Wirtschaft und Gesellschaft 19. Jahrgang (1993), Heft 4 the wage {or vectar af wages) in other industries. We denote ihe elasticity of the price wjth respect ta wage in the same indusLry by 11 = (dp/iJw) (wlp) where 0::;;; 11 < 1. Let the elasticity of the pri<.:e with respect to wages in other industries be 71"' =(iJp/dw?) (w"'/p) with 17* ::;;17. While 1J must be gre.ater than or equal to zera, 17* may be either positive or negative de­ pending on whether the goods produced in other sectors are substitutes or complements. In addition, let the elasticity of the consumer price in­ dex with respect to each product price be denoted by () !!! (dq/dp) (qlp) with 0 < 9 s; 1. Now, the solution to the union's maximization problern is given by the condition that its marginal rate of substitution bctwcen higher wages and higher employment is equal to a fraction of thc morgi­ nal loss o! emplayment: auta Cw/q) _ -hL' (w!p) au;aL - where h 1-n = 1 - (97} + Ll - B]r]*) ::;;; 1. [3J Obscrve that the fraction h is thc ratio of two elasticities. The numera­ tor is the elastidty of the real product wage with respect to the nominal wage chosen by the union. The denominator is the corresponding elasti­ city af the real consumer wage. If the two elasticities are the same, then h = 1 and thc wage implied by equation {3] is the same as the wage im­ plied by equation [2]. If the elasticity of the real consumer wage is grea­ tcr tha.n the elasticity of the real product wage, however, then h < 1 and the union gives less weight to emplayment loss than it would if prices were exogenous. Thus, the lawer is h, the higher t.he union's preferred wage. The weight given to employment loss, h., may be a non-monotanie function of the level at which wages are set. Consider, first. the case wüh perfectly competitive firms. If wages are set at the plant orfirm level, lhe wage in any single unit has a negl igible effect on product prkes, or 17 = 17* = 0 which implies that h = I. With firm-level bargaining in a competitive product market, prices are exogenaus from the bargainers' paint of view. To consider the opposite end of rhe spectrum, suppose wages are set at the national Ievel. Then all prices will increase as the wage increascs and B = 1 which again implies that h = 1. With fully centraUzed bargai­ ning, as with finn-level bargaining, both the rea) consumer wage and the real product wage will be increased in the samc propartion. The tra­ de-off between a highel' real consumer wage and employment rcmoins the same. Thus, the unions' optimal wage with national-lcvcl bargai­ ning is idt::ntical to the unians' optimal wage with local borgaining. In both t:ases, the unians bear the full consequences of a higher nominal wage. 428