Insiders and outsiders in wage determination 415 unemployed workers lack firm-specific skills possessed by members of a labor pool. They are therefore less productive than experienced workers. If he firm we are studying were to hire e21 inexperienced workers in period along with el skilled workers, one might quite generally write the revenue generated as s F(el, ez1), where F would have to be given a special property to represent the lower productivity of inexperienced workers For example, F(, y)>FG, x) whenever x>y )We will settle for a simple special case of this assumption, namely that the firm's revenue in the first period will be si f(e11)+si f(ez1) where is a fixed constant between zero and one. In period 2, the firms revenue from employing e1 experi enced and e22 inexperienced workers is si f(e12)+S2 f(e22) We are concerned with the wage rate of skilled workers in periods 1 and called Wn and W2, respectively. Unskilled workers have a reservation wage of wz, which we take to be the same in both periods. The reservation wage is determined by some mixture of unemployment compensation leisure, wages in casual employment, the availability of casual employ- ment, and other such factors Labor is the only variable factor of production. Thus the firm s objective is to achieve a large value of slf(en)+q(e2)]-uneln-u2e2+R{s2[f(en)+(e2)]-u2e12-u2e2 wherer is a discount factor For reasons touched on earlier the firm is assumed not to make payments to laid-off members of its labor pool If the firm operated in a series of spot markets for the two kinds of labor facing parametric wages, it would determine eu, e2l, e,2, and en by four independent marginal productivity conditions. (The discount factor would not matter at all, because there would be no intertemporal implications of any of the firms actions, so no reason for it to compare one period with another But the labor market of the model is not like that, and so the firm chooses its behavior differently. The story extends over two periods, As mentioned the firm starts with a pool of experienced workers, m in number. These workers are organized in a formal or informal union. For a first pass, we assume that the union is able simply to quote wages Wl and w12 for experienced labor in the two periods, while the firm is able to choose levels of employment unilaterally. Thus the firm also decides how many inexperienced workers e2 to hire in he first period, if any. They are freely available at the reservation wage w? (The parallel quantity e22 in the second period is unimportant, because the second period is--artificially-the last period, and so we forget about it. Our key assumption is that inexperienced workers hired in period 1 are z This is a simplification that could easily be dispensed with Scand J. of Economics 1985
Insiders and outsiders in wage determination 415 unemployed workers lack firm-specific skills possessed by members of a labor pool. They are therefore less productive than experienced workers. If the firm we are studying were to hire ezl inexperienced workers in period 1 along with ell skilled workers, one might quite generally write the revenue generated as slF(ell,e21), where F would have to be given a special property to represent the lower productivity of inexperienced workers. (For example, F(x,y)>F(y,x) whenever x>y.) We will settle for a simple special case of this assumption, namely that the firm's revenue in the first period will be sl f(ell)+sl@f(e21) where @ is a fixed constant between zero and one. In period 2, the firm's revenue from employing el, experienced and ez2 inexperienced workers is sl f(e12)+sz @f(e2z). We are concerned with the wage rate of skilled workers in periods 1 and 2, called wl and wlz, respectively. Unskilled workers have a reservation wage of w,, which we take to be the same in both peri~ds.~ The reservation wage is determined by some mixture of unemployment compensation, leisure, wages in casual employment, the availability of casual employment, and other such factors. Labor is the only variable factor of production. Thus the firm's objective is to achieve a large value of where R is a discount factor. For reasons touched on earlier, the firm is assumed not to make payments to laid-off members of its labor pool. If the firm operated in a series of spot markets for the two kinds of labor, facing parametric wages, it would determine ell, e,,, el,, and e,, by four independent marginal productivity conditions. (The discount factor would not matter at all, because there would be no intertemporal implications of any of the firm's actions, so no reason for it to compare one period with another.) But the labor market of the model is not like that, and so the firm chooses its behavior differently. The story extends over two periods. As mentioned, the firm starts with a pool of experienced workers, m in number. These workers are organized in a formal or informal union. For a first pass, we assume that the union is able simply to quote wages wll and w12 for experienced labor in the two periods, while the firm is able to choose levels of employment unilaterally. Thus the firm also decides how many inexperienced workers ezl to hire in the first period, if any. They are freely available at the reservation wage w,. (The parallel quantity ez2 in the second period is unimportant, because the second period is-artificially-the last period, and so we forget about it.) Our key assumption is that inexperienced workers hired in period 1 are This is a simplification that could easily be dispensed with. Scand. J. of Economics 1985
