5

THE IMPACT OF TECHNOLOGICAL CHANGE ON INCENTIVE PROVISION

by Maurizio Lisciandra∗∗ 1. Introduction

This paper attempts to theoretically substantiate the observation that high rates of technological change together with strong trade unions make output-related pay particularly costly for the employer who then cannot sustain it in the long term. The investigation draws on both the well-established principal-agent model and the anecdotic evidence of inside con-tracting in the developing years of the American iron and steel industry. In particular, by comparing piece-rate pay and fixed-pay in a setting closer to the historical case here discussed, we are able to appreciate which payment system is preferable. Finally, this stylised fact stimulates further analyses of the interaction between technological change, bargaining powers, and pay-ment systems which can be conducive to a better understanding of the agency problem and the use of incentive pay.

The interaction between incentive pay, technological change, and un-ions’ contractual strength is empirically relevant since firms often face the dilemma of how to remunerate workers and how much to invest in technol-ogy in order to raise productivity. Especially the growing manufacturing

∗ This paper was part of my Ph.D. thesis at the University of Cambridge (Trinity Col-

lege). I am particularly grateful to Prof. William Brown (University of Cambridge), Dr. Jo-chen Runde (University of Cambridge), Prof. David Marsden (London School of Econom-ics), and Prof. David Perez Castrillo (Universitat Autònoma Barcelona) for the helpful comments and valuable suggestions. I have also gained much from discussions with Dr. Ro-bert Evans (University of Cambridge). Usual disclaimer applies. Correspondence: Diparti-mento di Scienze Economiche, Università di Bologna (Italy); email: maurizio.lisciandra@ unibo.it.

Studi economici n. 95, 2008/2

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industries of the nineteenth century found themselves in the middle of a transformation, amid the old industrial practices along with the inherited methods of pay and the upcoming revolution of industrial organisation. The case of the so-called contract system emerging in the States during that ep-och is precisely one of those circumstances in which payment by results suffered severely from conflicting labour relationships that eventually ren-dered ineffective the provision of incentives. In particular, the high rates of technological change experienced by this industry did nothing but exacer-bate the “labour problem”, thereby playing a very important role in the de-cline of the incentive provision and revolutionising the industrial relations in that period. Hence, this investigation is significant to economic histori-ans, who attempt to understand the economic reasons behind the economic facts. Additionally, understanding the reasons behind the failure of a pay-ment system in a specific context is important when firms nowadays, within similar circumstances, aim at implementing best practices.

This historical event stimulates economic theory to challenge its frame-works by way of identifying limitations of theory itself and providing new predictions. The case of the contract system represents an appealing test to the explanatory power of agency theory and its principal-agent model. This could unveil in greater depth the mechanisms that characterise incentive pay and the role played by institutions such as organised labour. Hence, this work seeks to challenge the agency theory such that theory can be sub-jected to some degree of qualitative testing and then extended in order to respond to further contractual issues.

Although rather scanty, the literature revolving around this issue can be divided into three main components. First, economic history accounts such as Buttrick (1952), Novack and Perlman (1962), Doeringer (1968), Stone (1974), Chandler (1977), Elbaum and Wilkinson (1979), Englander (1987), Fleischman and Tyson (1996), and Lisciandra (2008) describe inside con-tracting and, in a few circumstances, specifically the contract system, sug-gesting the conflicting nature of industrial relations due to this payment system in an environment undergoing substantial technological change.

Second, although marginally with respect to their analyses, Freeman (1982), Jacoby (1984), Brown (1990), and Drago and Heywood (1995) provide empirical accounts which describe the weakness of piece-rate pay vis-à-vis time-rate pay when trade-unions have bargaining power or estab-lishments are threatened of unionisation. They all agree that firms tend to contrast unions’ influence in setting piece rates and assignments in the shop-floor, thereby management is more likely to use time-rate systems in an attempt to head off unions. However, no reference is made on techno-logical change and its impact on rate revision, further, data refer to internal

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workers rather than unionised subcontractors as in the case of the contract system.

The third component is referred to theory. There are two main models of the impact of trade unions on wages: the “efficient bargain” model and the “right to manage” model1. Both make use of a union’s utility function including members’ wages as well as employment. Unlike the model pre-sented in this paper, they fully endogenise the role of trade-unions in wage setting, they link wage levels to employment outcomes leaving technology and any risk-sharing considerations at the margins. In particular, the link between technology and trade union is essentially focused on the impact that technological change has on employment and, therefore, on which ex-tent unions resist technological change to avoid labour substitution, this re-gardless of the payment scheme adopted. Another strand of relevant theory refers to agency theory and the principal-agent problem. This is particularly suitable in our case because it is equally able to highlight the conflicting objectives between workers and employers but, in addition, introduces risk-sharing, uncertainty, and incentive intensity rather than wage levels. In fact, along these lines, comparisons between piece-rates and time-rates are abundant (e.g., Lazear 1995, Baker, Jensen, and Murphy 1998, and Lis-ciandra 2007) but to our knowledge no theoretical investigation has still carried out an analysis incorporating technological change and the role of trade-unions within the principal-agent model.

In specific, agency theory envisages only two types of conflicting inter-ests between principals and agents. On the one hand, the cost of effort, which is not internalised by the principal but negatively affects workers’ utility, and on the other hand, the wage cost which, evidently, increases workers’ utility but diminishes that of the firms. However, the case here presented reveals that the agency contract hides other potential conflicts that should be accounted for when designing a payment mechanism. Firstly, re-negotiation of the rates can be very costly. When there is a high level of technological change, rates quickly become obsolete. Thus, if workers have sufficient bargaining power, setting new rates generates con-flicts. Secondly, piece rates are “sticky”. Providing explicit incentives so-metimes means giving away part of the technological gains to workers be-cause rates cannot be adjusted immediately after the change in the technol-ogy or techniques has taken place, and thus under-investment is likely to occur. Thirdly, competition in the product market considerably penalises those firms that pay by the piece. Indeed, firms paying workers fixed wages

1 For an extensive review of trade union modelling see Kaufman (2002). A third model,

the union monopoly model, can be regarded as a special case of the right to manage model.

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can immediately benefit from the gains stemming from improved machin-ery, without incurring additional re-negotiation costs. This difference is ex-acerbated when trade unions have strong bargaining power within piece rate firms and drive piece rates upwards.

