Fukaura Atsuyuki

Fukaura, Atsuyuki

Nagasaki university's Academic Output SITE

The Seniority Paying System and a Human Capital Obsolescence in the Labor Management Firm

Nagasaki University's Academic Output SITE: NAOSITE

KEIEI TO KEIZAI, Vol.70 No.l, June 1990The Seniority Paying System and a Human Capital Obsolescence in the Labor Management FirmAtsuyukiFUKAURAI. INTRODUCTIONRecent works on the labor management firm (LMF)have been con-ducted to analyze a Japanese-style management. By considering the adjust-ment cost for the investment, Iwai (1989) has rationalized the seniority pay-'ing system in the LMF and verified it is the most efficient scheme for theLMF. But his assumption that the old workers have no contribution to out-put is counter factual. Turning our attention to a real world, we easilyrecognize the old workers matter a great deal, i. e., the old cannot workbeside the production lines but their experiences can be devoted to othersupplemental sectors.The main novelty is that we take into account the old generation's ef-fort to catch up with the young generation. This effort effects the total pro-duction in some manners, and is regarded as the alternative qualitative ad-justment channel for the labor input. We can discuss that this "qualitative"aspect is closely related to the seniority paying system. Much of emphasis inwhat follows focuses on how to characterize this "qualitative" features.In Section II , we introduce the basic framework that concentrateson the way through which the old workers contribute to the whole produc-tion. The main part, Section III , deals with the seniority paying system and-some related topics are remarked in Section N. Concluding remarks220 KEIEl TO KElZAl follow. IT. MODEL AND SOLUTIONS Notations we will use are given as follows, Lj: labor input, i = I , 2 where I means young generation and 2 means old one, nj: labor growth rate, L 1 : L z = I + n: 1 , for simplicity, we set Lz = I , K: capital input, where K 1 = K z = K, ki:capital-Iabor ratio. They can be written as kl =KlILl' kz =KzI I =Kl (I +n)IL l =kl (I +n) Yj=F(Kj, Lj), where Y 1 =L l/(k 1 ), Y z =L zl(k z) =j(k z) ; output, wj:wage rate, r: constant rental price for capital, 1Jf (n) : adjustment cost for labor input, where 1Jf no 1Jf nn > 0 . The budget constraint can be expressed as follows, (I +n)wl +wz + 2 Kr+1Jf(n) = (1 +n)/(kd +O(n)j(k z) [1 ] o (n) is the induced incentive of the old workers when the youngers are en-tried. This is observable for the LMF. Uzawa(I965) 's method to divide the human capital two sectors perfectly is not realistic because, in the ordinary Japanese firms, emplyees are required to be "all-round players" so the vague division would be dominated. In these circumstances, an interaction between sectors is signifi-cant factor for an efficient management. Moreover, concentrating the fact that the work division corresponds roughly to the seniority, it is reason-The Seniority Paying System 221 able to focus our attention on the old-young workers' interactions, inter-generational interaction. An basic idea is that new input embodies "new knowledge", which has been discussed by some authers(Romer(1986), Lucas (1988) ) . Subject to this constraint, the LMF determines k I, WI, W 2, n, so as to maximize the utility function defined over the received wage rate, U=U(WI, W2) [ 2 J Standard mathematical results characterize an interior solution by means of necessary conditions, that is, r=I'(kd au/aWl = I +n aU/aW 2 = I(k I) - I ~ n I' (k I ) + ~~ I(k 2 ) m. IMPLICATIONS III - 1 The seniority paying system in the LMF [3J [4J [ 5 J [ 3 J and [ 4 J are well known conditions, but note that [ 4 J charc-terizes the growth-oriented feature of the LMF (see I wai (1989) ). [5 J shows an optimal growth rate of labor, which is determined where a marginal cost (LHS) equals to a marginal benefit (RHS). [5 J yields K, a1Jf ao WI =/(k l ) ---I (k l ) --+- l(k 2 ) I +n an an [6J Hence, 222 KEIEI TO KEIZAI [ 7 ] Then, [ 8 ] where we use aL1/an= 1 and a2L 1/an 2 = o. What appears in [ 8 ] states that the cost change when n is increas-ed is devided to 1) a lowering of marginal productivity, 2) an increase of adjustment cost and 3) an induced incentive. It is worth to note that they all are the complementary adjustment channels for labor input. Neglecting Wand (), we go back to the classical world. Considering only W, Iwai(1989) 's conclusions are derived, that is, [8 ] is negative then the LMF constructs the wage profile based on ~he seniority rule. m - 2 effort function (a) The nature of () (n) If ()" has the negative sign then Iwai's conclusion is strengthened, however, the contrary case requires a little complicate consideration. When ()" is positive but sufficiently small, i.e., ()" < dE > 0), then the LMF adopts the seniority paying system (E is a value of ()" when [ 5 ] = 0 . Here we focus only on the behavior of () in order to clarify its prominency). We cannot determine the sign of ()" without the solid micro-founda-tions for () function. But to conjecture the behavior of our model, we will in-fer the shape as follows. First, we assume ()(O) = 1. [9 ] When the new labor input is equal to the old, the olders keep their effort con-stant. This may occur when all worker is identical or substitutional. Second, The Seniority Paying System 223 a(J(n) I > 0 an n= 0 [10J The first young worker will induce an extra effort of the olders. It is not unrealistic to assume that the marginal effort diminishes as n is increased, partly because the olders does not persevere forever and partly because the new knowledge becomes the common one as the newers become the majori-ty. See Fig- I. If (J" < E, the seniority paying system is established. The plausible (J (n) is also depicted. (J no-seniority zone (J" > 0 E=(J" seniority zone o~--~------~--------~------~------n++ n** n+ n* Fig- 1 (b) Optimal labor growth rate n The role of () (n) is clarified by considering the labor growth rate. Because any points on () (n) satisfies the first order condition for n, so we can 224 KEIEI TO KEIZAI not determine an unique optimal rate. This is because the effort function provides the qualitative adjustment channel for labor input. At 0 < n < n * *, because the higher wage corresponds to the higher effort, the seniority paying system implies a paying to one's effort or con-tribution, not only on the seniority itself. Hence, the seniority paying system do consistent with the productivity and works as an incentive scheme. However, for n** <n where the old workers contract their effort, and for n* < n, the olders are degraded to the "in-active input", i.e., the human capital obsolescence arises. In order to maximize the older's effort level, in other words, to derive the highest incentive from the given W2, n must be set at n**, where a{}(n) I =0 an n=n** . [l1J Lazear(1981) suggests that a seniority paying system discourages shirking. In his discussion the seniority system is itself an incentive scheme by "price (wage) ". In our model, to be consistent with an anti-shirking scheme, the LMF set the labor growth rate under n * *. In this sense, Our LMF can be equipped with the anti-shirking scheme by "quality", different-ly from Lazear (I 981) . W. SOME REMARKS First, it is worth to note that the seniority paying system is not re-jected even in stationary state when two generations' input are perfectly identical. In this case, the LMF faces the following problem and the first order conditions. Max u(w 1, W2) subject to L(w 1 +W2) + 2 rK= 2j(K, L) So whether w 1 < w 2 or WI> W 2 depends only on the preference structure of The Seniority Paying System 225 the LMF, that is, when the indifference curve of u (w 1, W 2) tangents with the budget constraint at the upper area than the 45 degree line, the LMF would accept the seniority system. The seniority system does not depend an input decision. Second, when n* < n, the LMF cannot even produce the output if the LMF would be at stationry state, n = 0 so the rational LMF is never in this area. In this sense, the LMF sets an entry barrier against the outside workers at n * . Suppose now the LMF is at n** and the labor pool is extended to n+ by, for example, the immigration. Set aside the problem whether the foreigner has the new knowledge, O(n++) =O(n+) then the LMF will con-tract the labor growth rate from n * to n + +. As the results, the entry barrier becomes more strictly. Third, we can infer why most Japanese firm adopts the seniority pay-ing system. The seniority system is desirable when [12] If the production function is linear then YLL = O. If so, it is more easy to satisfy [1 2] . Put differently, when the input ratio is fixed, the seniori-ty system is easily established. Whether the Japanese firms take on these characters or not must be questionable, however, here may be an important key concept to consider the seniority paying system in Japan. Suppose an ac-cepting the foreign workers enlarges 1Jf" (it is a reasonable assumption) then WI, foreigner's wage, must be decreased because the seniority system becomes more intensive, i.e.,[ 8] become smaller. Moreover, 0" may also be increased because of the demolalization. If so, n + + and n * * are declined then the entry barrier will be more enhanced. If (J" or j(k 1) increase with llf" proportionally then no change will be arised. This means the olders work more than before to accept the 226 KEIEI TO KEIZAI foreigners and not to contradict with the existing seniority system. This, however, is not a probable story. From above discussions, we do suspect that the openness of labor market never bring the desirable results. V. CONCLUSION We have examined the several features of the LMF. The effort induc-ed by the new employees and their fresh knowledge plays a key role. Our conclusions are summarized as follows. First, the adjustment cost cannot determine the optimal labor growth rate definitely. Second, the effort func-tion serves the qualitative adjustment mechanism, Third, under the special conditions, the LMF can determine the optimal labor input level. These results are able to give some implications for the Japanese economy. There are many directions in which we can extend our analysis. First, we have not fully scrutinized the shape and nature of the effort func-tion, so our analysis depends on some intuition, then, we must find the micro-foundation of 0 (n) (the forthcoming paper intends on doing it). Se-cond, we have formalized the effort effect by O'j(k z ) because production technology is OJ(k z ). If we treat it asj(k z , 0) like Romer (1989) then the ef-fort effect would bej'O'. This must be more general form. Third, it is most interesting trial to treat O(n)as a stochastic form. Because O(n)can be seen a technological shock so we can find a way for the business cycle theory. These problems will be no doubt an important area of the future research. The Seniority Paying System 227 REFERENCIES ~*£A, 1989, o~t~!ft~1'fElL&3fU:: L,,(o)B*J1:*, :EEH/E)[I*,~ IB*~ i1t1Vf'9'EJ Lazear, E. P., 1981, Agency, Earnings Profiles, Productivity, and Hours Restrictions, American Economic Review 21, pp.606-620. Lucus, R. E., 1988, On the Mechanics of Economic Development, Journal of Monetary Economics 22, pp.3-42. Romer, P. M., 1986, Increasing Return and Long-Run Growth, Journal of Political Economy, Vo1.94, no.5, pp.l002-1037. Uzawa, H., 1965, Optimal Technical Change in an Aggregative Model of Economic Growth, International Economic Review, Vo1.6, no.l, January, pp.18-31. 

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The Seniority Paying System and a Human Capital Obsolescence in the Labor Management Firm

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