Consider Bob's decision problem: Sunny Cloudy Rainy Beach 2 3 2 Park 3 3 2 Mall 2 3 4 Suppose the probability of Sunny is 0.3, the probability of Cloudy is p and the probability of Rainy is 1 - 0.3 - p. What is the largest value of p for which Mall maximises Bob's expected utility (that is, Mall is at least the equal-best choice)? Round your answer to two decimal places (e.g. 0.55)
Question
Consider Bob's decision problem:
Sunny Cloudy Rainy Beach 2 3 2 Park 3 3 2 Mall 2 3 4
Suppose the probability of Sunny is 0.3, the probability of Cloudy is p and the probability of Rainy is 1 - 0.3 - p. What is the largest value of p for which Mall maximises Bob's expected utility (that is, Mall is at least the equal-best choice)? Round your answer to two decimal places (e.g. 0.55)
Solution 1
To solve this problem, we need to calculate the expected utility for each location (Beach, Park, Mall) and find the value of p for which the Mall has the highest expected utility.
The expected utility for each location is calculated by multiplying the utility of each weather condition by the probability of that weather condition, and then summing these products.
For the Beach, the expected utility is: 20.3 + 3p + 2*(1 - 0.3 - p) = 0.6 + 3p + 2 - 0.6 - 2p = 2 + p
For the Park, the expected utility is: 30.3 + 3p + 2*(1 - 0.3 - p) = 0.9 + 3p + 2 - 0.6 - 2p = 2.3 + p
For the Mall, the expected utility is: 20.3 + 3p + 4*(1 - 0.3 - p) = 0.6 + 3p + 4 - 1.2 - 4p = 3.4 - p
We want the Mall to have at least the same expected utility as the Beach and the Park, so we set up the following inequalities:
2 + p <= 3.4 - p 2.3 + p <= 3.4 - p
Solving these inequalities for p gives:
p >= 0.7 p >= 0.55
The largest value of p that satisfies both inequalities is 0.55. Therefore, the largest value of p for which the Mall maximises Bob's expected utility is 0.55.
Solution 2
To solve this problem, we need to calculate the expected utility for each location (Beach, Park, Mall) and find the value of p for which the Mall has the highest expected utility.
The expected utility for each location is calculated by multiplying the utility of each weather condition by the probability of that weather condition, and then summing these products.
For the Beach, the expected utility is: 20.3 + 3p + 2*(1 - 0.3 - p) = 0.6 + 3p + 2 - 0.6 - 2p = 2 + p
For the Park, the expected utility is: 30.3 + 3p + 2*(1 - 0.3 - p) = 0.9 + 3p + 2 - 0.6 - 2p = 2.3 + p
For the Mall, the expected utility is: 20.3 + 3p + 4*(1 - 0.
Similar Questions
Consider the following decision problem of Alice:Sunny Cloudy RainyBeach 1 2 1Park 2 2 1Mall 1 2 3Suppose the probability of Sunny is 0.4 the probability of Cloudy is p ∈ [0, 0.6] and the proba-bility of Rainy is 0.6 − p. For what values of p is Mall an expected utility maximizer?[Write your answer as an interval; e.g.: [0.2, 0.4] or (0.3, 0.5], etc.]
Which is true for the following decision problem of Alice? Sunny Cloudy RainyBeach 1 2 2Park 2 3 3Mall 1 3 1 A. Beach is a strongly dominated choice for Alice B. Alice has no strongly dominated choices C. Mall is a strongly dominated choice for Alice D. Park is a strongly dominant choice for Alice
Below is the utility preferences for an individual: Movies Marginal Utility of Movies Marginal Utility of Movies per Dollar (PM=$10)PM=$10Books Marginal Utility of Books Marginal Utility of Books per Dollar (PB=$5)PB=$51 100 10 1 45 92 70 7 2 40 83 40 4 3 30 64 10 1 4 15 3 What is the utility-maximizing consumption bundle if the individual has $25 to spend?Multiple choice question.1 movie and 3 books5 books2 movies and 3 books2 movies and 1 book
Assume that product Alpha and product Beta are both priced at $1 per unit and that Ellie has $20 to spend on Alpha and Beta. She buys 8 units of Alpha and 12 units of Beta. The marginal utilities of the last unit of Alpha and Beta that she purchases are 40 utils and 20 utils, respectively. This indicates thatMultiple ChoiceEllie should make no change in consumption.given another dollar, Ellie should buy an additional unit of Beta.in order to maximize utility, Ellie should buy more Beta and less Alpha.in order to maximize utility, Ellie should buy more Alpha and less Beta.
Assume Alice’s preferences satisfy the axioms of the expected utility theorem. A risky assetyields $8 utility in a bull market, while it yields $3 utility or $0 utility with equal probability in abear market. The probabilities of a bull or a bear market are the same (i.e., 50%). What is Alice’sexpected utility from the risky asset?[Write your answer as a number with a maximum of two decimals, lik
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.