The principal-agent model of this paper will attempt to capture this evi-dence. In particular, this investigation can account for workers’ bargaining power by using a repeated moral hazard model and allowing the second-period reservation utility to change. The size of the change would depend on workers’ power and the extent of technological change. Holding the first period rates is also another way of affecting the standard outcome of the agency theory. Then a few extensions are introduced, which account for both a short-sighted manager, who cannot predict how technology will change the future production function, and a long-sighted manager, who conversely can plan future contracts with a correct estimate of technologi-cal change. Finally, three different bargaining outcomes are provided: 1) the no trade-union case, 2) the trade-union bargaining over the rates, 3) the sticky rates case, in which rates remain unchanged.

Besides capturing the unavoidable end of the contract system in the US iron and steel industry during the second half of the nineteenth-century this model will lead to further observations. Trade unions could reduce profits ei-ther by asking for a share of the gains stemming from technology or by hold-ing rates at sub-optimal levels, thus the employer would be induced to mini-mise unions power when innovations and productivity-enhancing technology is introduced. Yet, if the employer can predict in advance the amount of tech-nological change that will be introduced in the production process, he or she should also make all possible efforts to negotiate with the trade unions the corresponding new rates and try to anticipate their claims inside the contract.

This paper is arranged as follows. Next section will briefly sketch the problems revolving the subcontracting system existing in the second half of the nineteenth century in the United States. Section 3 will illustrate a simple principal-agent model, which will be intertwined with technological change and workers’ bargaining power. The model will allow for a comparison be-tween fixed pay and piece-rate pay. Section 4 will focus on the extensions of the basic model. This will help to explain why incentive pay may not be the solution to the “labour problem” but that it can turn into a sub-optimal choice when high technological change is coupled with strong trade-unionism. Computer simulation techniques are going to be used in order to understand diagrammatically the interwoven effects of the main variables, which are not readily intelligible from the common algebraic tools used for static analysis. Finally, concluding remarks will address further issues re-lated to the theoretical investigation.

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2. The Rise and Fall of the Contract System

Payment by results, as established for skilled workers in the booming period of the iron and steel industry in the United States, was so costly as to be unsustainable in the long run. The American iron and steel industry in the second half of the nineteenth-century was marked by the conflict be-tween the old industrial crafts, with its legacy of rules, traditions, and pay systems on the one hand and, on the other hand, the new concepts of indus-trial capitalism, with its hierarchies, a rational work organisation, tight market competition, and, not least, high rates of technological change2.

The system of contracting out production to highly skilled workers, which was in all likelihood inherited from the putting-out systems of the early English industrial revolution, was doomed to fail under the pressure of the many factors characterising the new stage of industrial capitalism that made this type of incentive very costly. However, this payment system was the building block of the labour relationships between companies and workers in large parts of the iron and steel industry. It gave sizeable profit and operational margins to skilled workers who contracted their work di-rectly with the companies by being paid for the amount of metal produced and by performing their tasks with the help of small gangs.

Initially, firms responded positively to this system because it was con-sidered a partnership between skilled hands and capital, and also it could displace some risk to the workers. Firms soon realised that it was simply unprofitable. Among the most important strains on this incentive system was the high level of technological change that marked the period and that considerably increased output for a given effort level. The main issue at stake was the division of surplus from this higher output. Furthermore, the piece rate that rewarded contractors was geared to the price of the final product (e.g., the bar iron), with a minimum base below which the piece rate could not fall. This was called the sliding scale mechanism. The large fluctuations in demand and the stagnant low prices put further strain upon the system. With strong trade unions backing the interests of contractors, re-negotiations were extremely costly and were marked by strikes and lockouts.

Two important setbacks to the sliding scale mechanism arose some time after its introduction. First, it implied that any surplus gained from a higher turnout was captured by the ironworkers if tonnage rates were left un-changed. Second, the risk-sharing idea behind the automatic adjustment

2 For comprehensive historical accounts see BITA (1902), Bridge (1903), Popplewell

(1906), Fitch (1911), Clark (1929, Vols. II and III), Temin (1964), and Allen (1979).

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was only apparent because much depended on the minimum base. For the workers a high minimum base granted a high coverage from the risk of the downward fluctuations of the price of bar iron and other reference prices for the sliding scale, thus transferring the risk almost entirely to the manu-facturers. Therefore, on the one hand, a rapid technological change set off a dispute over the massive gains stemming from the increased output, and on the other hand, the low prices of the final products to which the sliding scale was indexed made the sliding scale essentially inoperative.

As a whole, technological change severely undermined the contract sys-tem and the underlying piece rate scheme. On the one hand, the resulting increase in output per unit of labour needed prompt changes in piece rates if companies wanted to get the profits from their investments in new tech-nologies and face competition from internal non-unionised firms. On the other hand, the skill content was diminishing, thereby reducing the bargain-ing power of skilled workers and their differential earnings with respect to unskilled positions.

In summary, what was originally conceived as the solution for the la-bour problem – the contract system – turned out to be an inefficient instru-ment both as a compensation method and as a control device for industrial relations. The end of the contract system dissolved trade unionism, and as a result the power of skilled workers over bargaining and workplace issues came to an end. Furthermore, the same job of skilled workers was gradually transformed into a less critical production factor by altering the ratio be-tween capital and labour. Hence, the high rates of technological change challenged the contract system at its roots, and the sliding scale system with its binding minimum base exacerbated the labour problem. 3. The Model

As technological change occurs the production function changes and consequently the employer needs to update the rates. If the employer does not update the rates, piece-rate workers would adjust their effort according to the new technology. Since principals and agents have conflicting objec-tives we expect that workers would profit from the new technology at the expense of the employer. For example, workers may be induced to exert low effort levels due to income effects. In other circumstances, workers may exert the same effort level as before the introduction of the technologi-

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cal innovation and consequently earn more3. Therefore, according to the specification of workers’ utility functions, workers gain from technological innovations without paying the price for their introduction. Firms, in turn, want to reduce the benefits to workers and gain the whole surplus stem-ming from their investment. In other words, firms would like to grant workers the same reservation utility as before the introduction of the new technology.

Hence, technological innovation affecting workers’ performance indica-tors should give rise to the re-negotiation of rates. Piece rate workers op-pose a simple adjustment of the rates which would keep workers to their old participation constraint. Piece rate workers want to get the benefits of the technological advancement as well, particularly by forcing the firms to hold the old rates. In contrast, firms would like to adjust the rates so that they get the whole benefit from the technological innovation4. This is ex-actly what happened in the iron and steel industry in the second-half of the nineteenth-century in the United States when the contract system was in force. The high and enduring rate of technological innovation made piece rates quickly obsolete. Additionally, the steady low prices of the final out-put, to which the piece rates were tied, made inoperative the sliding scale system; thus, the minimum base became binding for long periods, thereby exacerbating the conflict between principals and agents. In effect, the minimum base became the actual rate to be negotiated and practically iden-tified the level of reservation utility that workers claimed and defended through their bargaining power when employers wanted to update the rates. In sum, well-organised workers drove rates to sub-optimal levels because they made rates re-negotiation extremely costly in terms of strikes, lock-outs, and output restrictions. Consequently, actual and ‘incidental’ labour costs went up draining resources from the introduction of new technology, and also making the competition with non-unionised firms and fixed pay firms difficult.

