The formula to calculate expected utility is:
\[ \text{E(u)} = \text{P1} \times \text{Y1}^{1.5} + \text{P2} \times \text{Y2}^{2.5} \]
Where:
Expected utility is a concept used in decision theory to measure the value or desirability of different outcomes. It enables individuals to make rational choices by considering the probabilities and utilities associated with each possible outcome.
Utility refers to the subjective satisfaction or preference an individual assigns to a particular outcome. It represents the individual’s evaluation of the desirability or worthiness of that outcome. The concept of utility acknowledges that people have different preferences and values, allowing decision-makers to quantify and compare these preferences.
The expected utility considers the probabilities of different outcomes and the utilities associated with those outcomes. It allows decision-makers to evaluate the potential outcomes of a choice by multiplying each outcome’s utility by its probability of occurring. By summing these expected utilities across all possible outcomes, decision-makers can determine the overall expected utility of a particular choice.
Expected utility theory also aligns with the principle of rationality. It suggests that individuals should choose the option that maximizes their expected utility, as they seek to optimize their well-being or satisfaction.
Let's assume the following values:
Using the formula:
\[ \text{E(u)} = 0.4 \times 100^{1.5} + 0.6 \times 200^{2.5} = 0.4 \times 1000 + 0.6 \times 32000 = 400 + 19200 = 339811 \]
The expected utility is 339811.