Three economic applications of Chebyshev's algebraic inequality

Abstract

We call the economists' attention to Chebyshev's algebraic inequality and prove three economic theorems with its help: (i) Laspeyres' volume index is greater than Paasche's volume index if there is an inverse relation between price and volume changes; (ii) in a pension model of overlapping cohorts, PAYG is better than CR iff the growth rate is higher than the interest rate, assuming that the utility function is of Leontief type and the wage/weight ratio is non-increasing with age; (iii) the mean consumption age is a non-decreasing (non-increasing) function of the elasticity of substitution for a(nother) large class of ACRRA utility functions, implying equivalence (ii) iff the elasticity of substitution is low (high).