However some questions arise. Do fixed pay schemes need to be up-dated as well once technological change occurs? Do they suffer from the same re-negotiation costs as piece rate payment schemes do? The answer to the first question is “yes”. In principle, rates must be changed with fixed

3 Both effects cannot arise from a CARA (constant-absolute risk aversion) utility func-

tion because this does not allow for income effects. 4 Once again, the type of adjustment (whether it is a reduction or an increase) of the in-

tensity of incentives depends on the workers’ utility function. In our case, we are going to use the CARA utility function because it is the only one that allows closed-form solutions, and its tractability is simple. In any case, this specific type of utility function does not affect the final results.

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pay as well in order to adjust effort to the new optimal levels. Thus, effort and salaries must be adapted to the new production function. However, the answer to the second question is “no”. Indeed, suppose there is no re-negotiation. In the fixed pay case, effort levels would remain the same be-cause they are contractually stated, but output rises due to technological change. Conversely, in the piece rate pay case, workers can reduce (or oth-erwise adjust) their effort levels trying to gain the extra surplus from tech-nological change. Thus, ceteris paribus, if contracts are not re-negotiated, under fixed pay the employer receives the full surplus from technological change even if he cannot get it optimally (i.e., by changing the effort and salaries rates) whereas fixed-pay workers would get nothing. Conversely, under piece rate pay not only would workers gain from the higher turnout, but they have the possibility to adjust their effort, which is not stated in the contract, and get part, if not all, of the surplus from the new technology. Therefore, the conflict arising from technological change is more marked in the piece rate case than in the fixed pay case. Consequently, in principle, fixed pay firms should encounter fewer problems when rates must be changed. However, the way re-negotiation is carried out depends heavily on the bargaining power of trade unions and on the share of the “pie” stemming from the new technology the latter can seize.

The subsequent two-period model will grant a certain bargaining power to a representative worker. Technological change occurs in the second pe-riod and it is multiplicative in the production function. Workers have the possibility to reject the contract in the second period (i.e., once the new technology has been introduced) if the contract does not grant them the same utility, as in the case in which rates are left unchanged. Therefore, the employer must take into account this possibility when making the proposal. This is a model that compares a piece rate pay with fixed pay when a fully rational employer can offer a single contract incorporating a set of rates, one for each period, without writing a new contract once technology has changed. This employer can be considered a “forward-looking” or “long-term” manager, and is one who knows exactly the amount of technological change that is going to be introduced in the second period5. Subsequently, the model is enriched by introducing a more general cost-of-effort function and by allowing for more than two periods.

5 This hypothesis is relaxed further below when a short-term manager is introduced.

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3.1. Piece Rate Pay Contract

The principal is risk-neutral and makes a take-it-or-leave-it offer of a share of output for each period. The agent is risk-averse, and if he does not accept the contract the principal earns zero profits. The production function is linear on effort e, which is unobservable to the employer and which is hit by a random component θ, the latter being unobservable by both parties. The level of output y is verifiable (i.e., observable by both parties and also by a potential third party), and is such that y = e + θ, where E(θ)=0 and var(θ)=σ2.

Agents cannot save or borrow, which means that they must consume their entire income by the end of the period. This will make the formalisa-tion much easier. The agent has an exponential utility function of the CARA type. The fixed part of the compensation is expressed by α, whereas β corresponds to the piece rate. The cost of effort c(e) is assumed to be equal to ½e2, such that it is a function of effort and it is increasing at an in-creasing rate6. The coefficient of absolute risk-aversion r is a positive con-stant. The resulting utility function for the agent is the following: U = –exp{–r[α+βy – c(e)]} (1)

Maximising an exponential utility function is equivalent to maximising its certainty-equivalent. We assume that technological change, which af-fects the second period production function, is linearly multiplicative on effort and is represented by k (≥1), such that y2 = ke2 + θ. Consequently, k is set equal to one in the first period. Thus, the certainty-equivalents for each period are the following:

CE1 = α1 + β1e1 – ½rσ2β1

2 – ½e12 (2a)

CE2 = α2 + β2ke2 – ½rσ2β2

2 – ½e22 (2b)

The principal, by maximising his profits, encounters two types of con-

straints. One is the participation constraint, which establishes that the contract must be at least as good as any possible alternative that is available to the worker. Specifically, the certainty-equivalent of the first period is set equal to zero. For the second period, the employer must take into account a different lower bound, which depends on the wage claims arising with the introduction

6 This type of function has a unitary second-order derivative. This is a simplifying as-

sumption that is relaxed further below.

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of new technology. Therefore, a certain bargaining power is granted to work-ers, who will be able to retain the surplus accruing from the improved tech-nology when first period’s rates are left unchanged. Hence, the second period certainty-equivalent must be at least equal to the certainty-equivalent calcu-lated at α1, β1, and at an effort level that represents the best effort exerted by the worker and realised according to the new level of technology.

The second type of constraint stems from the agent’s maximisation over his certainty-equivalents. This is the incentive-compatibility constraint, which imposes the best effort choice among those available to the agent for each period and which gives the following results: β1 = e1 and kβ2 = e2 (3)

Thus, the principal must choose those α1, α2, β1 and β2 that maximise ex-pected profits over two periods by taking into account overall four constraints. We replace the parameter rσ2 with ε in order to simplify the expression. An increase in the value of ε means either a higher workers’ risk-aversion or a higher variability of output. The principal’s problem is the following:

Principal’s Problem:

[ ]2211

211

ok

2111

ok11

22

22222

21

21111

22221111β,β,α,α

ekβ and eβ

)β,(αe21εβ

21)β,(αkeβαe

21εβ

21keβα

0e21εβ

21eβα

s.t.

)keβαkeeβα(eMax2121

==

−−+≥−−+

≥−−+

−−+−−

(4)

The expression ek°(α1,β1) is worker’s optimal effort level calculated at

the first-period rates by taking into account the technological change occur-ring in the second period (i.e., ek°=β1k). The right-hand side of the second-period participation constraint corresponds to the surplus accruing to the worker due to his bargaining power. The optimal contract is the following:

22

242*22

2*2

22*12

*1

)k(2)k(k1k

kk

)k(21

k1

ε+ε−−−

=αε+

=β

ε+−ε

=αε+

=β

(5)

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The contract proposal is a sort of map of rates which varies according to the technological change occurring between the two periods7. As predicted by the standard principal-agent theory, “risk” (i.e., ε) has a negative impact on the intensity of incentives, β. The optimal β1 decreases as k increases, whereas β2 gets asymptotically close to one. This pattern is not surprising given the specification adopted for the workers’ utility function, wherein there are no income effects. Indeed, the optimal effort levels chosen by the agent are such that e2 is higher than e1, because technological improve-ments make worthwhile an increase in labour productivity in order to ex-ploit the higher capital productivity. This increase is greater the greater is technological change.

