EUROPEAN UNIVERSITY INSTITUTE, FLORENCE DEPARTMENT OF ECONOMICS Repository. Research Institute 320 University European Institute. E U I WORKING Cadmus, on INSTABILITY AND INDEXATION IN A LABOUR- MANAGED ECONOMY - A GENERAL EQUILIBRIUM University QUANTITY RATIONING APPROACH Access by it ick European Will Bartlett and Gerd Weinrich Open Author(s). Available içit The 2020. European University Institute University of Western Ontario © Badia Fiesolana Department of Economics in 50016 S. Domenico di Fiesole Social Science Centre Italy London, Canada N6A 5C2 Library EUI This paper was written while the second author was a Jean Monnet Fellow the at the European University Institute and presented at the Fourth Inter­ by national Conference on the Economics of Self-Management in Liège, Belgium, July 15-17, 1985. produced version BADIA FIESOLANA, SAN DOMENICO (FI) Digitised Repository. Research Institute University European Institute. Cadmus, on University Access European Open Printed in Italy in September 1985 Printed Italy September 1985 in in (C) Weinrich Will Gerd Bartlett and (C) reproduced in any form without without any reproduced form in No part may No part be of paper this European University Institute University European Institute - 50016 San Domenico (FI) Domenico - - San 50016 (FI) Author(s). Available permission of of author. permission the All rights All rights reserved. The 2020. Badia Fiesolana Badia Fiesolana © in Italy Library EUI the by produced version Digitised Repository. Research Institute University European managed economy based upon the general equilibrium quantity ra­ may lead to highly perverse and unstable price dynamics, as en­ Abstract households seek to maximize utility in consumption and leisure cient level of activity. the dynamics and guide the labour-managedtion economyscheme is to presentedan effi­ which would dogenousreverse the featuresdirection of the of system. An easily implemented indexa­ tioning paradigm. It is shown that such an economy in which firms seek to maximize value added per working hour, and Institute. Cadmus, The paper presents a macroeconomic analysis of a labour- on University Access European Open Author(s). Available The 2020. © in Library EUI the by produced version Digitised Repository. Research Institute University European Institute. Cadmus, on University Access European Open Author(s). Available The 2020. © in Library EUI the by produced version Digitised Repository. 1 . Introduction After several years of galloping inflation, the internation­ Research al Monetary Fund has persuaded the Yugoslav government to peg the interest rate charged to labour-managed firms in the country's 1 Institute industrial sector to one percent above the rate of inflation. In this paper we present a macrodynamic analysis of a labour-man- aged economy which illustrates, within the confines of a relatively University simple model, the significance and drawbacks of this measure. The model applies the method of quantity rationing (see Grandmont, 1982) to the problem of a labour-managed economy in European which firms attempt to maximize income per working hour, and householdsInstitute. (hereafter "consumers") attempt to maximize a utility function Cadmus, with arguments consumption and leisure. The agents who, as work­ on University ers, manage firms, supply goods and demand labour, are of course the same agents who in another guise act as consumers and demand Access goods and supply labour; but in their various roles they react to European Open different sets of signals. This feature of the labour-managed economy enables us to provide a particularly clear analysis of Author(s). both quantity and price dynamics. Available The This dual role of the worker-managers, as producers and at 2020. © the same time consumers, has been implicitly recognized in sever­ in al models of the labour-managed firms such as Sen (1966) where Library the firm attempts to directly maximize the utility of the members in consumption and leisure, and Domar (1966) where an income-per- EUI member-maximizing cooperative faces an internal labour supply the by constraint. However, on account of the partial equilibrium na­ ture of these analyses, the significance and implications of the interaction of these two facets of worker behaviour have not been produced fully appreciated. version Digitised Repository. Research Institute University European quently in response to changes in demand perceived to be of a ducted. In section 2 we riumassume, framework, in keeping in whichwith wethe quantity-raallow non-Walrasian trades to be con This reflects the stylized fact that tioning in the paradigm,short run, that in mostquantities adjust faster than prices. ments for example) to the rate of inflation eliminates