416 R.M. Solow thereby transformed into experienced workers in period 2. Moreover, they become members in good standing of the union in period 2. In other words the initial insiders do not care at all about the welfare of outsiders, but any who are hired by the firm are thereafter on a par with other insiders. The central question addressed in this paper is the effect of this intertemporal connection on the firms employment decision and the unions wage-setting In the set-up as we have described it, the firm s choice of eu will satisfy s,f(eu=wu subject to the usual boundary conditions. If"<" holds at e1=0, the firm employs no skilled workers; if">"holds at e1=m, the firm employs its whole labor pool in the first period Taking the first period by itself, it would be in the firms interest to hire some inexperienced workers if s1'(0)>U2 and the best number to hire, still looking only at the first period would be determined by the obvious marginal-productivity condition. In fact assume that this inequality is not satisfied If the only consideration were first-period profit, the firm would not choose to hire any of the unem ployed. This condition is perhaps excessively strong. It can be read as imiting the model to periods in which s is not too large. It corresponds to what employers often say, especially in not very good years, though that does not guarantee its truth. But the firm has yet another motive to hire inexperienced workers in the first period: to train experienced workers for period 2. This motive becomes effective if the firm anticipates that its second-period employment of experienced workers might profitably exceed m. When this factor is taken into account the firm would be impelled to hire unemployed workers in period 1, even though first-period results by them- selves would not justify it, provided that S1f”(0)-u2+R[s2f(m)-u12]>0 If this inequality is satisfied, ezl is determined by S1f"(e21)-u2+R[52f(m+e21)-u12]=0 These are, in summary, the first-order conditions with respect to ez1 for the firms problem of maximizing slen)+of(e2)-ne1-2e2:+R{If(en)+qfe2)]-u2en subject to the constraints en<m and e12<m+e2l. If, as we suggested Scand J of Economics 1985
thereby transformed into experienced workers in period 2. Moreover, they become members in good standing of the union in period 2. In other words, the initial insiders do not care at all about the welfare of outsiders, but any who are hired by the firm are thereafter on a par with other insiders. The central question addressed in this paper is the effect of this intertemporal connection on the firm's employment decision and the union's wage-setting decision. In the set-up as we have described it, the firm's choice of ell will satisfy subject to the usual boundary conditions. If "<" holds at ell=O, the firm employs no skilled workers; if ">" holds at el =m, the firm employs its whole labor pool in the first period. Taking the first period by itself, it would be in the firm's interest to hire some inexperienced workers if and the best number to hire, still looking only at the first period, would be determined by the obvious marginal-productivity condition. In fact we assume that this inequality is not satisfied. If the only consideration were first-period profit, the firm would not choose to hire any of the unemployed. This condition is perhaps excessively strong. It can be read as limiting the model to periods in which st is not too large. It corresponds to what employers often say, especially in not very good years, though that does not guarantee its truth. But the firm has yet another motive to hire inexperienced workers in the first period: to train experienced workers for period 2. This motive becomes effective if the firm anticipates that its second-period employment of experienced workers might profitably exceed m. When this factor is taken into account the firm would be impelled to hire unemployed workers in period 1, even though first-period results by themselves would not justify it, provided that If this inequality is satisfied, ezl is determined by These are, in summary, the first-order conditions with respect to e2,for the firm's problem of maximizing subject to the constraints ell<m and e12<m+ezl.If, as we suggested Scand. J. of Economics 1985