ε+=

ε+=

2

3*2

2*1

kke

k1e

(6)

There is another reason why e2 is higher than e1. Since the first-period

piece rate affects the second-period participation constraint, the employer is induced to reduce β1 because a higher β1 would increase workers’ surplus for the second period. As a result, a low β1 reduces the leverage effect on e1. In the extreme case, if k is particularly high, it is convenient to shift the whole production process to the second period because the product value of the first period is trivial when it is compared with the second period’s. Higher β1’s can only cause higher costs in terms of higher reservation util-ity in the second period.

The overall expected profits with piece rates ΠPR are increasing in k and decreasing in ε as it can be easily inferred from the expression below.

( )ε++

=β−α−+β−α−=Π 2

4

22221111PR k21kkekeee (7)

7 It may happen that α is negative. This result is plausible when considering the cost of

capital rental. For instance, in case of no production, skilled ironworkers could lose money because they gathered their own production inputs at their expense. Yet, we must bear in mind that theoretically α is a transfer between principal and agent.

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3.2. Fixed Pay Contract

According to the principal-agent model, a fixed pay contract can be real-ised under two circumstances. One is fixed pay with monitoring, where the employer can perfectly observe effort. The employer bears the cost of moni-toring but gains from a perfect observability of effort because workers cannot adopt any moral hazard behaviour. Hence, the employer can enforce a spe-cific effort level through a forcing contract. This means that the principal can claim before the court the fulfilment of the contract, which prescribes the ef-fort level to be supplied in exchange for a fixed pay level. The second cir-cumstance arises when the principal gives in to moral hazard, which occurs when effort control is prohibitively expensive or impossible to perform. In this case, the principal guarantees minimum earnings that are compatible with the low effort level exerted by the agent who profits from the lack of control. In this modelling, the first type of contract is chosen because it is a better way of comparing it with the piece rate case. Moreover, there is no need to take into consideration the low effort level parameter; however we must bear in mind that monitoring is costly and should be deducted from the overall profits as a sort of lump sum allocated to effort control.

Following the same logic for piece rate pay, workers would hold the first period’s rates and ask for the utility accruing once technological change has occurred8. However, in this case, workers would gain nothing from holding the rates because their pay is fixed and is not linked with the production level. Thus, the right-hand side of the second period’s participa-tion constraint is zero. In other words, “sticky” rates have no impact on workers’ utility with fixed pay unless workers make an explicit request on the share of technological gain9.

In order to hold the worker to the job, the principal must provide a fixed pay that satisfies the participation constraint for each period. Analytically,

0e21 and 0e

21 2

22211 ≥−α≥−α (8)

8 In a fixed pay contract the contractual rates are defined by the fixed salary but also by

the effort level to be supplied. 9 Further below, a higher bargaining power is assigned to workers, such that they can

gain a positive surplus from technological change. It can be argued that, in order to make a fair comparison, fixed pay workers should get the same surplus as piece rate workers; how-ever, we must take into account the bargaining mechanisms that occur for each specific con-tractual arrangement, and it is for precisely this reason that fixed pay workers do not have the same contractual terms as piece rate workers.

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These constraints are both binding and are inserted into the objective function of the principal. The whole expression is maximised according to the effort levels of each period. Thus, the principal offers a fixed pay con-tract that adjusts the rates according to the new level of technology achieved in the second period. The result is the following,

2*2

*2

*1

*1

k21 ke

21 1e

=α=

=α= (9)

Expected profits are as follows:

( )1k21 2

FP +=Π (10)

3.3. Comparison between the Two Payment Schemes By comparing the two cases we can explore in what circumstances piece

rates are preferable to fixed pay and vice versa as technological change oc-curs. Therefore, we must analyse the size of the difference between ΠFP and ΠPR. Once again, we should bear in mind that the fixed pay case does not take into account the monitoring costs. Analytically we have

( )( )ε+

−ε++ε=Π−Π=Π 2

2

PRFP k211kD (11)

DΠ turns out to be increasing in k and ε, as shown in fig. 1, where DΠ is

depicted for two levels of risk. As k increases, fixed pay becomes ceteris paribus more profitable with respect to piece rate pay as one can see from the increasing curves. This is a very important result. By paying by fixed pay the employer collects the entire surplus of the increased productivity, and this gets larger during periods of high technological and technical en-hancement. As mentioned before, piece rate profits increase with techno-logical improvements but the resulting surplus must be shared with the worker. Additionally, the more important the risk component the less fa-vourable is piece rate pay. This last result is in line with the normal predic-tions of the principal-agent theory. Thus, the gap between the two payment schemes becomes larger as ε and/or k increase as highlighted from fig. 1.

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Fig. 1 – Comparison between the two payment systems

Fig. 2 – Comparison with monitoring costs

monitoring costs

fixed pay preferable

piece rate pay preferable

However, these results do not take into account the role of monitoring

costs which would reduce fixed pay profits. The moral hazard theory is based on the observation that monitoring of employee efforts is costly and imperfect but the magnitude of the cost depends on several factors. For in-

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stance, both the number of workers and the degree of hierarchy affect nega-tively monitoring costs (Oi, 1983); capital-intensive firms producing through assembly lines benefit from machine pacing, thereby making moni-toring less critical (Brown, Philips, 1986). Finally, although Piore and Sa-ble (1984) argue that new technologies tend to increase monitoring difficul-ties, the evidence on monitoring costs in the course of technological devel-opment is conflicting as suggested more extensively by Appelbaum and Albin (1988). Therefore, piece rate pay could outperform fixed pay up to a certain level of k in those jobs where monitoring costs are rather high. In fig. 2, the horizontal line depicts a possible amount for monitoring costs, which should be subtracted to the fixed-pay profits. For those values of k such that the DΠ lies above this line, fixed pay is still preferable. Yet, the difference-in-profits function tends asymptotically to a finite value as k→∞, which means that for high levels of monitoring costs, piece rate pay can be preferable however large k might be.

