Do profit maximizers take cold showers?

Transcription

1 Bond Univerity Bond Buine School Publication Bond Buine School Do profit maximizer take cold hower? Neil Campbell Jeffrey J. Kline Bond Univerity, Follow thi and additional work at: Recommended Citation Campbell, Neil and Kline, Jeffrey J., "Do profit maximizer take cold hower?" (2001). Bond Buine School Publication. Paper Thi Working Paper i brought to you by the Bond Buine School at epublication@bond. It ha been accepted for incluion in Bond Buine School Publication by an authorized adminitrator of epublication@bond. For more information, pleae contact Bond Univerity' Repoitory Coordinator.

2 1 Do profit maximizer take cold hower? Neil A. Campbell a, J. Jude Kline b, *, a Department of Applied and International Economic, Maey Univerity, Private Bag 11222, Palmerton North, New Zealand b School of Buine, Bond Univerity, old Coat, Queenland, Autralia March 2001 Abtract A firm take a "cold hower" if removal of a protective ubidy induce invetment in a cot-reducing technology. We how that if the invetment lower marginal cot everywhere, then profit maximizer never take cold hower. However, if the invetment doe not lower marginal cot everywhere, a profit maximizer may take a cold hower. Keyword: Protection; Cold Shower JEL claification: F13 *Correponding author. Tel.: ; Fax: addre: Jeffrey_Kline@Bond.edu.au (J.J. Kline).

3 2 1. Introduction There i now a reaonably extenive literature on the idea that taking protection away from a firm can omehow improve it performance (a cold hower) 1. In thi paper we will ay that a firm i ubjected to a cold hower whenever it incentive to invet in a cot-reducing technology i heightened by a reduction in protection. Theoretical contribution to thi literature typically either deviate from profit-maximizing firm, ue trategic effect, or ue limited liability in order to obtain the cold hower effect. Corden (1974) and Martin (1978) ue a Scitovky-type 2 framework with a utilitymaximizing, but not profit-maximizing, entrepreneur. Vouden and Campbell (1994) and Horn, Lang and Lundgren (1995) ue a principal-agent framework. Campbell (1998) ue limited liability to generate a cold hower. Rodrick (1992) and Lambon (2000) ue trategic (game-theoretic) effect from multiple invetor where the incentive for each to invet i affected by how much the other invet. In thi note we conider a ingle profit-maximizing firm protected by a per unit ubidy with the option of inveting in a cot-reducing technology. We provide a ufficient condition on the cot-reducing technology to guarantee that cold hower never occur when the ubidy i removed. The condition i that the technology lower marginal cot everywhere. Thi emphaize that cold hower are difficult to obtain in a profitmaximizing etting without trategic effect. We then ue thi reult to contruct an example of a cot-reducing invetment that generate a cold hower. 1 For a dicuion of thi literature ee Campbell (1998). 2 Modeling the entrepreneur or manager a a utility maximizer rather than a profit maximizer i a tradition which goe back to Scitovky (1943).

4 3 2. Analyi Conider a ingle dometic firm producing a good that i old at the world price p. In addition to the price, the firm receive a ubidy of on each unit old. The firm ha the option of paying I to invet in a new technology. The invetment will be ucceful with probability g (0,1]. If the new technology i ucceful then the firm cot function change from C (x) to C (x) where C i ( x) > 0, C i ( x) > 0 for i=,. If the new technology i not ucceful, then the cot function continue to be C (x). It i aumed that a ucceful invetment lower total cot, i.e., C ( x ) < C ( x ) where x and x are the repective profit-maximizing choice of output under ubidy > 0. Under ubidy the profit level i π i = ( p + ) xi C( xi ) for i =,. iven a ubidy level, we define the firm incentive to invet A a the difference between expected profit from inveting and expected profit from not inveting: A [ gπ + (1 g) π I ] π The following quetion arie: Will a profit-maximizing firm having rejected an invetment at a ubidy level > 0, ever chooe to invet if the ubidy i reduced? In anwer to thi we can ay the following: Propoition 1. If the invetment lower expected marginal cot everywhere, C ( x) < C ( x) for all x, then the incentive to invet rie with the ubidy, A = g( x x ) > 0.

