《宏观经济学 Macroeconomics》课外读物：Insiders and Outsiders in Wage Determination

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Scand J of Economics 87(2), 411-428, 1985 Insiders and Outsiders in Wage Determination Robert m. solow* Massachusetts Institute of Technology, Cambridge, MA, US A firm starts with a group of insiders or seasoned workers. There is also a large pool of outsiders who are initially less productive, but are transformed into insiders after one period of employment. The firm gains from having a large pool of insiders, some of whom may be laid off in bad years. Insiders gain from keeping their numbers small. If the insiders set the erally, they will choose a path that-in this extreme case--prevents empl outsiders even if future employment prospects are good. If the wage path is set by bargaining, the extra advantage to the firm permits employment of some outsiders y bienterat situations The labor market is still something of a puzzle for macroeconomics. at least since Pigou (1933), it has been clear to mainstream theory that an atomistically competitive labor market could not produce the sort of per- sistent unemployment we see. (I take the proposal that the real-world labor arket is actually in market-clearing equilibrium with respect to some (mis)perceived demand and supply conditions to be a clever jeu d'esprit and not a serious description of modern capitalist economies in prolonged recession )That still leaves a wide variety of possible market institutions d fections"to be analyzed For a long time mainstream macroeconomics more or less ignored the problem of finding an adequate description of the labor market that would fit comfortably with the rest of accepted theory. In the past decade however, there has been a true renaissance in this field with alternative models appearing almost monthly. The result has been a better understand- ing of the implications that follow from the long-term character of the employment-relation, and from the prevalence of explicit and implicit bar gaining. This is surely one of the good effects of the movement to reconcile macroeconomic and microeconomic modes of analysis. Success is not yet Any interesting ideas in this paper are part of a larger project on which I am collaborating with Frank Hahn. The faulty execution is all mine. I thank Lars Calmfors, Henrik Horm Andrew Oswald and the discussants for both helpful and disturbing comments. I have tried to take account of some of their suggestions, but have not had time to follow up all of ther Scand J. of Economics 1985

Scand. J. of Economics 87 (2), 41 1--428, 1985 Insiders and Outsiders in Wage Determination Robert M. Solow* Massachusetts Institute of Technology, Cambridge, MA, USA Abstract A firm starts with a group of insiders or seasoned workers. There is also a large pool of outsiders who are initially less productive, but are transformed into insiders after one period of employment. The fm gains from having a large pool of insiders, some of whom may be laid off in bad years. Insiders gain from keeping their numbers small. If the insiders set their wage unilaterally, they will choose a path that-in this extreme case-prevents employment of outsiders even if future employment prospects are good. If the wage path is set by bilateral bargaining, the extra advantage to the firm permits employment of some outsiders in some situations. I. Background The labor market is still something of a puzzle for macroeconomics. At least since Pigou (1933), it has been clear to mainstream theory that an atomistically competitive labor market could not produce the sort of persistent unemployment we see. (I take the proposal that the real-world labor market is actually in market-clearing equilibrium with respect to some (mis)perceived demand and supply conditions to be a clever jeu d'esprit and not a serious description of modern capitalist economies in prolonged recession.) That still leaves a wide variety of possible market institutions and accompanying "imperfections" to be analyzed. For a long time mainstream macroeconomics more or less ignored the problem of finding an adequate description of the labor market that would fit comfortably with the rest of accepted theory. In the past decade, however, there has been a true renaissance in this field, with alternative models appearing almost monthly. The result has been a better understanding of the implications that follow from the long-term character of the employment-relation, and from the prevalence of explicit and implicit bargaining. This is surely one of the good effects of the movement to reconcile macroeconomic and microeconomic modes of analysis. Success is not yet * Any interesting ideas in this paper are part of a larger project on which I am collaborating with Frank Hahn. The faulty execution is all mine. I thank Lars Calmfors, Henrik Horn, Andrew Oswald and the discussants for both helpful and disturbing comments. I have tried to take account of some of their suggestions, but have not had time to follow up all of them. Scand. J. of Economics 1985