So far, c(e) was set equal to ½e2, so that the second-order derivative is equal to one. However, a more general form can be introduced by letting the second-order derivative assume a different value, for example the pa-rameter c. Consequently, the cost-of-effort function will be c(e)=½ce2. The difference in profits in a two-period model will be:

)kc(c21ck

c21

)kc(c21k

c21kD 2

2

2

42

PRFP +ε−ε

+=+ε+

−+

=Π−Π=Π (12)

Suppose c=1, the same result as in the basic model is obtained. Fig. 3

depicts the pattern of the difference-in-profits curves for two different val-ues of c.

For harder jobs (i.e., high c), the difference between the two payment schemes becomes trivial and, when monitoring costs are added to the fixed pay scheme, piece rate pay may prevail. From the above expression we re-alise that the difference-in-profits function is upward bounded, and its limit

is 2c2

1 ε+ . Consequently, as c increases and/or ε decreases relatively low

monitoring costs are enough to make piece rates preferable. It is worth-while noting that c can represent the worker’s ability to perform a specific task. The higher the ability the lower is c. Consequently, when analysing the output-related pay applied to skilled workers in the iron and steel indus-try, we should take into account that c was relatively lower for them than for other ironworkers. Thus, this is an important result: when technological change occurs, skilled workers should be paid fixed pay.

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Fig. 3 – Difference in Profits for different values of c

The model can be further enriched by the introduction of several techno-

logical advances taking place over several periods. In the same fashion as depicted by the two-period model each single technological shock gives rise to a sort of “re-negotiation” in which a worker would not give up the surplus he or she could earn with a higher productivity of capital. In order to allow comparison between different periods we must set the same tech-nological change between the first and the last period; in other words, the level of technology that is achieved in the last period is exactly the same for each case; what eventually changes is just the number of renegotiations. Further, within each case the same increment of technology between peri-ods is assumed. Finally, the overall duration of the contracts must be the same10. As a consequence, technological level (TL) at period i is as follows:

t1,...,ifor )1t(

)1k)(1i(1TLi =−

−−+= (13)

The parameter k denotes the level of technology in the last period

whereas t corresponds to the number of periods or, alternatively, the num-

10 In the optimisation problem, additional periods increase profits because they are simp-

ly added. Thus, we had to divide the overall profits of each contract by the number of pe-riods, t, in order to make the comparison possible.

21

ber of possible re-negotiations minus one. At period one technology is set to one. For example, for a three-period model technological level would be TL1=1, TL2=(1+k)/2, TL3=k, for a four-period model TL1=1, TL2=(2+k)/3, TL3=(1+2k)/3, TL4=k, and so on for an increasing number of periods. Thus, by following the same procedure as in the two-period model, we can obtain the profits for the three-period and four-period models.

Fig. 4 shows the curves of profits according to the number of techno-logical waves. Each profits curve denotes the average profits when different numbers of re-negotiations are hypothesised in the piece rate pay scheme. The main prediction is that as the number of periods increases, profits un-der piece rates get lower, and the difference between fixed pay profits and piece-rate profits gets larger the higher the total technological advancement k over the whole time span.

Fig. 4 – Average profits as t changes (ε = 0.1)

This pattern can be attributed to the “re-negotiation” cost. Even if the production function, as well as the rates, is immediately adjusted according to the improved technology, each time the employer must divert additional surplus to the worker. Furthermore, as inferred from the basic two-period model, at high levels of k, the bulk of the production process is moved to the last period, but with additional periods, the last period is increasingly shorter. This also explains the reduction of profits for greater t’s. Fixed pay follows a similar pattern. When more periods are added, profits per period

22

tend to be lower, but the difference is less noticeable than in the piece rate case. However, the pattern for the fixed pay case is exclusively due to the form of the production function and the cost-of-effort function, because in the fixed pay contract there is no rate re-negotiation. Fig. 5 shows the dif-ference in profits between the two payment schemes (i.e. (ΠFP–ΠPR)(t)). A greater number of technological waves occurring in a specific time span considerably reduces the chances to adopt piece rate pay with respect to fixed pay as one may notice from the larger difference in profits. Addition-ally, as k increases, a rapid technological change makes piece rate pay an increasingly inferior option.

Fig. 5 – Comparison as t grows (ε = 0.1)

4. Extensions to the Basic Model The analysis is now extended by allowing for different contractual struc-

tures, which are compared with each other. In particular, three cases are considered. One case is without trade unions, and represents a sort of benchmark for the other two because the employer cannot do better than that. The other two cases depict different roles for trade unions and contrac-tual outcomes. In one case, as in the model initially introduced, the bargain-ing power of trade unions originates from a positive second-period reserva-tion utility, and two rates, one for each period, are set. In the third case, rates are hold to their first period level, thus the employer can choose only

23

one set of rates valid for both periods. These contractual structures stem-ming from different institutional conditions are analysed according to the time-span of the contract itself, thereby allowing for two types of managers, a long-term and a short-term manager, the latter being unaware of the tech-nological change occurring in the second period, thus renegotiating the rates period by period. Finally, the differences in profits with technological change and without technological change for each compensation scheme are compared, so as to understand which system gives a competitive advan-tage when introducing an improved technology. If we show that the differ-ence in profits with and without technological change under fixed pay is higher than the difference in profits with and without technological change under piece rate pay, we have provided evidence that the gain accruing from technological change is higher under fixed pay than under piece rate pay. A major feature of this comparison is that the difference in profits of fixed pay cancels out the monitoring costs, which are supposed to be the same both for the case with technological change and for that without tech-nological change. Therefore, the comparison between the two payment sys-tems can be analysed without making any conjecture over monitoring costs.

Six different cases can arise according to the type of manager and the bargaining power of trade unions. The employer can be of two types: 1. a forward-looking or long-term manager (as that of the previous

model); 2. a conservative or short-term manager.

The long-term manager knows how much technological change will be introduced in the second period and incorporates this information in the contract from the first period. The short-term manager offers a contract pe-riod by period, as technological change is unknown. Thus, with a short-term manager, the first contract makes only a provision for the first period without any reference to the technological change occurring in the second period. We assume that the type of manager is independent of workers’ power but it is related, for example, to the level of knowledge of techno-logical change, personal returns to the manager, duration of the period in office. – Three different institutional structures can occur. – The no-trade-unions case (NTU). – Trade unions affecting negotiation of rates (NR). – Sticky rates (SR).

In the NTU case workers have no power whatsoever in affecting bar-gaining and contractual outcomes, and consequently they get no surplus from the introduction of the new technology. The employer optimally pro-poses two rates, one for each period: (α1,e1) and (α2,e2) for fixed pay

24

(α1,β1) and (α2,β2) for piece rate pay. The long-term manager chooses these rates at the beginning of the first period, whereas the short-term manager updates rates immediately after technological change has occurred. Overall profits are the same for both the long-term manager and the short-term manager (see tab. A below). This means that in non-unionised firms, long-term managers cannot profit from their knowledge in advance over techno-logical change relatively to their short-term colleagues.

