Chez Paul Is Contemplating Either Opening Another Restaurant or Expanding

question 22

Essay

Chez Paul is contemplating either opening another restaurant or expanding its existing location.The payoff table for these two decisions is: $$\begin{array} { l | c c c } & &{ \text { State of Nature } } \\\text { Decision } & s _ { 1 } & s _ { 2 } & s _ { 3 } \\\hline \text { New Restaurant } & - \$ 80,000 & \$ 20,000 & \$ 160,000 \\\text { Expand } & - \$ 40,000 & \$ 20,000 & \$ 100,000\end{array}$$ Paul has calculated the indifference probability for the lottery having a payoff of $160,000 with probability p and $80,000 with probability (1p)as follows: $$\begin{array} { r c } \text { Amount } & \text { Indifference Probability } ( p ) \\\hline - \$ 40,000 & .4 \\\$ 20,000 & 7 \\\$ 100,000 & .9\end{array}$$
a.Is Paul a risk avoider, a risk taker, or risk neutral?
b.Suppose Paul has defined the utility of $80,000 to be 0 and the utility of $160,000 to be 80. What would be the utility values for $40,000, $20,000, and $100,000 based on the indifference probabilities?
c.Suppose P(s₁) = .4, P(s₂) = .3, and P(s₃) = .3. Which decision should Paul make? Compare with the decision using the expected value approach.

---

Definitions:

Headaches

A common physical ailment characterized by pain in any region of the head, varying greatly in intensity, pattern, and cause.

Null Hypothesis

A default hypothesis that there is no significant difference or effect, typically to be tested against an alternative hypothesis.

Employment Status

Refers to an individual's current work situation, which can be categorized into employed, unemployed, or out of the labor force.

Independence

Independence in statistics means that two events have no influence on each other, indicating that the occurrence of one event does not affect the probability of the other occurring.