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158

tercyclical. Unfortunately, however, this result does not help to account for the puzzle that shifts m labor demand appear to result in large changes in employment. The problem is that with long-term contracts, the wage is no longer playing an allocative role. That is, firms do not choose employment taking the wage as given. Rather, the level of employment as a function of the state is specified in the contract. And, from (10.49), this level is the level that equates the margmal product of labor with the marginal disutihty of additional hours of work.

As a result, the model implies that the cost to the firm ol varying the amount of labor it uses changes greatly with its level of employment. Suppose the firm wants to increase employment marginally in state i. To do this, it must raise workers compensation to make them no worse off than before. Since the expected utihty cost to workers ol the change is p, V{L,), must rise by p, ViL,)/ U{C). 1 bus the marginal cost lo the firm of increasing employment in a given stale is proportional lo V{L,). If labor supply is relatively inelastic, V{L,) is sharply increasing in L,, and so the cost of labor lo the firm is much higher when employment is high than when il is low. Thus, for example, embedding this model of contracts in a model of price determination like that ol Section 6.11 would not alter the result that relatively inelastic labor supply creates a strong incentive for firms lo cut prices and increase employment in recessions, and lo raise prices and reduce employment in booms.

In addition lo failing to predict relatively acyclical labor costs, the model fails to predict unemployment: as emphasized above, the implicit contract equates the marginal product of labor and the marginal disutility of work. The model does, however, suggest a possible explanation for apparent unemployment. In the efficient contract, workers are not free to choose their labor supply given the wage; instead the wage and employment are simultaneously specified lo yield optimal risk-sharing and allocative efficiency. When employment is low, the marginal disutility ot work is low and the hourly wage, C/L,, is high. Thus workers wish that they could work more at the wage the firm is paymg. As a result, even though employment and the wage are chosen optimally, workers appear to be constrained in their labor supply.

10.6 Insider-Outsider Models

The analysis in Section 10.5 assumes that the firm is dealing with a fixed pool of workers. In reality, there are two groups of potential workers. The first group-the insiders-are workers who ha\ e some connection with the firm al the time of the bargaining, and whose interests are therefore taken into account in the contract. The second group-the outsiders-are workers who have no initial connection with the firm but who may be hired after the



"Important contributions to the insider-outsider literature include Shaked and Sutton (1984); Solow (1985); Gregory (1986); Lindbeck and Snower (1988); Blanchard and Summers (1986, 1987); Oswald (1987); and Gottfries (1992).

contract is set. This distinction may be important for both fluctuations and unemployment-

Insiders and Outsiders and the Cyclical Behavior of Labor Costs

Consider a firm and a set of insiders. The firm and the insiders bargain over the wage and employment as functions of the state. Hours are fixed, so labor input can vary only through changes in the number of workers. The firms profits are

7 = AFdi + Lo) - w,L, - WoLo, (10.50)

where Lj and Lo are the numbers of insiders and outsiders the firm hires, and wi and wo are their wages. As before, A is random, taking on the value A, with probability p,. The insiders have priority in hiring; thus Lq can be positive only if Li equals the number of insiders, Lj.

Oswald (1987) and Gottfries (1992) argue that labor markets have two features that critically affect the problem facing the firm. The first is that, because of normal employment growth and turnover, most of the time the insiders are fully employed and the only hiring decision concerns how many outsiders to hire. Taking this to the extreme, here we assume that 1/ always equals Ij. Since the insiders are always employed, their utility depends only on their wage:

ui = U{w,), GC) > 0, [/"() < 0. (10.51)

The second feature of labor markets emphasized by Oswald and Gottfries is that the wages paid to the two types of workers cannot be set independently: in practice, the higher the wage that the firm pays to its existing employees, the more it must pay to its new hires. Again adopting an extreme form for simplicity, we assume that wo rises one-for-one with Wf:

Wo = Wi- c, > 0. (10.52)

Finally, we assume that the insiders have sufficient bargaining power and that the gap between insider and outsider wages (c) is sufficiently smaU that the firm is always able to hire as many new workers at w/ - as it wants. Thus the model applies most clearly to a firm that faces a strong union or that must pay a high wage for some other reason.

It is convenient to think of the firms choice variables as w/ and to jn each state, wq is determined by wi and equation (10.52); 1/ is fixed at I/.



As in the previous section, the hrm must provide the insiders with expected utihty of at least . The Lagrangian for the firms problem is thus

X = X P> \-AiF(Li + Lo,) - wLi - (Wfi - c)Loi] + A

X Pt U{wn)

The first-order condition for La is

pAA,F(Li + La)-{wn-c)] = 0,

A,F(Li + Loi) = , - c.

- Uo -

(10.53)

(10.54)

(10.55)

Equation (10.55) implies that, just as in a conventional labor demand problem, but in sharp contrast to what happens with implicit contracts, employment is chosen to equate the marginal product of labor with the wage. The reason is that outsiders, who are the workers relevant to the marginal employment decision, are not involved in the original bargaining. The insiders and the firm act to maximize their joint surplus. They therefore agree to hire outsiders up to the point where their marginal product equals the wage they must be paid; the outsiders preferences are irrelevant to this calculation. The first-order condition for wj, is

-Pi(Li +Lo,) + Kpi V(wii) = 0.

This implies

t/(Wfi) =

Ll + La

(10.56)

(10.57)

Since to; is higher in good states, (10.57) implies that V(wii) is higher. This requires that w/, is lower-that is, that the wage is countercyclical. Intuitively, the firm and the insiders want to keep the expenses of hiring outsiders down; they therefore lower the wage in states where employment is high. In short, this model implies that the real wage is countercychcal and that it represents the true cost of labor to the firm.

It is easy to think of changes that weaken these results. For example, if there are states in which some insiders are laid off, for those states the contract would equate the marginal product of labor with the opportunity cost of insiders time rather than with the wage. Similarly, if there is not an unlimited supply of outsiders, this would tend to make the wage increasing rather than decreasing in A. Such changes, however, do not entirely undo the result that insider-outsider considerations reduce the cyclical sensitivity of the marginal cost of labor to firms.



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