The NR case arises when trade unions are able to reduce employers’ surplus by imposing that a share of the surplus stemming from technologi-cal change accrues to workers. The long-term manager incorporates work-ers’ claims in the whole two-period contract; thus second period rates are negotiated before the beginning of the first period. A short-term manager does not (or cannot) anticipate workers’ claims arising from technological change already in the first period. The short-term manager deals with them only once the innovation has occurred, therefore second period rates are negotiated at the end of the first period. Hence, the outcome of the first pe-riod is taken as given and workers’ bargaining power is only introduced in the rate re-negotiation of the second period in the form of a positive reser-vation utility, whose size depends on technological change.

In the piece rate case, a long-term manager in a NR bargaining structure corresponds to what has been presented in the model of the previous sec-tion: trade unions’ claims would set the second-period reservation utility to be equal to the surplus stemming from technological change by holding the first-period rates constant and correspondingly adjusting effort to the new production function. As already examined in the previous section, the piece rate case should be compared with a fixed pay case where trade unions would like to hold the first-period rates and gain from technological change. However, a fixed pay contract establishes not only the pay rate but also the level of effort thereby keeping the participation constraint binding. Consequently, fixed pay workers would not gain from keeping the same rates of the first period, because it is implicit that effort cannot be adjusted (unlike the piece rate system)11.

Therefore, in order not to replicate the results of the previous section, we grant fixed pay workers the power to get the same pay rate (α1) and to profit from technological change through reduced workload; namely in the second period workers would like to deliver the same output as in the first

11 From the viewpoint of fixed pay workers, this case would be the same as the NTU case. It would also be the same for the employer as well, who can propose a contract that in the second period would give to workers the same utility of the first period (i.e., zero in our case). Indeed, eventually workers’ participation constraint would be binding in both periods; thus, asking the same utility of the first period would bring about no effect.

25

period and get the whole surplus from technological change in terms of lower effort levels. As a consequence, only a contract that grants this in-creased utility would be accepted. This last bargaining structure considers stronger trade unions, which are able to gain from technological change without limiting their bargaining power to the status quo of the first period. Analytically, since y1 = e1 + θ, the introduction of new technology would change the production function such that y2 = ke2 + θ. If workers want to profit fully from technological change by getting the same salary, they

should set e2 equal to ke1 such that 1

12 y

keky =θ+= ; in other words,

workers reduce effort but deliver the same output. If we grant this type of power to workers, the participation constraint of the second period must

take the form 2

11

222 k

e21e

21

⎟⎟⎠

⎞⎜⎜⎝

⎛−α≥−α

12.

The last case under examination is when rates are sticky (SR)13. This setting forces long-term managers to write only one rate for both periods or, alternatively, imposes on short-term managers no rates re-negotiation in the second period such that only the first period rate is applied. This is an un-welcome outcome for the employers who cannot maximise their second pe-riod profits. As a result, the employer can only marginally profit from the introduction of new technology. Piece rate workers have the possibility of gaining from the improved technology over the entire second period. By contrast, fixed pay workers do not gain any surplus because their rates re-main unchanged; however, they could considerably constrain the profits of fixed pay firms.

In tab. A, by comparing the three different contractual structures, which

12 As one can see from the appendix, eventually the worker is going to work more in the

second period contrarily to what his initial intentions were. In effect, this contract must be seen as the outcome stemming from a possible threat that trade unions can put into effect in the second period if rates are not changed by accounting for the different production rates. As a consequence, by maximising the programme, the principal simply anticipates this threat and includes the relevant cost in the programme.

13 Several reasons may lead to sticky rates not just trade-unions’ bargaining power. 1. Em-ployers may fear that re-negotiation costs are going to be high once technological change will take place. High cost of re-negotiations may be due, for instance, to too favourable conditions to workers under the new contractual terms because they have strong bargaining power; work-ers’ retaliation may be very costly by causing strikes, stoppages, etc. 2. Trade-unions may have bounded rationality, being unaware that rate revision can improve workers’ payoffs. 3. Both employers and employees may have entrenched habits such that they prefer not to reset rates. 4. Labour contracts may expire at a different date with respect to the date of introduction of new technology, thus rates cannot be revised until the expiration of old contracts.

26

correspond to three distinct trade union bargaining powers, we realise that employers are seriously damaged by sticky rates.

All profits in the last column are lower than all corresponding profits of the NR case14. Evidently, the NR profits are lower than the correspond-ing profits of the no-trade-unions case. Sticky rates do not allow employ-ers to profit from the implementation of new technologies, and this, of course, becomes a serious impediment when technology has a consider-able impact on the production process. Sticky rates are not advantageous to fixed pay workers either. Consequently, under fixed pay contracts, moving from sticky rates to negotiated rates would represent a Pareto im-provement.

The same observation is valid for piece rate contracts with short-term managers. Indeed, piece rate workers already get their maximum surplus by negotiating the rates; forcing the short-term manager to hold the rates would not grant workers any additional surplus. Conversely, with long-term managers, piece rate workers gain more by holding the rates fixed rather than negotiating a higher reservation utility before signing the con-tract as in the NR case. Excluding the latter case, when technological change occurs, it is beneficial to negotiate apposite rates such that both parties can profit from the improved technologies. However, by holding the rates fixed, a piece rate worker would immediately gain from the in-troduction of the technology and this is an important difference in the atti-tude of trade unions to negotiating piece rate contracts compared to fixed pay contracts.

In summary, when trade unions are able to influence the outcome of workers’ contracts (especially piece rate contracts) a new technology must not be introduced abruptly but should be discussed with trade unions and its benefits negotiated. Even those firms that offer fixed payments would find it beneficial to negotiate new rates (i.e., wages and effort) and grant some surplus to the workers. It is worthwhile noticing that a long-term manager reduces workers’ surplus in all instances when compared with a short-term manager. Lower surplus for workers is translated into higher profits. Hence, a manager who has preventive knowledge of the amount of technological change and incorporates this knowledge into the contract is better off.

14 Short and long-term managers offering fixed pay are the only exception to this pat-

tern, but only for very low levels of k. This means that a reasonable technological enhance-ment is enough to make all the NR cases preferable with respect to all SR cases.