5 4 Proof Since π = ( p + ) x C ( x ), π = x by the envelope theorem. Similarly, π = x. Therefore, A = g( x x ). Now with the repective output quantitie choen to maximize profit, we have the following marginal revenue equal marginal cot relationhip: ( p + ) = C ( x ) and ( p + ) = C ( x ). Therefore, C ( x ) = C ( x ). Now if C ( x) < C ( x) for all x, then we mut have x < x ince C > 0. Thi implie A = g( x x ) > 0 Q.E.D. The intuition i traightforward. If the ubidy i increaed by $1, then a profitmaximizing firm will benefit by one dollar for each unit it i currently producing. Profit maximization implie that a mall change in the ubidy will have a negligible effect on profit via output repone. If the firm chooe to invet, the increaed ubidy net it $ x with probability g and $ x with probability (1-g). If the firm doen t invet it get an addition $ x for ure. Since the cot of invetment I doe not change with the ubidy, the incentive to invet will rie with the ubidy if and only if

6 5 gx + ( 1 g) x > x, or equivalently, g ( x x ) > 0. But clearly x > x whenever the new technology ha lower marginal cot. Thi reult how that obtaining a cold hower in a profit-maximizing etting will require the cot-reducing technology to raie marginal cot omewhere. We now give one uch example. We aume, for implicity, that the invetment i alway ucceful (g=1). Thi not only lightly implifie the analyi, but alo emphaize that we do not require uncertainty to achieve a cold hower reult. The world price p = 20 and the cot of the 2 x invetment I = 20. The old and the new technologie are: C ( x) = + 150, 2 and ( ) = x 2 C x ne might imagine a cae where an invetment lead to a technology with a lower overhead and thu lower total cot, but a higher marginal cot. When = 1 the invetment i rejected ince: 1 x = 21, x = 10.5, π = 70.5, π = 90.25, A = However, when =0 the invetment i accepted ince: 0 x = 20, x = 10, π = 50, π = 80, A = 10. Let ee why the reduction in the per unit ubidy lead to the cold hower. Since the marginal cot of the old technology i lower, the firm produce more with that technology than with the new technology. Since the ubidy i paid per unit of output, the ubidy benefit uer of the old technology more. When the ubidy i removed, the firm weigh the true benefit and cot and opt for the new technology. Finally, we remark that the choice of competition doe not eem to be relevant to the reult of thi paper. They hold for a ubidy ued in non-competitive market a well.

7 6 Firt conider an oligopoly of firm in the home country elling in a competitive world market. The marginal benefit to one of thee firm of a dollar rie in the ubidy will till be equal to the output level produced by the firm and Propoition 1 hold. Next, conider a ubidized dometic firm in an oligopoly world market with quantity competition. Here again the marginal benefit to the dometic firm of a dollar rie in the ubidy equal the output level produced by the firm. The key reaon for thi irrelevance i that we are only conidering invetment by one firm, or if you like, non-trategic invetment. Rodrik (1990) and Lambon (2000) howed cold hower can come from trategic invetment, o Propoition 1 might fail in that etting.

8 7 Reference Campbell, N.A., Can We Believe in Cold Shower? Journal of Economic Integration 13, Corden, W.M., Trade Policy and Economic Welfare, Clarendon Pre, xford. Horn, H., Lang, H. and Lundgren, S., Managerial Effort Incentive, X-Inefficiency and International Trade. European Economic Review 39, Lambon, V. E., Sunk Cot, Entry, and the Timing of Cot-Reducing Invetment. International Journal of Indutrial rganization 18, Martin, J.P., X-Inefficiency, Managerial Effort and Protection. Economica 45, Rodrik, D., Cloing the Technological ap: Doe Trade Liberalization Really Help? In: Helleiner,. (Ed.), Trade Policy, Indutrialization and Development: New Perpective, xford Univerity Pre, xford, pp Scitovky, T., A Note on Profit Maximiation and It Implication. Review of Economic Studie 11, Vouden, N.J. and Campbell, N.A., The rganizational Cot of Protection. Journal of International Economic 37,