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Artículos

Vol. 16 No. 54 (2021)

A small contribution from the rational theory of consumer to solving differential equations first-order inhomogeneous with initial and final conditions

DOI:
https://doi.org/10.29201/eseconomia.v16i54.49
Submitted
June 1, 2024
Published
January 12, 2021

Abstract

This investigation based on the theory of the rational consumer answers the following question: What condition must function yt
satisfy for the inhomogeneous first-order differential equation t tt x xy  = + α with boundary conditions 0 0y 0 T x x > = to have a unique solution? To do this, a problem of a rational consumer that maximizes his total discounted utility (with his subjective discount rate) on a non-perishable consumer good, in continuous time in a finite planning horizon, subject to the discounted present value (with the real interest rate) of his planned consumption is equal to his initial (positive) wealth and does not leave inheritance.

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