27

Tab. A – Different Bargaining Structures by Different Types of Managers

NTU NR SR

Shor

t-Ter

m M

anag

er

Fixe

d Pa

y ( )0S

k121 2

=

+=Π

2

2

2

4

k21kS

k21k

−=

+=Π

0Sk

==Π

Piec

e R

ate

Pay

( )0S

k2k

)1(21

2

4

=ε+

+ε+

=Π

( ) ( )

( )22

2

4

2

2

121kS

k2k

12k2

ε+−

=

ε++

ε+−ε+

=Π

( )

( )2

2

2

2

121kS

1k1

ε+

−=

ε+

ε+=Π

Long

-Ter

m M

anag

er

Fixe

d Pa

y ( )0S

k121 2

=

+=Π

( )22

24

2

4

1k22

kkS

1k2k

−

−=

−=Π

( )

0S4k1 2

=

+=Π

Piec

e R

ate

Pay

( )0S

k2k

)1(21

2

4

=ε+

+ε+

=Π

( )

( )22

2

2

4

k2

1kS

k21k

ε+

−=

ε++

=Π

( )( )

( ) ( )( )22

222

2

22

k8

1kk1S

k4k1

ε+

−+=

ε++

=Π

4.1. Difference in Profits with and without Technological Change The comparison of the profit levels for each contractual scheme is im-

portant because it explains which payment scheme is the most profitable according to different institutional conditions when technology is intro-duced as a parameter. However, we may also want to understand which type of contract achieves the highest profit gains when an output-enhancing technology is introduced. This analysis is important because we can com-pare the impact that the same technological shock has on competing firms applying different compensation schemes. Indeed, there may be payment

28

schemes that ceteris paribus are more beneficial than others when new technologies or techniques are introduced in the production process. In or-der to carry out this analysis we need to calculate the difference between profits with technological change and profits without technological change (see the Appendix and tab. A). As mentioned above, by calculating this dif-ference, monitoring costs for fixed pay are cancelled out. This allows a more precise comparison between the two compensation schemes15.

The simulations carried out within the three different bargaining struc-tures suggest that when trade unions do not possess any bargaining power (i.e., NTU case), the impact of technological change is basically equivalent for both compensation schemes, to wit, two firms, one adopting piece rates and the other fixed pay, will approximately gain equally from technological change. Small differences arise when the risk component becomes impor-tant and technological improvements become significant; in such a case, fixed pay is slightly more favourable than piece rate pay.

Marked differences arise when trade unions secure certain levels of sur-plus from technological change through their bargaining power. From fig. 6 to fig. 9 the NR and SR cases are shown for different types of manager. These graphs depict the difference between the profit gains from techno-logical change under fixed pay and the gains from technological change under piece rate pay for a large set of risk/technological change combina-tions. Thus, positive values signal that technological shocks increase profits for fixed pay firms more than they do for piece rate firms and vice versa for negative values. One can immediately appreciate that applying fixed pay is preferable for the large majority of bargaining structures and levels of tech-nological change. In particular, shortterm managers applying piece rates, who must re-negotiate rates in the second period (i.e., NR case), are very vulnerable to workers’ requests as workers can claim a large share of tech-nological gain. Most probably this was the long-term outcome that could be applied to the emerging American iron and steel industry. Managers up-dated the rates only when the urge for a change due to the innovations be-came significant. This imposed increasingly high reservation wages to skilled workers, who did not accept worse conditions than those acquired through the technological innovations. However, applying output-related pay, like the contract system, was inefficient vis-à-vis a fixed payment scheme that could ensure larger profits even by allowing for some surplus

15 Suppose the gains from technological change for fixed pay are the following: ΠFPk–

ΠFP. Where ΠFPk is equal to the two-period profits with technological change k(>1) in the

second period, whereas ΠFP is equal to the two-period profits when there is no technological change, namely k=1 in both periods. It is easy to show that difference between profits cancel out monitoring costs that apply to both cases.

29

to be shared with the workers. Under the NR bargaining structure, long-term managers still gain more by applying fixed pay rather than piece rate pay but without the marked difference experienced by short-term managers.

Fig. 6 – Difference between Gains from Technological Change, NR – Short-Term Manager

Fig. 7 – Difference between Gains from Technological Change, NR – Long-Term Manager

The SR case with long-term managers also shows unequivocally that

fixed pay offers higher incremental profits than piece rate pay. By contrast, with a short-term manager, piece rate pay may prevail for very large levels

1 23

45

k

00.5

11.5

2 Risk

-2

-1

0

1

2

DifferencebetweenGains

1 23

45

k

00.5

11.5

2 Risk

12

34

5

k

00.5

11.5

2 Risk

-2

-1

0

1

2

12

34

5

k

00.5

11.5

2 Risk

Difference between Gains

Difference between Gains

30

of k. This pattern is mostly explained by the utility functions of the CARA type. Under piece rates and short-term managers, as rates are held fixed, workers increase their effort for increasingly larger levels of k because there is no substitution of effort for leisure due to income effects. Con-versely, fixed-pay profits suffer much from the cost of keeping the rates (and therefore the effort level) to their first period level. Yet, fixed pay with a long-term manager can internalise technological change into the single rate which is going to be applied for both periods. Fig. 8 – Difference between Gains from Technological Change, SR – Short-Term Manager

Fig. 9 – Difference between Gains from Technological Change, SR – Long-Term Manager

12

34

5

k

00.5

11.5

2 Risk

-2

-1

0

1

2

Difference between Gains

23

45

00.5

11.5

12

34

5

k

00.5

11.5

2 Risk

-2

-1

0

1

2

Difference between Gains

23

45

00.5

11.5

Difference between Gains

Difference between Gains

31

Even if not reported in the graphs, which depict the difference between the profit gains from technological change of fixed pay and piece-rate pay, the level of the gains are higher when rates are negotiated rather than pre-served to their first period level. In other words, regardless of the payment system, sticky rates do not allow to take full advantage of technological change. This corroborates the conclusion of the previous section, to wit, overall profits under sticky rates are always lower than negotiated rates. Again, trying to bargain over the rates is extremely important for employers if they want to profit from improved technologies.

5. Conclusion This investigation has highlighted the limitations of the use of a specific

incentive scheme – the contract system – that played a very important role in the history of industrial relations in the iron and steel industry of the United States. A growing industry, such as that of iron and steel in the sec-ond half of the nineteenth-century, could not indefinitely sustain a piece rate system that was originally born within an industrial organisation that did not experience the rates of production and technological change and the dynamics of the industrial relations that marked that sector in that specific historical epoch.

