• Completeness: there always exists a preference relation between two elements.
• Transitivity: the preference relation is transitive.
• Local Nonsatiation: there always exists, locally, an elements that is prefered over an element.
  • Often the strong monotonicity is assumed under the name of nonsatiation.

A consumption set parametrized by the quantities of each goods is considered.

A point in the consumption set is called a bliss point if it is prefered over all the other points.

The property of local nonsatiation implies the nonexistence of bliss point.

• There's only one indifference curve that contains a consumption bundle.

Assuming strong monotonicity of preference,

• Higher indifference curve is prefered
• Indifference curve are downward sloping
• They never cross one another

Maginal utility is the utility of a next unit of goods given some amount of goods is already consumed. This concept is only meaningful when cardinal utility is used.

If two state \( S_1, S_2 \) are distinguishable by just one quantifiable variable \( g \), the marginal utility of the change in \( g \) is given by:

\begin{equation*} \frac{\Delta U}{\Delta g}\bigg|_{\mathrm{c.p.}}. \end{equation*}

It is often assummed that the limit

\begin{equation*} \frac{\partial U}{\partial g} = \lim_{\Delta g \to 0} \frac{\Delta U}{\Delta g}\bigg|_{\rm c.p.} \end{equation*}

exists, and the diminishing marginal utility corresponds to

\begin{equation*} \frac{\partial^2 U}{\partial g^2} < 0. \end{equation*}

It is a function of any parameters that describe the outcomes, that describes the order of happiness between outcomes

• the definite value of the utility function does not matter just like temperature.
• the percentage increase of utility function is meaningless.