412 R.M. solow at hand, however. Some persistent and macroeconomically significant char- acteristics of the labor market still elude plausible explanation One of the hardest nuts to crack, it seems to me, is to explain why employed workers do not compete for existing jobs by offering to work at jobs for which they are qualified at a wage lower than that currently being paid to incumbents. Some current theories have an answer to that question but an unacceptable one, at least to me. In some contract theories, firms are allowed to make payments to currently unemployed members of their labor ool The result is usually the "indifference principle": in the optimal contract, workers are equally well off whether employed or laid off. That answers the question all right, but only by flying in the face of the common observation that laid-off workers are glad to find work, and their families often celebrate the event. This is discussed in the survey by azariadis Stiglitz(1983) There are also sensible models that contradict the indifference principle nd show why any labor-market equilibrium must exhibit a utility-differen- tial in favor of employed workers. A current favorite rests on the assump- tion that firms are able only imperfectly to measure the effort being put out by their employees. These"efficiency wage"models are ably outlined by Yellen (1984). If the indifference principle ruled many workers would presumably rest on the job, since being found out and fired would be painless. The equilibrium utility-differential between employed and unem ployed must be enough to induce the equilibrium amount of effort from the employed. There is probably something to this story, though I am not sure how it coheres with the fact that many employment contracts differentiate explicitly between ordinary layoff and discharge"for cause The interesting thing about this sort of model is that an unemployed worker would be motivated to offer to work at a bit less than the going wage;it is the employer who would refuse the deal. The reason, of course is that the employer would reckon that the worker, once employed at lower wage, would have less than the appropriate reason to fear being fired and would therefore be inclined to do less than the appropriate amount of work. The trouble with this story is that the unemployed workers ought to keep trying. There is always the chance that the next firm will be tempted After all, unemployed workers do try; what they don' t do is engage in wage-cutting. If this model were really describing a major part of what happens in labor markets, I would expect to see more wage-cutting offers on the part of the unemployed especially since many of them can demor strate that their current unemployment does not result from having been fired for caus I hasten to confess that l, personally, do not find this reluctance to be so great an intellectual problem; but that is only because l, personally, do find it hard to imagine that the unemployed do so little undercutting of Scand J. of Economics 1985

at hand, however. Some persistent and macroeconomically significant characteristics of the labor market still elude plausible explanation. One of the hardest nuts to crack, it seems to me, is to explain why unemployed workers do not compete for existing jobs by offering to work at jobs for which they are qualified at a wage lower than that currently being paid to incumbents. Some current theories have an answer to that question, but an unacceptable one, at least to me. In some contract theories, firms are allowed to make payments to currently unemployed members of their labor pool. The result is usually the "indifference principle": in the optimal contract, workers are equally well off whether employed or laid off. That answers the question all right, but only by flying in the face of the common observation that laid-off workers are glad to find work, and their families often celebrate the event. This is discussed in the survey by Azariadis & Stiglitz (1983). There are also sensible models that contradict the indifference principle and show why any labor-market equilibrium must exhibit a utility-differential in favor of employed workers. A current favorite rests on the assumption that firms are able only imperfectly to measure the effort being put out by their employees. These "efficiency wage" models are ably outlined by Yellen (1984). If the indifference principle ruled, many workers would presumably rest on the job, since being found out and fired would be painless. The equilibrium utility-differential between employed and unemployed must be enough to induce the equilibrium amount of effort from the employed. There is probably something to this story, though I am not sure how it coheres with the fact that many employment contracts differentiate explicitly between ordinary layoff and discharge "for cause". The interesting thing about this sort of model is that an unemployed worker would be motivated to offer to work at a bit less than the going wage; it is the employer who would refuse the deal. The reason, of course, is that the employer would reckon that the worker, once employed at a lower wage, would have less than the appropriate reason to fear being fired, and would therefore be inclined to do less than the appropriate amount of work. The trouble with this story is that the unemployed workers ought to keep trying. There is always the chance that the next firm will be tempted. After all, unemployed workers do try; what they don't do is engage in wage-cutting. If this model were really describing a major part of what happens in labor markets, I would expect to see more wage-cutting offers on the part of the unemployed, especially since many of them can demonstrate that their current unemployment does not result from having been fired for cause. I hasten to confess that I, personally, do not find this reluctance to be so great an intellectual problem; but that is only because I, personally, do not find it hard to imagine that the unemployed do so little undercutting of the Scond. J. of Economics 1985

