It is well known that profit sharing arrangements Pareto-dominate fixed wage contracts. Share agreements are (far) less than ubiquitous, however. This paper offers a solution of this ”fixed wage puzzle“ by adopting a perspective of bounded rationality. We show
that share arrangements that fulfill ”plausible“ constraints are not generally acceptableto both firms and unions

Jerger, Jürgen

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 Joint Discussion Paper Series in Economics by the Universities of Aachen · Gießen · Göttingen  Kassel · Marburg · Siegen ISSN 1867-3678    No. 13-2010  Jürgen Jerger and Jochen Michaelis   The Fixed Wage Puzzle: Why Profit Sharing Is So Hard to Implement                  This paper can be downloaded from http://www.uni-marburg.de/fb02/makro/forschung/magkspapers/index_html%28magks%29  Coordination: Bernd Hayo • Philipps-University Marburg Faculty of Business Administration and Economics • Universitätsstraße 24, D-35032 Marburg Tel: +49-6421-2823091, Fax: +49-6421-2823088, e-mail: hayo@wiwi.uni-marburg.de  Gießen Marburg Kassel Siegen Aachen Göttingen MAGKS The Fixed Wage Puzzle: Why Profit Sharing Is SoHard to ImplementJürgen Jerger1University of RegensburgJochen Michaelis2University of KasselApril 20101Jürgen Jerger, University of Regensburg and Osteuropa-Institut Regensburg, Univer-sitätsstr. 31, 93053 Regensburg, Germany. Email: juergen.jerger@wiwi.uni-regensburg.de.Phone: ++49-(0)941-9432697.2Jochen Michaelis, University of Kassel, Nora-Platiel-Str. 4, 34127 Kassel, Germany.Email: michaelis@wirtschaft.uni-kassel.de. Phone: ++49-(0)561-8043562.AbstractIt is well known that profit sharing arrangements Pareto-dominate fixed wage contracts.Share agreements are (far) less than ubiquitous, however. This paper offers a solutionof this”fixed wage puzzle“ by adopting a perspective of bounded rationality. We showthat share arrangements that fulfill”plausible“ constraints are not generally acceptableto both firms and unions.Keywords: Profit Sharing, Share Economy, Remuneration SystemsJEL Classification: E24, J3311 IntroductionIt is well known that profit sharing arrangements Pareto-dominate fixed wage contracts.In particular, profit sharing schemes may give rise to higher productivity of workers(Bental and Demougin 2006); allow for an efficient risk distribution (Brouwer 2005);and foster employment by reducing the marginal cost of labor (Weitzman 1985; Jergerand Michaelis 1999). Despite these arguments, share agreements are more the exceptionthan the rule (Pendleton et al. 2001).The inconsistency between the desirability of profit-sharing schemes in theory andtheir rare use was already noted in Weitzman (1985) and termed the”fixed wage puzzle“by Kirstein and Kirstein (2007). Weitzman’s explanation of this puzzle invokes anexternality. Whereas the excess labor demand created by share contracts is beneficialfor a society, individual firms have an incentive to revert back to a fixed-wage contract ifeveryone else maintains profit sharing. This externality, however, vanishes when thereis a negotiation over the parameters of a share contract (Holmlund 1990).In this paper, we show that the fixed wage puzzle can be understood by invokinga mild form of bounded rationality. Specifically, we assume that instead of thinkingthrough the whole bargaining and adjustment processes of a changeover from fixedwages to share contracts, unions and firms consider to implement a share solution withsome plausible properties to be detailed below. A share contract is reached if and onlyif both parties prefer it relative to the fixed wage solution.In the next section, we present the basic model and the fixed wage solution thatserves as a benchmark. Section 3 presents three changeover scenarios, section 4 con-cludes.22 Basic Model and Fixed Wage SolutionWe consider an economy populated by a large number of monopolistically competitiveand symmetric firms producing revenue R by means of labor N according to R = θ ·Nα,where 0 < α < 1. θ ∼ (1, σ2θ) denotes a revenue shock. Since we confine ourselves to thesectoral level and the analysis of symmetric firms, we can do away with firm indices.1Each firm faces a monopoly union whose behavior is driven by the maximization ofthe utilitarian Stone-Geary functionU = N ·(W 1−γ1− γ−B1−γ1− γ), (1)where W denotes the real wage, B the exogenously given alternative income, and γ > 0the Arrow-Pratt measure of relative risk aversion.The sequence of events is as follows. First, the union sets the wage rate W afterwhich the revenue shock θ is revealed. Then the firm decides about the level of em-ployment. This sequence ensures that fixed wage contracts do not completely isolateworkers from uncertainty since employment will depend on the realization of θ.Solving the dynamic game, we have first to consider the firms’ decision, which issummarized by the labor demand scheduleN =(αθW)11−α. (2)Expected employment is thus given byE(N) =( αW)11−α·Θ, (3)1Our focus on the incentives to arrive at a share agreement also allows us to ignore the macroeco-nomic consequences.3where Θ = 1 +α·σ2θ2(1−α)2. Note that E(N) depends positively on σ2θ due to the convexityof the labor demand schedule (2).Maximizing the expected value of (1), observing (3), yields W = η · B, whereη ≡ µ1/(γ−1) and µ ≡ α + (1− α)γ. The optimal wage does not depend on σ2θ , i.e. therevenue shock shows up in employment only.2 For further reference, expected utilityand expected profits in the fixed wage solution are given as follows:E(U) =1− αµ(αηBµ)11−αΘ (4)E(Π) = (1− α)(αηB)α1−αΘ (5)3 Changeover Scenarios3.1 Three Plausible SuggestionsThe”straightforward“ comparison between fixed and flexible wage arrangements looksat the differential, both in union utility and profits, between the two bargaining out-comes (Jerger and Michaelis 1999). However, since the theoretical possibility of aPareto-improvement via a bargaining process might be difficult to evaluate, firms andunions might consider”plausible“ instead of optimal share arrangements. Clearly, thedifficulty is the specification of plausibility. In this paper, we offer three different sce-narios. First, we look at a share contract that ensures that the total wage is equal to thefixed wage”on impact“ , i.e. when employment is still at the level that prevails under afixed wage contract. Second, we analyze a contract that leaves the wages of incumbentworkers unchanged after the adjustment of employment under the share contract tookplace. Finally, we consider whether it makes sense for a firm to offer a share contract2This property, however, is due to the fact that the labor-demand schedule is iso-elastic (MacDonaldand Solow 1981).4unilaterally.A share contract specifies workers’ remuneration as some base wage ω that is com-plemented by a share λ of the difference between revenue per worker and the base wage.3Formally: W = ω+λ(θR(N)−ωN)/N . Clearly, a given level of total remuneration canbe achieved via an infinite number of combinations of ω and λ. To pin things down,we assume ω = B.3.2 Total Wage Equivalence on ImpactA plausible minimum requirement from the viewpoint of workers for a change from fixedwages to a share contract is that incumbent workers’ wages remain the same as long asemployment is unaltered. This requirement implies λ = α(η−1)η−α. Expected employmentis given by E(N) = (α/B)1/(1−α)Θ. Clearly, total remuneration is lower than undera fixed wage contract after the adjustment to this employment level. Expected utilityand expected profits are readily computed asE(U) =11− γ(ψ1−γ − 1)( αBµ)11−αΘ (6)E(Π) = (1− α)2ηη − α(αB)α1−αΘ, (7)where ψ ≡ (η(2− α)− 1)/(η − α). Comparing (4)-(5) to (6)-(7) leads to the followingresult:Proposition 1 Unions will agree to a share contract (ω, λ) =(B, α(η−1)η−α)if and onlyif the degree of relative risk aversion γ is less than unity. Firms will always accept thisshare contract since profits are higher than under fixed wages.3This revenue sharing is economically equivalent to profit sharing (Michaelis 1997).5We are only aware of two empirical studies that directly estimate the crucial param-eter, i.e. the unions’ degree of relative risk aversion. Farber (1978) in a study of theUS United Mine Workers over the period 1948-1973, finds a γ of about 3. Carruth andOswald (1985) derive an estimate of 0.8 – slightly below the benchmark of proposition1 – from the behavior of unions in the coal and steel industries in the United Kingdomover the period 1950-1980. The literature on the degree of relative risk aversion ofhouseholds arrives at values of γ between 1 and 5 (Watt 2002, Dohmen et al. 2010).Hence, risk aversion might well explain the reluctant use of share contracts.3.3 Total Wage Equivalence after Employment AdjustmentIncumbent workers may object to the changeover scenario of the last subsection forthe simple reason that in equilibrium, i.e. after the adjustment of employment, theirtotal wage will be lower than the fixed wage. Thus, the next plausible suggestion is ashare contract that leaves wages unchanged after employment is adjusted to the profit-maximizing level. With ω = B, this requires λ = α(η−1)1−α. The algebraic solution canbe omitted because the intuition is rather straightforward. It is summarized in thefollowingProposition 2 Unions will always agree to a share contract (ω, λ) =(B, α(η−1)1−α).Firms, however, will not accept this share contract since profits are lower than underfixed wages.Unions benefit unambiguously since employment rises, whereas total remunerationper worker remains the same (by assumption). This clearly implies declining profits.63.4 Share Offer of FirmsThe two previous scenarios looked at specific share contracts. Now we ask whetherit may benefit a firm to unilaterally offer some positive share λ to the union. Therationale