Proposition 3 .sx Suppose lambda varies across activities but is constant for any given activity .sx Then , if formula , the equilibrium wage w * is a decreasing function of lambda .sx That is , workers with the highest damage potential ( lowest lambda ) receive the highest wage .sx Note :sx This proposition depends formally on lambda being a constant for any given activity and may not hold if lambda varies with e and L. Proposition 4 .sx If lambda is a constant for a given activity , then the production function fL,e can be expressed as a generalized Solow function of the following type ; formula for some g. Proof .sx See Appendix .sx The intuitive meaning of our result is as follows .sx Each activity has a unique lambda .sx If activities are heterogeneous , they may have different values of lambda , in which case workers with the highest damage potential will always receive the highest wages .sx Activities that are less susceptible to damage will always offer lower wages .sx By restricting ourselves to this special class of production functions , we arrive at a positive monotonic relationship between the wage rate and the damage potential .sx In other production functions , this relationship may not be positive or even monotonic .sx Let us examine the non-monotonic case briefly .sx Consider two activities , A and B , of which the former is the more susceptible to damage from a low supply of effort .sx A has two strategy options .sx The first is to pay a higher wage than B's to preclude workers from reducing effort and causing damage .sx The second is to offer a wage rate lower than B's and put up with some damage due to worker demotivation .sx Under certain conditions on the production function , each of these strategies could be equally profitable .sx By restricting ourselves to a specific class of production functions , we ensure that lower wages will not fully offset the damage from worker demotivation and preclude such a multiplicity of options .sx Proposition 5 ( The Solow Region) .sx Let w>0 and e(w ) be three times differentiable , such that , e(w ) , e'(w)>0 and e''(w)<0 .sx Then :sx ( i ) there is at most one w o such that formula ; and ( ii ) formula for formula , for some mu >0 .sx Proof .sx We have .sx formula .sx ( i ) Suppose that w o is such that formula .sx Then , .sx formula .sx It follows that w o is unique from Theorem A1 in the Appendix .sx ( ii ) This follows directly from the continuity of E' w .sx Square .sx Proposition 5 implies that , if it exists , the Solow wage is unique .sx In the region of this wage , the elasticity of effort is a decreasing function of the wage .sx Hence within this region it is always true that higher wages are paid to workers with higher damage potential ( provided lambda is constant for each activity) .sx III .sx PROPERTIES OF THE WAGE DISTRIBUTION .sx We have just derived the wage rate as an increasing function of the damage potential of workers .sx Let us now try to interpret the nature of the wage differentials generated by the model .sx A simplistic way of interpreting the wage differentials in the model is in terms of heterogeneous labour .sx Suppose that skills are variable across workers .sx Suppose also that there are differences in the skill requirements of different activities .sx Assume that firms that have more complex equipment require the more skilled workers .sx Then , if skills and jobs do not match , firms with relatively costly equipment will be susceptible to a greater degree of damage .sx In this case , firms that are more susceptible to damage will pay a higher wage as a strategy to recruit the more skilled workers .sx However , the existence of wage differentials for heterogeneous labour is not very interesting from either a theoretical or a sic !sx empirical point of view .sx The main theoretical puzzle , as mentioned earlier , is to explain why wage differentials exist even when workers have identical skills .sx In fact , this question becomes especially important in the context of a number of empirical studies which indicate the existence of wage differentials for apparently homogeneous labour .sx Let us briefly summarize the essential aspects of this literature .sx Dickens and Katz ( 1987 ) , for instance , have examined the nature of wage differences across industries for both union and non-union workers using American data .sx Their findings indicate that there are large differences in wages for seemingly similar workers .sx Substantial wage differences persist even when union status and standard individual characteristics are controlled .sx Similarly , Krueger and Summers's studies ( 1987 , 1988 ) indicate that workers' industry affiliations exert a substantial impact on their wages , even after controlling for human capital variables and a variety of job characteristics .sx There is , however , some controversy in the literature on the importance of true 'industry effects' as an explanation of the observed wage dispersion .sx Murphy and Topel ( 1987 ) , for instance , argue that actual wage differentials are more likely to arise from the unobserved heterogeneity in workers' abilities .sx However , Gibbons and Katz ( 1989 ) dispute the excessive emphasis placed by Murphy and Topel on unmeasured ability to explain actual wage differentials :sx they argue that the empirical evidence can be consistent with both the 'industry effect' and the 'unmeasured ability' explanations of wage dispersion .sx They argue that , in practice , the wage changes of workers shifting to other industries for exogenous reasons ( such as plant closures ) seem to be consistent with the 'industry effect' explanation of wage dispersion .sx In contrast , the wage changes of workers shifting because of endogenous reasons ( such as voluntary quits ) seem to fit in better with the 'unmeasured ability' explanation of wage dispersion .sx In other words , the actually observed wage differentials are obviously generated by a variety of different factors .sx Let us now see how our efficiency wage model helps to provide an understanding of the existence of wage differentials for labour of homogeneous potentiality .sx We had earlier introduced the concept of 'damage potential' .sx We shall now make use of this concept for providing the rationale for various aspects of wage dispersion .sx There are two possible ways of interpreting damage potential .sx We shall call them the 'shirking' and 'performance' interpretations .sx Let us clarify this further by making a conceptual distinction between the two .sx We define shirking to be the conscious act of reducing effort .sx Efficiency wage models normally assume that workers shirk when not perfectly monitored .sx Since perfect monitoring is difficult , penalties such as unemployment are required