Simultaneous Substitution and Utility Maximization: An MRS Analysis with a Fixed Budget

Abstract

This paper models consumer choice, allowing simultaneous buying and selling of two goods. Unlike standard
models, consumers endogenously determine their trading position. A fixed budget component represents
savings or borrowing. Using a Cobb-Douglas utility function, we show optimal consumption requires equating
the Marginal Rate of Substitution (MRS) with an effective price ratio, incorporating buy/sell decisions.
Deviations from this condition drive simultaneous substitution, increasing utility. The model highlights how
consumers actively reshape their consumption bundles through trade, offering a more realistic perspective than
traditional approaches.