for that may be that the union is willing to reduce the base wage componentin order to foster employment. This in turn might lead to higher profits. The sequenceof events thus is λ−ω−θ−N , where the monopoly union sets ω. Looking at the firms’problem, we start from the expected profit function E(Π) = (1− λ)(1− α)(α/ω)α1−αΘ.Maximizing with respect to λ yields the first-order condition∂E(Π)∂λ= 0 ⇒∂ω∂λ= −ω(1− α)α(1− λ). (8)If the ω requested by the monopoly union declines in λ according to (8) or faster, firmshave an incentive to offer such a share component to their workers. Writing unionutility as a function of both ω and λ and maximizing with respect to ω, treating λ asgiven, leads to the optimal base wage demand ω = αηBα(1−λ)+λ. From this, it is clear thatunions reduce their base wage claim according to∂ω∂λ= −ω(1− α)α(1− λ) + λ. (9)By comparing this result to (8), it is immediately clear that for any positive λ, thereduction of the base wage claim is lower than what firms would need in order to offershare contracts. This establishesProposition 3 Firms have no incentive to offer a positive share of profits to workers,although unions would react by lowering the base wage.Only if the moderation of the base wage is complemented by an increase in laborproductivity, a unilateral offer of a share contract might be possible (see Koskela and7Stenbacka 2006).4 ConclusionsIn most firms, fixed wage contracts are in effect and serve as a natural benchmark fora share contract. From this benchmark, however, plausible changeover suggestions arelikely to be refused by one party involved. Fixed wage contracts thus exert quite some”normative power of the factual“ – and this power may well prevent more efficient shareagreements. We show that plausible share arrangements are unlikely or impossible tobe accepted. Only if workers display a relatively moderate degree of risk aversion andagree to a share contract under which total remuneration declines relative to the fixedwage contract, there is a possibility for a mutually acceptable changeover from fixedwages to a share arrangement.One should note that this analysis is an application of the general and recentlyvery fruitful analysis of bounded rationality. Under unbounded rationality (and theassumptions concerning technology and union utility in this paper), a share agreementclearly Pareto-dominates a fixed wage agreement. We thus offer a new perspective onthe well-known fixed wage puzzle.References[1] Bental, Benjamin and Dominique Demougin (2006): ”Incentive Contracts andTotal Factor Producitivty”, International Economic Review 47: 1033-1055.[2] Brouwer, Maria (2005): ”Managing uncertainty through profit sharing contractsfrom medieval Italy to Silicon Valley”, Journal of Management and Governance 9:237-255.8[3] Carruth, Alan and Andrew Oswald (1985): ”Miners’ Wages in Post-war Britain:An Application of a Model of Trade Union Behaviour”, Economic Journal 95:1003-1020.[4] Dohmen, Thomas, Armin Falk, David Huffman, Uwe Sunde, Jürgen Schupp andGert Wagner (2010): ”Individual Risk Attitudes: New Evidence from a Large,Representative, Experimentally-Validated Survey”, IZA Discussion Paper 1730,forthcoming in: Journal of the European Economic Association.[5] Farber, Henry (1978): ”Individual Preferences and Union Wage Determination:The Case of the United Mine Workers”, Journal of Political Economy 86: 923-942.[6] Holmlund, Bertil (1990), ”Profit Sharing, Wage Bargaining, and Unemployment”,Economic Inquiry 28: 257-268.[7] Jerger, Jürgen and Jochen Michaelis (1999): ”Profit Sharing, Capital Formationand the NAIRU”, Scandinavian Journal of Economics 101: 257-275.[8] Kirstein, Roland and Kirstein, Annette (2007): Inefficient Intra-Firm IncentivesCan Stabilize Cartels in Cournot Oligopolies, mimeo, February 2007.[9] Koskela, Erkki and Rune Stenbacka (2006): ”Flexible and Committed Profit Shar-ing with Wage Bargaining: Implications for Equilibrium Unemployment”, Journalof Economics 87: 159-180.[10] McDonald, Ian M. and Solow, Robert M. (1981): ”Wage Bargaining and Employ-ment”, American Economic Review 71: 896-908.[11] Michaelis, Jochen (1997), ”On the Equivalence of Profit and Revenue Sharing”,Economics Letters 57: 113-118.9[12] Pendleton, Andrew, Erik Poutsma, Jos van Ommeren and Chris Brewster (2001):Employee share ownership and profit-sharing in the European Union, Luxembourg:Office for Official Publications of the European Communities.[13] Watt, Richard (2002): ”Defending Expected Utility Theory”, Journal of EconomicPerspectives 16: 227-230.[14] Weitzman, Martin L. (1985): ”The Simple Macroeconomics of Profit-Sharing”,American Economic Review, 75: 937-953.

The Fixed Wage Puzzle: Why Profit Sharing Is So Hard to Implement

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The Fixed Wage Puzzle: Why Profit Sharing Is So Hard to Implement

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