Hence, if a (1 — a) < 1, both the internalization and the competition effect work in the same direction, and a larger n reduces ф (and employment, output and welfare, while increasing inflation). On the other hand, if a (I — a) > 1, the internalization and the competition effects work in opposite directions; hence, ф may increase or decrease with n. Some tedious algebra reveals that ф is indeed hump-shaped in n if a > <r, where a = (1 — a)-1 and д = (1~^ /3g > 0.1()
This discussion can be summarized in:
Result 6: For a given level of CBC,
a) If the elasticity of substitution among different types of labor is sufficiently small (a < a), then economic performance and welfare are uniformly decreasing in the number of unions.
b) Otherwise, economic performance and welfare are hump-shaped in the number of unions, and there is an intermediate degree of centralization that maximizes economic performance and welfare.
Two examples of this result follow. The first involves the same parameters as in Figures 1 and 2, plus a now fixed j3g = 3.5 and a very large a — 20, so that a (1 — a) = 5.11 We then have
By contrast, if we choose a small a ~ 2, so that a (1 — a) ~ 1/2, we then have a monotonic relationship:
Result 5 is in stark contrast with the conventional wisdom and with the arguments of Calmfors and Driffill (1988), who conjecture that the relationship between economic performance and the degree of centralization of wage setting should be U-shaped.12 That conjecture is predicated upon three assumptions:
a) Internalization of aggregate effects by each union is always decreasing in n.
b) Competition in the labor market is always increasing in n.
c) The internalization effect dominates for small n, while the competition effect dominates for large n.
By contrast, our model yields results that are compatible with (a), but need not yield (b) and never yields (c).13 The reason for these differences are simple, and chiefly have to do with the way the number of unions affects the competitive structure of the labor market. As we have argued before, we can think of the elasticity of demand for union fs labor with respect to its relative wage as an index of the competitiveness of the labor market: the less elastic demand, the more monopoly power. In our setup, this elasticity may be increasing or decreasing in n. quick payday loans
And as n becomes very large labor demand does not become infinitely elastic; rather, its elasticity converges to the technological parameter a. Hence, even with infinitely many unions each retains some monopoly power, and therefore the fact that each does not internalize the consequences of its actions (precisely because n is large) is detrimental to welfare.