Production, safety, exchange, and risk. Kjell Hausken

Transcription

1 Production, safety, excange, and risk Kjell Hausken Abstract: Two agents convert resources into safety investment and production wile excanging goods voluntarily. Safety investment ensures reduction of costly risk. Hig unit cost of safety effort reduces bot productive effort and safety effort, wic reduces income. Keywords: production; safety; excange; risk; trade; price. Classical excange teory was developed by Smit (1776) and Ricardo (1817). More recent accounts are Allen (2000), Arrow et al. (1961), Hausken and Moxnes (2005a, 2005b) and Taylor (1993). Recently, excange teory and conflict ave been merged, accounting for production and figting (see Anderton, 1999; Anderton et al., 1999; Bowles and Gintis, 1993; Hausken, 2004; Rider, 1999; Skaperdas and Syropoulos, 2001). Tis article makes one step furter accounting for safety investment in an excange model. Safety risk as not received muc attention in te economics literature. 1 Safety concerns are often considered as constraints imposed by law and regulations. Firms face risks due to internal factors related to production, equipment failure, uman failure, due to interaction wit oter firms witin te industry, or external factors. Te latter can be societal canges in general, or targeted action suc as crime, teft, espionage, acking, blackmail, terrorism. Asce and Aven (2004) argue tat safety measures ave a value in an economic sense, and consider for one firm te business incentives for investing into safety. Similarly, Viscusi (1986) considers market incentives for safety.

2 Recent canges in US accounting laws ave made CEOs liable to legal malpractice if accounting information is found to be fraudulent. Tis as caused a certain panic among firms as to weter tey sould invest more in information assurance tecnologies, given tat an increase in suc investments could lead to a decrease in firms productivity. Firms, most of wic ave finite resource constraints, are tus naturally led to determine optimal investments in information assurance tecnologies versus production tecnologies. Te former can be perceived as investment to reduce te risk of legal malpractice. Tis article intends to understand te factors tat influence te trade-off between safety and productive investment during excange. Eac agent i can produce one good i, but also attaces utility to anoter good j, i, j = 1, 2, i j. Agent i as a resource R i (e.g., a capital good, or labour) wic can be converted wit unit conversion cost a i into productive effort E i, and wit unit cost b i into safety effort S i, were R = a E + bs S = ( R a E )/ b (1) i i i i i i i i i i Te production cost coefficient a i, were 1/a i is te productive efficiency, measures te resources required to maintain te agent and macinery e uses in production. Analogously, 1/b i is te safety efficiency. As a practical aid, it may be convenient to tink of good i as a consumption good suc as oil, and te resource R i as a capital good suc as oil drilling equipment. Alternatively, te product may be a consumption good suc as fis, and te resource R i a capital good suc as fising nets. Te productive effort E i is designed to generate good i, i.e., extract income from resources currently employed. Witout risk, te production function for good i or income Y i takes te simple form Yi = Ei, were is te productivity parameter, wit no need for safety effort [Hirsleifer, (1995), p.31]. Wit risk, te expected income is ri Yi = Ei( 1 f ( ri, Si) ) = Ei 1, 0 f ( ri, Si) 1 cs i i (2) were c i is a parameter tat scales te safety effort relative to te risk r i. A large c i reduces te risk more efficiently. Te risk function f(r i, S i ) increases in te risk r i, f / r i > 0, wic reduces income, and decreases in te safety effort S i, f / S i <0, wic constrains risk. Te functional form is cosen for convenient analytical solutions. Te agent can invest eavily in safety effort, wic reduces te risk considerably, but tat also reduces te production due to te budget constraint in (1). Hence, te agent faces a trade-off between E i and S i. Agent 1 exports an amount X 1 of good 1 to agent 2 in excange for an amount X 2 in return. Te agents ave equivalent Cobb-Douglas preferences for te two goods, wit utilities α 1 α α ( ) ( ) 1 α U = Y X X, U = X Y X, X = P X, α [0,1] (3) were α is te relative preference parameter for good 1 for bot agents, and P 2 is an interior terms-of-excange price denoting te price of good 2 in terms of good 1. To determine te first order conditions, we let agent 1 coose E 1 and X 1, and agent 2 coose E 2 and X 2, simultaneously and independently, to maximise utility. Tis gives

3 Ui Ri Rbr i i i / ci Rr i i = 0 Ei =, Si =, E a bc i i i i 2 ( Rc i i br i i) Y =, Rc br i i i i i ( ac i i) (4) Proposition 1: Te productive effort E i increases in te resource R i and in te risk reduction efficiency c i, and decreases in bot unit costs a i and b i, and in te risk r i. Proposition 2: Te safety effort S i increases in te resource R i and risk r i, and decreases in te unit cost b i of safety effort, and in c i. Proposition 3: Te income Y i increases in te resource R i and in c i, and decreases in bot unit costs a i and b i, and in te risk r i. Especially interesting among tese results is tat ig unit cost of safety effort reduces bot productive effort and safety effort, and tus of course reduces income. Focusing on 1 reducing b i is tus beneficial. We next insert X 2 = P2 X1 into te first equation in (3) and differentiate U 1 wit respect to X 1, and tereafter insert X1 = PX 2 2 into te second equation in (3) and differentiate U 2 wit respect to X 2. Tis gives U X U 1 2 = 0 X1 = Y1(1 α), = 0 X2 = Y2 1 X2 To determine te market equilibrium condition, inserting (5) into (3) gives te price equation X1 Y1(1 α) P2 = = (6) X Y α 2 2 Te price P 2 of good 2 in terms of good 1 is determined endogenously on a supply-demand basis. Wen agent 1 acquires more resources (R 1 increases), e produces more (Y 1 increases), exports more (X 1 increases), and te price P 2 = X 1 /X 2 increases. Conversely, wen te relative preference parameter α for good 1 increases so tat bot agents attac iger utility to good 1 tan to good 2, te demand for good 1 increases, causing a lower price P 2 of te less valuable good 2 in terms of te more valuable good 1. Inserting (5) into (3) gives te utilities α 1 α α 1 α α U = Y Y, U = Y Y (1 α) (7) Essential for te utilities is te agents preference α for goods. Agent 1 does better if good 1 is more preferred, and conversely if good 2 is preferred. α (5)

