(5) RSCE = [[Sigma].sub.i] [differentials]lnTC(Q)/[differentials] [lnQ.sub.i],
If RSCE equals 1.0, production of Q exhibits constant returns to scale, whereas RSCE less than (greater than) 1.0 indicates increasing (decreasing) returns to scale.
Scale economies for a give vector or outputs (e.g [Q.sup.B] on OX in Figure 1(a)) is commonly measured by ray scale economies (RSCE) which are defined as
A complete analysis of an industry's cost manifold, as shown in Figure 1 (b), requires, therefore, measures of RSCE, PSSCE, and [CC.sub.i,j] be estimated for output bundles differing in a scale along given output ray (e.g.
Fortunately, the formulations of RSCE, PSSCE, and [CC.sub.i,j] in Equations (2), (3), and (4), respectively, permit estimates of scale economies and cost complementarities for various output vectors along the overall cost manifold.
For example, agency stock and mutual companies in the fourth quartile exhibit relatively large and statistically significant ray scale economies, i.e., RSCE = 0.704 for agency mutual companies and RSCE = 0.731 for agency stock companies.
With regard to intergroup comparisons, the results show that stock companies generally exhibit lower ray scale economies (i.e., have a higher measure of RSCE) than mutual companies.