A time-scale variational approach to inflation, unemployment and social loss

Abstract

Both inflation and unemployment inflict social losses. When a tradeoff exists between the two, what would be the best combination of inflation and unemployment? A well known approach in economics to address this question is writing the social loss as a function of the rate of inflation p and the rate of unemployment u, with different weights, and then, using known relations between p, u, and the expected rate of inflation π, to rewrite the social loss function as a function of π. The answer is achieved by applying the calculus of variations in order to find an optimal path π that minimizes total social loss over a given time interval. Economists dealing with this question use a continuous or a discrete variational problem. Here we propose to use a time-scale model, unifying the results available in the literature. Moreover, the new formalism allows for obtaining new insights into the classical models when applied to real data of inflation and unemployment.