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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.
Consider the portfolio allocation problem of maximizing expected exponential utility [] of final wealth W subject to = ′ + (′) where the prime sign indicates a vector transpose and where is initial wealth, x is a column vector of quantities placed in the n risky assets, r is a random vector of stochastic returns on the n assets, k is a vector of ones (so ′ is the quantity placed in the ...
In microeconomics, the expenditure function represents the minimum amount of expenditure needed to achieve a given level of utility, given a utility function and the prices of goods. Formally, if there is a utility function u {\displaystyle u} that describes preferences over n goods, the expenditure function e ( p , u ∗ ) {\displaystyle e(p,u ...
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.
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.
The graph shows the maximum amount of one person's utility given each level of utility attained by all others in society. [1] The utility–possibility frontier (UPF) is the upper frontier of the utility possibilities set, which is the set of utility levels of agents possible for a given amount of output, and thus the utility levels possible in ...