 Decision Theory Questions

Subject Mathematics Decision Theory

Question

You are risk neutral, and care only about your income.

With probability p, you will catch a disease that reduces your income from y, its level when you are healthy, to y-k, where k > 0. A vaccine is available, at cost c, that reduces the probability of your catching the disease from p to q<p.

a) Suppose that you know the values of p, q, y, k, and c, so that the only thing about which you are uncertain is whether you will catch the disease. Write the condition that determines whether or not you should buy the vaccine.

b) Now suppose that you know y, k, and c, but neither p nor q . Which is more relevant to your decision, the percentage amount by which the vaccine reduces the probability of catching the disease (what is usually reported in the press), or the absolute amount? Explain.

c) How do your answers to (a) and (b) change if you are a risk-averse expected-utility maximizer?

Solution Preview

This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.

Expected (Net) Income:
(1 - p)y + p(y – k) No Vaccine
(1 – q)(y – c) + q(y – c – k) Vaccine

Vaccinate if:
(1 - p)y + p(y – k) < (1 – q)(y – c) + q(y – c – k)

(1 – p + p)y – pk < (1 – q + q)(y – c) – qk...

This is only a preview of the solution. Please use the purchase button to see the entire solution

Related Homework Solutions

Forensics \$10.00
Mathematics
Forensics
Decision
Case
Investigation
Confidence
Sample
Deviation
Hypothesis
Statistics Problem \$8.00
Statistics
Mathematics
Probability
Events
Workdays
Data
Symbols
Functions
Binomial Distribution
Conditions
Mixed Strategy Equilibrium \$18.00
Mathematics
Game Theory
Mixed Strategy Equilibrium
Payoff
Algebra
Matrix
Computation
Functions
Stunt Number
Digits
R Programming Problems \$75.00
Statistics
R Programming
Mathematics
Codes
Functions
Data Sets
US
Graphics
Density
Predictors
Reports
Columns
Counts
Tables
Applied Statistics Questions \$40.00
Applied Statistics
Health
Pollution Levels
Pulmonary Function Tests
Cigarettes
Patients
AUC
Predictive Model
Estimation
Cross Validation
Mathematics
R Programming
Introduction to Operations Research Questions \$40.00
Mathematics
Algebra
Operations Research
Microsoft Excel
Equations
Functions
Variables
Statements
Conditions
Graphs
Tables
Products
Integers
Machines
Profit
Feasible Solution
Live Chats