Insiders and outsiders in wage determination 413 wage because they think it is an improper or undignified thing to do, and because they would not like others to do it unto them if roles were reversed as they might be next time. But I realize full well that this is not the way economics is supposed to model the world, and so I mention it only as a Galilean remark(i.e, something best muttered to oneself). That leaves us without a good explanation of the behavior of the unemployed, and I will not provide one here. We have better prospects of modelling the behavior of the other parties in he labor market: employers and employed workers. By itself, that would go some way toward explaining(or explaining away) the reticence of the unemployed. Once they have concluded a formal or informal agreement with their workers and achieved the desired level of employment under that agreement, employers often announce simply that they are not hiring Unemployed workers, knowing the state of affairs, may not bother to ti Of course an explanation is required of employers' behavior but that may be easier. I have already mentioned one such explanation; Lindbeck Snower(1984)have another(see below); and this paper will provide a third Any attempt to model a unionized labor market in anything less than the longest run must start with a strategic choice about the degree of centralia tion in collective bargaining. Economists in many European economies such as the Nordic ones, gravitate toward the assumption of centralized bargaining between an all-inclusive trade union and a single employer this is natural in economies where nearly 90 of blue-collar workers belong to a union, and where collective bargaining tends to occur at the national level. My model is more suited to U. S. conditions where only about a third of blue-collar workers and fewer than a quarter of all workers are orga nized, and even industry-wide bargaining is far from universal. In such a situation, both parties know that there is, out there, a large number of nonunion workers, even if a firm is dealing with a disciplined union Nonunion workers may, of course, lack some of the skills, especially the firm-specific skills, possessed by union members. The particular problem I want to study is the effect on wage-bargaining of the presence of that unorganized fringe This paper shares a basic orientation with Lindbeck Snower(1984) Most models of bargaining and contracting in the labor market pay attention only to the conflict of interest between the firm-employer and its labor pool or group of attached potential employees. when there is involuntary unem- ployment, however, the interests of employed and unemployed workers also diverge. This is obviously the case if the indifference principle does not hold. Even if it does there is a conflict of interest between workers under the contract and those -new entrants to the labor force and others who are currently without a contract of any kind, and are seeking long-term membership in a labor pool. the basic similarity between this paper and the 27-858472 Scand J, of Economics 1985

Insiders and outsiders in wage determination 413 wage because they think it is an improper or undignified thing to do, and because they would not like others to do it unto them if roles were reversed, as they might be next time. But I realize full well that this is not the way economics is supposed to model the world, and so I mention it only as a Galilean remark (i.e., something best muttered to oneself). That leaves us without a good explanation of the behavior of the unemployed, and I will not provide one here. We have better prospects of modelling the behavior of the other parties in the labor market: employers and employed workers. By itself, that would go some way toward explaining (or explaining away) the reticence of the unemployed. Once they have concluded a formal or informal agreement with their workers and achieved the desired level of employment under that agreement, employers often announce simply that they are not hiring. Unemployed workers, knowing the state of affairs, may not bother to try. Of course an explanation is required of employers' behavior, but that may be easier. I have already mentioned one such explanation; Lindbeck & Snower (1984) have another (see below); and this paper will provide a third. Any attempt to model a unionized labor market in anything less than the longest run must start with a strategic choice about the degree of centralization in collective bargaining. Economists in many European economies, such as the Nordic ones, gravitate toward the assumption of centralized bargaining between an all-inclusive trade union and a single employer. This is natural in economies where nearly 90% of blue-collar workers belong to a union, and where collective bargaining tends to occur at the national level. My model is more suited to U.S. conditions where only about a third of blue-collar workers and fewer than a quarter of all workers are organized, and even industry-wide bargaining is far from universal. In such a situation, both parties know that there is, out there, a large number of nonunion workers, even if a firm is dealing with a disciplined union. Nonunion workers may, of course, lack some of the skills, especially the firm-specific skills, possessed by union members. The particular problem I want to study is the effect on wage-bargaining of the presence of that unorganized fringe. This paper shares a basic orientation with Lindbeck & Snower (1984). Most models of bargaining and contracting in the labor market pay attention only to the conflict of interest between the firm-employer and its labor pool or group of attached potential employees. When there is involuntary unemployment, however, the interests of employed and unemployed workers also diverge. This is obviously the case if the indifference principle does not hold. Even if it does, there is a conflict of interest between workers under the contract and those-new entrants to the labor force and others-who are currently without a contract of any kind, and are seeking long-term membership in a labor pool. The basic similarity between this paper and the 27-858472 Scand. J. of Economics 1985