to prevent workers from shirking .sx Performance , in contrast , is not completely dependent upon monitoring , even though it is definitely influenced by it .sx We define performance to encompass a wide array of attributes which determine the effectiveness of work .sx For instance , performance can depend upon how intensely workers concentrate on their jobs ; mistakes are bound to happen if workers concentrate insufficiently .sx Performance can also depend upon factors such as the willingness of workers to take initiatives and function flexibly .sx We can intuitively visualize the difference between shirking and performance as follows .sx If workers are carefully watched over , they cannot idle on the job ; that is , shirking can be prevented by perfect monitoring .sx Nevertheless , this by itself cannot guarantee good performance .sx Workers can either inadvertently mishandle equipment or be inflexible and not take the proper initiatives .sx That is , there is a discretionary element to the effectiveness of work which is difficult to control by pure monitoring .sx The standard rationalization of wage dispersion relies on the strike threat or shirking model .sx If firms are heterogeneous and monitoring imperfect , the uneven impact of the damage potential from shirking can generate a wage distribution for homogeneous labour .sx Firms more susceptible to damage will offer a higher wage rate .sx We have just proved the formal conditions necessary for this result to hold .sx If monitoring also happens to be relatively more difficult in firms that have a greater susceptibility to damage , then workers in such firms will receive wages that are disproportionately higher in relation to their effort levels .sx That is , in the shirking model of wage dispersion , some workers can get higher wages by the fortuitous fact of being in firms particularly susceptible to damage .sx This case corresponds closely to the 'industry effect' explanation of wage dispersion .sx Therefore under these circumstances all workers will obviously prefer to be in the high-paying firms .sx Suppose that workers acquired perfect information about the wage distribution .sx Then there will be queueing for the high-paying jobs .sx However , workers do not have any credible way of offering to work effectively at these jobs for a lower wage .sx Hence under these circumstances the high-paying jobs will be rationed to the workers .sx We shall now provide an interpretation of wage dispersion which relies on the concept of performance .sx We shall abstract from shirking as a potential cause of damage .sx We ignore the shirking problem by assuming that workers are costlessly and perfectly monitored .sx Let workers be of homogeneous potentiality :sx that is , all workers can be assumed to have the same intrinsic capabilities .sx However , the effectiveness of their work will vary depending upon the effort levels that they are willing to commit .sx Let contracts with regard to effort be fully specified and costlessly and perfectly enforced ; in other words , assume that there is perfect information regarding all aspects of the production process .sx Therefore , the only source of potential damage for firms comes from bad performance - as defined earlier .sx Firms with costly and complex equipment require a high level of performance .sx They cannot tolerate mistakes or the lack of proper initiatives from the workers .sx Hence in this context they will specify contracts that require a high level of effort .sx Workers will be paid a proportionately higher wage to compensate them for the higher levels of effort .sx Firms less susceptible to damage do not require the same high standards of performance .sx They can tolerate less effective workers .sx Hence they specify contracts paying a lower wage .sx That is , the heterogeneity in the required performance standards of different firms can also provide a theoretical rationale for the existence of a wage distribution for labour of homogeneous potentiality .sx However , the implications of the performance interpretation for wage differentials is different from that of the shirking interpretation .sx The wage dispersion generated by the performance interpretation is compatible with a market-clearing equilibrium under perfect information , in which neither the employers nor the workers have any incentive to deviate from the equilibrium .sx As long as contracts are implemented , employers will be satisfied with the given wage distribution .sx Let us consider the workers' point of view .sx We shall assume that there is no intrinsic job satisfaction attached to any activity .sx Work involves disutility .sx Since by assumption workers possess perfect information and there is market-clearing , they will be indifferent between the different occupations .sx To shift to a higher paid job involves costs in the form of more effort-intense concentration , willingness to accept inconvenience or exercise initiative .sx The allocation of jobs can then be determined on a random basis .sx The normative implications of the performance model are also quite different from those of the shirking model .sx In the shirking model wage differentials can be considered to be normatively 'unjust' , because some workers get higher wages solely as a consequence of their industry affiliation .sx In contrast , wage differentials are normatively 'just' in the performance model because some workers are putting in more effort than others .sx In this sense , there is obviously a correspondence between the performance interpretation of wage differentials and the 'unmeasured ability' explanation of wage dispersion .sx The latter explanation considers wage differentials to be justified on account of the intrinsic differences in the unmeasured abilities of workers .sx The performance interpretation , however , focuses on differences in the levels of effort rather than ability .sx Obviously , in any concrete situation all these various factors may have some influence in generating wage differentials .sx The performance-based interpretation of wage dispersion , incidentally , may help to explain some empirical aspects of inter-industry wage dispersion which are difficult to reconcile with the shirking model .sx In a recent paper , Akerlof and Yellen ( 1988 ) have argued that certain aspects of inter-industry wage dispersion cannot be rationalized by optimizing versions of the efficiency wage hypothesis .sx They concede that the shirking model may explain the wage dispersion , for instance , of machine operators across industries on the basis of differences in monitoring costs .sx However , they argue that it is difficult to explain the wage differences , for instance , of secretaries across industries with the same model .sx