A Time-Scale Variational Approach to Inflation, Unemployment and Social Loss

TL;DR

This paper introduces a unified time-scale variational framework to optimize social loss by balancing inflation and unemployment, providing new insights into classical models with real data applications.

Contribution

It develops a novel time-scale variational approach that unifies continuous and discrete models in economic analysis of inflation and unemployment tradeoffs.

Findings

Unifies continuous and discrete variational models in economics.

Provides new insights into classical inflation-unemployment models.

Applied to real data, enhances understanding of social loss optimization.

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 consists to write 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 $\pi$, to rewrite the social loss function as a function of $\pi$. The answer is achieved by applying the theory of the calculus of variations in order to find an optimal path $\pi$ that minimizes the 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 available results in the literature. Moreover, the new formalism allow us to obtain new insights to the classical models when applied to real data of inflation and unemployment.