414 R.M. Solow one by Lindbeck Snower is that they both focus on this important and neglected aspect of the labor market; see also McDonald solow( 1985) The difference between the present paper and Lindbeck Snower's is that the latter focusses mainly in hiring and firing costs and the incumbent workers ability to exploit the market power that these costs confer, where- as here we concentrate on skill differences(which are also mentioned by Lindbeck Snower) and longer-run considerations concerning the ultimate of the labor pool. In addition, Lindbeck Snower focus on the firms decision whether to replace some or all of its incumbent workers with outsiders, whereas we take it for granted that the firm cannot or will not do that, and look only at the firms decision whether to make a marginal addition to the size of its labor pool Both papers succeed in showing how the wage policy of the incumbent group of workers is affected by the presence of unemployed outsiders neither solves the problem of accounting for the passive behavior of the outsiders. Lindbeck Snower observe that outsiders who succeed in gaining employment by undercutting and replacing some incumbents might find themselves ostracized by the remaining insiders That rings true, but it is just a particular aspect of the""-constraint mentioned earlier. In the part of the field that they cover, the two papers are complementar I. Outline of a Model We now start the formal specification of the model, explaining the notation The story extends over two periods, but we are mainly concerned what happens in the first. That is because the second period being last"period, has special characteristics that are of no real significance The firm starts with a pool of experienced workers, m in number. If it employs ell of them in period 1 it will generate an output whose market value is si f(eu. Here s, is a parameter describing the state of the firms product market in the first period. The state is entered multiplicatively for onvenience and simplicity. Similarly in period 2, if the firm employs e12 skilled workers they will generate a revenue S2 f(e12). For now we treat sr and sz as known; but eventually we will want to think of s2 as a random variable of known distribution labor pool. Some of these may be new entrants or re-entrants to the av, p There is also available a large supply of workers who belong to no firm force; but others may be workers who have held jobs with other firms bu have been laid off with no prospect of recall, for the usual reasons. These If this model is to be developed further, it would have to encompass a fairly large number of periods, of which all but the last few would

one by Lindbeck & Snower is that they both focus on this important and neglected aspect of the labor market; see also McDonald & Solow (1985). The difference between the present paper and Lindbeck & Snower's is that the latter focusses mainly in hiring and firing costs and the incumbent workers' ability to exploit the market power that these costs confer, whereas here we concentrate on skill differences (which are also mentioned by Lindbeck & Snower) and longer-run considerations concerning the ultimate size of the labor pool. In addition, Lindbeck & Snower focus on the firm's decision whether to replace some or all of its incumbent workers with outsiders, whereas we take it for granted that the firm cannot or will not do that, and look only at the firm's decision whether to make a marginal addition to the size of its labor pool. Both papers succeed in showing how the wage policy of the incumbent group of workers is affected by the presence of unemployed outsiders; neither solves the problem of accounting for the passive behavior of the outsiders. Lindbeck & Snower observe that outsiders who succeed in gaining employment by undercutting and replacing some incumbents might find themselves ostracized by the remaining insiders. That rings true, but it is just a particular aspect of the "propriety1'-constraint mentioned earlier. In the part of the field that they cover, the two papers are complementary. 11. Outline of a Model We now start the formal specification of the model, explaining the notation as we go along. The story extends over two periods, but we are mainly concerned with what happens in the first. That is because the second period, being the "last" period, has special characteristics that are of no real significance.' The firm starts with a pool of experienced workers, m in number. If it employs ell of them in period 1 it will generate an output whose market value is sl f(ell). Here sl is a parameter describing the state of the firm's product market in the first period. The state is entered multiplicatively for convenience and simplicity. Similarly in period 2, if the firm employs e12 skilled workers they will generate a revenue s2 f(elz). For now we treat sl and s2 as known; but eventually we will want to think of s2 as a random variable of known distribution. There is also available a large supply of workers who belong to no firm's labor pool. Some of these may be new entrants or re-entrants to the labor force; but others may be workers who have held jobs with other firms but have been laid off with no prospect of recall, for the usual reasons. These ' If this model is to be developed further, it would have to encompass a fairly large number of periods, of which all but the last few would count. 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 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=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 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