The investigation has shown how costly applying piece rate pay can be when high rates of technological innovation are coupled with strong trade unions. By using agency theory, it has shed some light on the conflicting nature of piece rate pay compared to fixed pay as new technology is intro-duced. Piece rate workers can immediately (i.e., without rate changes) profit from new technology both by the higher output brought about by the improved technology and by adjusting their effort levels, since the latter are not contractually stated. If we accept that in reality the expiration date of labour contracts usually differs from the date of introduction of new tech-nology, then piece rate workers have the time to earn additional surplus un-til the new contract is discussed and subsequently signed. This makes rates negotiation very difficult. Workers could stake their advantage in the con-frontation with their employer when second-period rates must be negoti-ated. If employers attempt to limit this advantage, workers could threaten to go on strike. Therefore, rates are likely to be sticky because rates updating will not be as easy as implementing new technology. Conversely, fixed pay workers, given the nature of their contract, do not in general gain any bene-fit from technological change because, on the one hand, a higher production does not affect their pay, and on the other hand, their effort level is contrac-

32

tually stated and monitored. Thus, fixed pay workers cannot exert lower ef-fort levels unless they re-negotiate rates. This makes their bargaining power weaker compared to piece rate workers.

The theoretical analysis leads to further conclusions. Firstly, the em-ployer would be extremely tempted to get rid of trade unions when new technology is introduced. Indeed, trade unions can considerably reduce profits either by asking for a share of the gains stemming from technology or by holding rates at sub-optimal levels. For example, ironmasters con-tinually appealed to strike breakers coming from the South and from Europe as they were non-unionised and asked for lower rates (Krause 1992). This had the twofold effect of not only reducing union control in the plants but also of aligning the participation constraint to lower levels. In other words, the surplus that skilled workers wanted to claim was sustain-able only by virtue of the strength of their trade unions and not because of the market conditions. The mechanisation brought about by the change in technologies and the resulting specialisation of labour reduced the profes-sionalism and the skills previously required; this increased workers substi-tutability thereby reducing the actual reservation utility. Secondly, the choice of the payment system has an important impact on industrial rela-tions and the production process. Where the payment system introduces several negotiations over the surplus stemming from technological change, the consequences are either stop-and-go production processes or employ-ers’ reluctance to introduce new technology. Emblematic examples are the U.S. iron and steel industry for the former, and the well-known case of Lin-coln Electrics for the latter (Milgrom, Roberts, 1992). In particular, an ex-tension to the model would be the endogenisation of technology, where one may expect that piece rate pay would result in a lower level of investment. However, in the iron and steel industry, strong trade unions coupled with piece rate pay did not severely undermine investments in innovative tech-nologies. On the contrary, both the growing demand of iron and steel and the necessity to de-skill jobs, which would have reduced workers’ bargain-ing power, required increasingly higher investments on production and process innovations16. Thirdly, according to the theoretical investigation, the employer should predict in advance the amount of technological change that will be introduced in the production process, and consequently should make all possible efforts to negotiate the corresponding new rates with the trade unions and try to anticipate their claims in advance.

16 In turn, explicit incentive pay continued to survive because it was nonetheless consi-

dered the most efficient way to control moral hazard (Stone, 1974).

33

Appendix The case of no technological change leads to the same profits levels for each

type of manager and for each degree of involvement of the trade unions in the bar-gaining process.

Tab. A1 – No technological change

Fixed Pay

121,1e

21,1e

21

22

11

=Π

=α=

=α=

+

Piece Rate Pay

The case with technological change leads to the following results.

Tab. A2 – NTU Case

Shor

t- an

d Lo

ng-T

erm

Man

-ag

er

Fixed Pay 2

22

11

k21,ke

21,1e

=α=

=α=

Piece Rate Pay ( )

( )22

24

22

2

22

3

2

2

111

k2

kk,k

k,k

ke

11

21,

11,

11e

ε+

−ε=α

ε+=β

ε+=

⎟⎠⎞

⎜⎝⎛

ε+−ε

=αε+

=βε+

=

ε+=Π

ε+=β⎟

⎠⎞

⎜⎝⎛

ε+−ε

=αε+

=

ε+=β⎟

⎠⎞

⎜⎝⎛

ε+−ε

=αε+

=

+ 11

11,

11

21,

11e

11,

11

21,

11e

21

2

2

22

1

2

11

34

Tab. A3 – SR Case Sh

ort-T

erm

M

anag

er Fixed

Pay 21,1e =α=

Piece Rate Pay ε+

=β⎟⎠⎞

⎜⎝⎛

ε+−ε

=αε+

=ε+

=1

1,1

12

1,1

ke,1

1e2

21

Long

-Ter

m M

anag

er

Fixed Pay

2

2k1

21,

2k1e ⎟

⎠⎞

⎜⎝⎛ +

=α+

=

Piece Rate Pay

( )( )( )

( ) ( )ε++

=β⎥⎦

⎤⎢⎣

⎡

ε++−ε

=α

ε++

=ε+

+=

2

22

2

2

2

2

22

2

1

k2k1,

k2k1

21

,k2

k1ke,k2

k1e

Tab. A4 – NR Case

Shor

t-Ter

m M

anag

er Fixed

Pay 2

24

22

11

k21kk,ke

21,1e

−+=α=

=α=

Piece Rate Pay

( ) ( ) ε+=β

ε+

−+

ε+

−ε=α

ε+=

ε+=β⎟

⎠⎞

⎜⎝⎛

ε+−ε

=αε+

=

2

2

22

2

22

64

22

3

2

1

2

11

kk,

121k

k2

kk,k

ke

11,

11

21,

11e

Long

-Ter

m M

anag

er

Fixed Pay

22

46

22

2

2

2

12

2

1

)1k2(2k3k4,ke

1k2k

21,

1k2ke

−−

=α=

⎟⎟⎠

⎞⎜⎜⎝

⎛

−=α

−=

Piece Rate Pay

ε+=β

ε+ε−−−

=αε+

=

ε+=β

ε+−ε

=αε+

=

2

2

222

242

22

3

2

2122121

kk,

)k(2)k(k1k,

kke

k

1,)k(2

1,k

1e

35

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Abstract The Impact of Technological Change on Incentive Provision

The simple trade-off between incentive and risk, which is crucial to the agency problem, is not a sufficient explanation for the ineffectiveness of a specific output-related pay such as the contract system adopted in the US iron and steel industry during the second half of the nineteenth-century. The high rate of technological innovation along with workers’ extensive bargaining power made output-related pay a sub-optimal solution. This stylised fact unveils the conflicting nature of piece-rate pay compared to fixed pay as new technology is intro-duced and stimulates an analysis of the interaction between technological change, bargain-ing powers, and payment systems which can be conducive to a better understanding of the agency problem and the use of incentive pay. Key words: Incentive Contracts, Inside Contracting, Unions, Technological Change. JEL Classification: J33, J51, N31, O33 Final version received November 2008