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.
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