this in­ price dynamics imply that the equilibrium so established is un­ permanent nature. In section 3 we proceed to develop the analy­ one case to an inflation-spiral, in another case to a deflation- tonnement mechanism. In section 5 we show that the long-run ing quantities (i.e. production), but industries,adjust prices firms onlyreact infre­to changes in demand by initially adjust collapse of the economy. In the sixth section it is shown how sis of the existence of equilibrium, and in section we4 demon­ the "simple" indexation of fixed costs (rents, or interest pay­ as soonstable. as prices become free to adjust. This leads in strate its "temporary" stability, by considering a quantity tâ­ is is presented which will guide our labour-managedly, a proposal economywhich we towardsrefer to as stability"progressive but rentdoes not, indexationby itself, result in efficiency. Final­ full employment and price stability. Institute. Our model, therefore, adopts an explicit general equilib­ Cadmus, on University Access European Open Author(s). Available The 2020. © in Library EUI the by produced version Digitised 3. Repository. 2. The Model We assume that the economy consists of one firm and one con­ Research sumer-worker. This is not a restriction of generality since the analysis could easily be extended to the case of having m identi­ Institute cal firms and n identical consumers. However, setting m = n = 1 avoids an otherwise more complicated notation and allows us to University represent the whole analysis graphically which will be very in­ structive . European 2.1 Firm1s Behaviour Institute. The firm produces a composite consumption good using labour Cadmus, by means of a differentiable production technology c = f (1) with on f' > 0, f" < 0, f(0) 0 and f' (0) = °°. It has to pay a fixed University rent r for the use of other inputs the level of which is fixed Access throughout the period under consideration. For given output European price p, the firm may observe constraints on consumer goods de­ Open mand, c, and on labour supply, I. The firm's objective is to maximize value-added per working hour, i.e. V = /pf (1) - r//l. Author(s). Available Since p cannot be influenced by the firm, this amounts to the The same as maximizing real value-added per hour, i.e. 2020. © in f(1) " £ v max --- ---- - 1) 1 P P Library s . t. (i) 1 > 0 EUI (ii) 1 < I the (iii) f (1) < c by The solution to the program yields the firm's effective la- cLir — — s r ” “ bour demand 1 (—,0 ,1 ) and its effective goods supply c (—,c,l) = produced dr—— ^ d# r s» r f(l (—,c,l)). Denoting with 1 (—) and c (—) the firm's uncon­ strained transaction offers (i.e. when (ii) and (iii) of the version Digitised Repository. Research Institute University above problem are deleted) and setting 1:= min the {l,f "'(c)}, European firm's effective labour demand is strained decision is obviously Institute. Figure 1 illustrates the firm's decision problem. The real value-added associated with the firm's uncon­ id (ï,ï> =• Cadmus, P on University _ _ . Tld*.r, =, Access _ o _ min {1 (-),1} , if Ï > f"1 European Open P Figure 1 Author(s). Available The 2020. © in evidently if if Ï < f_1 Library EUI the (-) (£) P P by produced version 4. Digitised Repository. Research It is immediate to see that Institute d* dl > 0 < 0 d(-) P University 2.2 Consumer's Behaviour The consumer receives a fixed rent income r and he can en­ European gage to work a number of hours 1 for which he then receives the Institute. labour income VI, for given value-added per hour V. This means Cadmus, that, to the consumer, V is an exogenously given datum. Possi­ on bly observing constraints on consumer goods supply, c, and on University labour demand, I, the consumer then has to solve the problem: Access max u(c,l) European Open s .t . (i) c £ 0 (ii) 0 < 1 < L Author(s). (iii) pc < VI + r Available (iv) c < c The 2020. © (v) 1 < Ï in where u(c,l) = U(c, L - 1) is a utility function which is in­ Library creasing in c, decreasing in 1, and U is strictly quasi-con­ EUI cave; L denotes the upper bound of hours the consumer can phys­ the ically work. by The solution to the above problem yields the consumer's g v r - - effective labour supply 1 (—, —,c,l) and his effective consump­ produced tion goods demand c^(—,— ,c,Ï), the latter being equal to P P t V g v r - - 2 version — 1 (—,~,c,l) + — , by the assumptions on the consumer's utility P P P P Digitised 6. Repository. silVir V r function. If 1 ) and c ) denote the consumer's uncon- P P P P strained labour supply and goods demand (i.e. when (iv) and (v) Research in the above problem are deleted), then quasi-concavity of U im­ plies r Institute c - — s V r - - . s* .V r, T rn 1 (~,-,c,l) = min {1 , 1, max {0, ____ P } V d* V r V dfc'.V r.