Policonomics » LPsection » Consumption I: Utility maximisation

Consumption I: Utility maximisation

Summary

In this Learning Path we look at consumer behaviour from a theoretical perspective, trying to solve the basic problem we all face every day: how to get as much of what we want or need without blowing our budget.

The basics:

Utility and budget:

Consumption duality I:

Utility maximisation

Utility maximisation must be seen as an optimisation problem regarding the utility function and the budget constraint. These two sides of the problem, define Marshallian demand curves.

An individual is therefore faced with the following problem: faced with a set of choices, or baskets of goods, and a fixed budget, how to choose the basket which maximises their utility?

If we know an individual’s utility function, and we know their budget, we have the two restrictions necessary to maximise their utility. This can be done graphically, with the point where budget and utility function meet defining an optimum, as shown in the adjacent figure.

It can be also done mathematically, through a Lagrangian, where the first derivatives determine a system of equations that can be resolved by submitting our utility function to the restriction presented by the budget:

Video – Utility maximisation:

We have started by learning about the very basics of consumer theory. How much we like (or need) goods configure utility functions representing our preferences. This utility functions, when contrasted with our budget constraint, lead us to resolve our maximisation problem: get the most utility with a given budget. However, we could ask ourselves: what if I wanted to get a given utility for the lowest possible cost? How price changes affect our wellbeing? Is there some way to actually draw these utility functions?

Consumption I: Budget constraint