4 References Allen, B. (2000) Te future of microeconomic teory, Journal of Economic Perspectives, Vol. 14, No. 1, pp Anderton, C.H. (1999) Appropriation possibilities in a simple excange economy, Economics Letters, Vol. 63, No. 1, pp Anderton, C.H., Anderton, R.A. and Carter, J.R. (1999) Economic activity in te sadow of conflict, Economic Inquiry, Vol. 37, No. 1, pp Arrow, K.J., Cenery, H.B., Minas, B.S. and Solow, R.M. (1961) Capital-labor substitution and economic efficiency, Review of Economics and Statistics, August, Vol. 43, No. 3, pp Asce, F. and Aven, T. (2004) On te economic value of safety, Risk Decision and Policy, Vol. 9, No. 3, pp Bowles, S. and Gintis, H. (1993) Te revenge of omo economicus: contested excange and te revival of political economy, Journal of Economic Perspectives, Vol. 7, No. 1, pp Calow, P. (Ed.) (1998) Handbook of Environmental Risk Assessment and Management, Blackwell Sciences, Oxford. Feber, D.J., Feldmeier. J.M. and Crocker, K.J. (2003) Te economic effects of road safety improvements: an insurance claims analysis, Journal of Risk and Insurance, Vol. 70, No. 4, pp Fiscoff, B., Lictenstein, S., Slovic, P., Derby, S.L. and Keeney, R.L. (1981) Acceptable Risk, Cambridge University Press, Cambridge. Hausken, K. (2004) Mutual raiding and te emergence of excange, Economic Inquiry, Vol. 42, No. 4, pp Hausken, K. and Moxnes, J.F. (2005a) Te dynamics of bilateral excange and division of labor, International Journal of Modern Pysics C, Vol. 16, No. 1, pp Hausken, K. and Moxnes, J.F. (2005b) Te dynamics of multilateral excange, International Journal of Modern Pysics C, Vol. 16, No. 4, pp Hirsleifer, J. (1995) Anarcy and its breakdown, Journal of Political Economy, Vol. 103, No. 1, pp Jones-Lee, M.W. (1989) Te Economics of Safety and Pysical Risk, First Blackwell, Oxford. Kotz, H. and Scafer, H-B. (1993) Economic incentives to accident prevention: an empirical study of te German sugar industry, International Review of Law and Economics, Vol. 13, No. 1, pp Oi, W.Y. (1974) Economics of product safety, Bell Journal of Economics, Vol. 5, No. 2, pp Oi, W.Y. (1995) Safety at wat price, American Economic Review, Vol. 85, No. 2, pp Ricardo, D. (1817) On te principles of political economy and taxation, in Sraffa, P. (Ed.) wit te collaboration of M. Dobb, Te Works and Correspondence of David Ricardo, pp , Cambridge University Press, London. Rider, R. (1999) Conflict, te sire of excange: violence is te sire of all te world s values, Journal of Economic Beavior and Organization, Vol. 40, No. 3, pp Rose, N.L. (1990) Profitability and product quality economic determinants of airline safety performance, Journal of Political Economy, Vol. 98, No. 5, pp Skaperdas, S. and Syropoulos, C. (2001) Guns, butter, and openness: on te relationsip between security and trade, American Economic Review Papers and Proceedings, Vol. 91, No. 2, pp Smit, A. (1776) Te Wealt of Nations, Te University of Cicago Press. Swinbank, A. (1993) Te economics of food safety, Food Policy, Vol. 18, No. 2, pp Taylor, M.S. (1993) Quality ladders and Ricardian trade, Journal of International Economics, Vol. 34, Nos. 3 4, pp Tomas, S. (1999) Economic and safety pressures on nuclear power: a comparison of Russia and Ukraine since te break-up of te Soviet Union, Energy Policy, Vol. 27, No. 13, pp Viscusi, W.K. (1986) Market incentives for safety, Harvard Business Review, Vol. 63, No. 4, pp

5 Notes 1 See Calow (1998), Fiscoff et al. (1981), and Jones-Lee (1989) for economic approaces to safety. Muc literature focuses on public safety. See Feber et al. (2003) for te economic effects of road safety improvements, Swinbank (1993) for te economics of food safety, Tomas (1999) for economic and safety pressures on nuclear power, Rose (1990) for economic determinants of airline safety, Oi (1974, 1995) for te economics of product safety, Kotz and Scafer (1993) for economic incentives to accident prevention.