Insiders and outsiders in wage determination 417 earlier, the union is able to impose the condition that e21=0 unless en=m then that constraint must be observed too. These constraints come into play only if s2f(m)>W12. Otherwise e12 is determined by S2f(e1)=1 These considerations define the demand for labor facing the union, to which it must respond in quoting the wage rates for periods I and 2. The next step is to specify the unions preferences. For the first period, the union's objective is assumed to be eu(/m, where wo is the reser vation wage for insiders, possibly larger than W2. Two immediate observa- tions are called for:(a) it is more usual to write U(u)-Uo with U()strictly concave but for now we set U(w)=w for simplicity and leave the general concave utility function for discussion later; cf also Pencavel (1985); (b)the factor I/m can usually be omitted because it is an exogenous constant, but here it matters because the second-period membership of the labor pool m+ez and that is endogenous via the unions choice of w1. Thus the relevant objective in period 2 is (m+e21)e12(w12-Wo)and the unions complete objective function is 1(u1-u0)+R(m+e21)en412-u0 The union is assumed to discount utility at the same rate that the firm uses to discount profit. The important thing about this formulation is that the union suffers a direct utility-loss when its members are unemployed For given employment in any period, the union is worse off the larger its In principle, now, the union knows e11, e12, and e21 as functions of Wjl nd w1. It chooses wn and w12 to maximize(5)where e 11 is defined as function of Wn by (1)and either e21=0 and e12 is defined by(4)or e21 is defined by (3)and e1=m+e21 Our strategy is to maximize for the union and search out the circum- stances under which the union will set values of wu and wj which induce the firm to choose e21=0. when will the current incumbents select a wage policy that excludes outsiders from employment? It is to be emphasized that the insiders take full account of the fact that outsiders hired this period will be insiders next period In fact, what may induce the incumbents to set a wage that has the effect of excluding outsiders from current employment is precisely the realization that enlarging the pool of insiders now will lead in the future to a higher unemployment rate among members and/or to the setting of lower wages in the future in order to avoid that unemployment The device that the incumbents use to diminish or eliminate the current employment of outsiders is the setting of a high enough wage for next period so that employers foresee no need to enlarge the pool of skilled Scand J of Economics 1985

Insiders and outsiders in wage determination 417 earlier, the union is able to impose the condition that e21=0 unless ell=m, then that constraint must be observed too. These constraints come into play only if s2f '(m)>w12. Otherwise e12 is determined by These considerations define the demand for labor facing the union, to which it must respond in quoting the wage rates for periods 1 and 2. The next step is to specify the union's preferences. For the first period, the union's objective is assumed to be ell(wll-wo)lm, where wo is the reservation wage for insiders, possibly larger than w2. TWO immediate observations are called for: (a) it is more usual to write U(w)- Uo with U(.) strictly concave but for now we set U(w)=w for simplicity and leave the general concave utility function for discussion later; cf. also Pencavel(1985); (b) the factor l/m can usually be omitted because it is an exogenous constant, but here it matters because the second-period membership of the labor pool is m+eZl and that is endogenous via the union's choice of w12. Thus the relevant objective in period 2 is (m+e21)-1e12(w12-~o) and the union's complete objective function is The union is assumed to discount utility at the same rate that the firm uses to discount profit. The important thing about this formulation is that the union suffers a direct utility-loss when its members are unemployed. For given employment in any period, the union is worse off the larger its membership. In principle, now, the union knows ell, e12, and ezl as functions of wll and w12 It chooses wll and w12 to maximize (5) where ell is defined as a function of wl by (I) and either e21 =0 and e12 is defined by (4) or e21 is defined by (3) and el2=rn+ezl. Our strategy is to maximize for the union and search out the circumstances under which the union will set values of wll and w12 which induce the firm to choose e21=0. When will the current incumbents select a wage policy that excludes outsiders from employment? It is to be emphasized that the insiders take full account of the fact that outsiders hired this period will be insiders next period. In fact, what may induce the incumbents to set a wage that has the effect of excluding outsiders from current employment is precisely the realization that enlarging the pool of insiders now will lead in the future to a higher unemployment rate among members, and/or to the setting of lower wages in the future in order to avoid that unemployment. The device that the incumbents use to diminish or eliminate the current employment of outsiders is the setting of a high enough wage for next period so that employers foresee no need to enlarge the pool of skilled Scand. J. of Economics 1985

