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Exponential Utility Function for different risk profiles. In economics and finance, exponential utility is a specific form of the utility function, used in some contexts because of its convenience when risk (sometimes referred to as uncertainty) is present, in which case expected utility is maximized. Formally, exponential utility is given by:
A possible solution is to calculate n one-dimensional cardinal utility functions - one for each attribute. For example, suppose there are two attributes: apples and bananas (), both range between 0 and 99. Using VNM, we can calculate the following 1-dimensional utility functions:
Therefore, the preferences at t = 1 is preserved at t = 2; thus, the exponential discount function demonstrates dynamically consistent preferences over time. For its simplicity, the exponential discounting assumption is the most commonly used in economics. However, alternatives like hyperbolic discounting have more empirical support.
A single-attribute utility function maps the amount of money a person has (or gains), to a number representing the subjective satisfaction he derives from it. The motivation to define a utility function comes from the St. Petersburg paradox: the observation that people are not willing to pay much for a lottery, even if its expected monetary gain is infinite.
Isoelastic utility for different values of . When > the curve approaches the horizontal axis asymptotically from below with no lower bound.. In economics, the isoelastic function for utility, also known as the isoelastic utility function, or power utility function, is used to express utility in terms of consumption or some other economic variable that a decision-maker is concerned with.
Leontief utility functions represent complementary goods. For example: For example: Suppose x 1 {\displaystyle x_{1}} is the number of left shoes and x 2 {\displaystyle x_{2}} the number of right shoes.
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A Cobb-Douglas utility function (see Cobb-Douglas production function) with two goods and income generates Marshallian demand for goods 1 and 2 of = / and = /. Rearrange the Slutsky equation to put the Hicksian derivative on the left-hand-side yields the substitution effect: