the course of the general discussion since it is the wage certainty not the wage constancy that is important. IIL EXPECTED PROFITS AND ALTERNATIVE STRATEGIES The firm will make a profit in period t given by: m+=P29(L4)-w:L The present value of expected profits evaluated at the beginning of period one is given by E(m)=∑(1+r)E{Pg(L1)-w2L4}, where r is the discount rate and the mappings (4)define the distributions of w, and Lt There is a minor complication introduced by the parameter p in the utility function and the discount rate r. i will set r= p to keep things simple. with the framework developed the following proposition can be shown come Proposition 1. Provided the feasibility constraint is satisfied, the strategy s, with tant wage and employment yields larger expected profits than S2 with a stochastic wage Notice that the worker's expected utility and the firm,s expected profits are evaluated at the beginning of period one, when future values of the state variables are unknown The expected values are, therefore, the prior or unconditional values. Developing the formal proof of the proposition for this case does not seem worth while result is constant capital nly for the long-run shutdown decision ssary if S1 was not deir t effects familiar isher interest theory but not central to the issues here