Public Finance

Theoretical Tools of Public Finance: Constrained Utility Maximization

3

3.1 Preference and Indifference Curves 3.2 Utility Mapping of Preferences

3.3 Budget Constraint
3.4 ConstrainedChoices 3.5 The Effect of Prices Changes

Constrained Utility Maximization
Utility Function. A mathematical function representing an individual’s set of preferences, which translates her well-beingfrom different consumption bundles into units that can be compared in order to determine choice.

Constrained Utility Maximization. The process of maximizing the wellbeing (utility) of an individual,subject to its resources (budget constraint). Models Mathematical or graphical representations of reality.

Constrained Utility Maximization
3.1 Preferences and Indifference Curves
 FIGURE 1Constrained Utility Maximization
3.1 Preferences and Indifference Curves

Indifference Curve (IC). A graphical representation of all bundles of goods that make an individual equally well off.Because these bundles have equal utility, an individual is indifferent as to which bundle he consumes.

Indifference curves have two essential properties, both of which follow from the more-is-betterrule:

1. Consumers prefer higher indifference curves. 2. Indifference curves are always downward sloping.

Constrained Utility Maximization
3.1 Preferences and Indifference Curves
 FIGURE 2Constrained Utility Maximization
3.2 Utility Mapping of Preferences
Underlying the derivation of indifference curves is the notion that each individual has a well-defined utility function.

Autility function is some mathematical representation

U = f(X1, X2, X3, …),
where X1, X2, X3, and so on

are the goods consumed by the individual and
f

is some mathematical function thatdescribes how the consumption of those goods translates to utility.

Constrained Utility Maximization
3.2 Utility Mapping of Preferences
3.2.1 Marginal Utility

Marginal utility (MU). The additional...