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# 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 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.
Document type :
Journal articles

https://hal.inria.fr/hal-01067346
Contributor : Estelle Bouzat Connect in order to contact the contributor
Submitted on : Tuesday, September 23, 2014 - 1:56:30 PM
Last modification on : Thursday, May 2, 2019 - 2:14:37 PM

### Identifiers

• HAL Id : hal-01067346, version 1
• ARXIV : 1304.5269

### Citation

Monika Dryl, Agnieszka B. Malinowska, Delfim F. M. Torres. A Time-Scale Variational Approach to Inflation, Unemployment and Social Loss. Control and Cybernetics, Polish Academy of Sciences, 2013, Special issue on: Mathematical Modelling, Fractional Calculus and Time Scales, 42 (2), pp.399-418. ⟨hal-01067346⟩

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