418 R.M. Solow workers. Since the current productivity of outsiders is assumed to be low that is enough to exclude them from current employment The interpretation we have in mind can be restated from another point of view. The industry is subject to fluctuating demand for its product. Since the firm assumes no long- run responsibility for its workers, it will hire outsiders at their reservation wage any time their current(marginal)pro- ductivity exceeds that wage. Suppose market conditions in period i are not so good (i.e, S, not so large) that outsiders can be profitably employed on that basis. The possibility exists that they might be hired any way if period 2 Is expected to be prosperous enough (i.e, S2 large enough) so that the firm rill need an enlarged pool of skilled workers then. This possibility will be frustrated if the insiders choose to convert the improving market prospects into a sufficiently high wage for period 2 that the firms demand for labor can be satisfied out of its existing pool of trained workers. If that is the general outcome, then we have a partial explanation of the persistence of unemployment in a mildly cyclical economy II. Details In this section it is shown that the model described does have the general property just mentioned. Under unrestrictive assumptions, the wage policy of the insiders will exclude the employment of unskilled outsiders unless their current productivity exceeds the wage at which they are available Thus outsiders will be hired, even at the reservation wage, only in very It is the virtue(or the vice)of additivity that e1 and e21 are independent of Wu. If only period I were at stake, insiders would have no reason to worry about the hiring of outsiders because-in this formulation--they do not compete with eu. We can restrict attention to the second tern and consider the insider-union as choosing w1 to maximize the expression vu)=(m+e21)-le12(-u) What does V look like as a function of w? (I omit the subscript 12 occasionally when the emphasis is on the running variable. To begin with, it is obvious that(2)determines a critical value w", say, with the property that e21>0 if and only if w1252f' (m). Since I have all along assumed si to be such that s1 f(0)-W2<, it follows from(2) that w*<S2f(m) hese observations can be summarized in the following way. For very high alues of wj2, specifically those higher than S2f'(m), the firm will not fully employ even its initial labor pool in period 2, given the state S2 expected to rule then. That being so, e21=0. For values of w1 a bit below S2f' (m)the ScandJ of Economics 1985

workers. Since the current productivity of outsiders is assumed to be low, that is enough to exclude them from current employment. The interpretation we have in mind can be restated from another point of view. The industry is subject to fluctuating demand for its product. Since the firm assumes no long-run responsibility for its workers, it will hire outsiders at their reservation wage any time their current (marginal) productivity exceeds that wage. Suppose market conditions in period 1 are not so good (i.e., sl not so large) that outsiders can be profitably employed on that basis. The possibility exists that they might be hired anyway if period 2 fs expected to be prosperous enough (i.e., s2 large enough) so that the firm will need an enlarged pool of skilled workers then. This possibility will be frustrated if the insiders choose to convert the improving market prospects into a sufficiently high wage for period 2 that the firm's demand for labor can be satisfied out of its existing pool of trained workers. If that is the general outcome, then we have a partial explanation of the persistence of unemployment in a mildly cyclical economy. 111. Details In this section it is shown that the model described does have the general property just mentioned. Under unrestrictive assumptions, the wage policy of the insiders will exclude the employment of unskilled outsiders unless their current productivity exceeds the wage at which they are available. Thus outsiders will be hired, even at the reservation wage, only in very good states. It is the virtue (or the vice) of additivity that e12 and ezl are independent of wll. If only period 1 were at stake, insiders would have no reason to worry about the hiring of outsiders because-in this formulation-they do not compete with ell. We can restrict attention to the second term of (5) and consider the insider-union as choosing w12 to maximize the expression What does V look like as a function of w? (I omit the subscript 12 occasionally when the emphasis is on the running variable.) To begin with, it is obvious that (2) determines a critical value w*, say, with the property that e2,>0 if and only if w12s2 f '(m). Since I have all along assumed sl to be such that sl@fl(0)-w2<0, it follows from (2) that w*<s2 ff(m). These observations can be summarized in the following way. For very high values of w12, specifically those higher than s2 f '(m), the firm will not fully employ even its initial labor pool in period 2, given the state s2 expected to rule then. That being so, e21=0. For values of w12 a bit below s2 ff(m) the Scand. J. of Economics 1985

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