Uncertainty

Question 1

What are the properties of states of nature?

Answer 1

1. Exhaustive set (contains all states)
2. Mutually Exclusive
3. Exogenous

Question 2

What are the properties of agents?

Answer 2

1. Agents interpret all states the same
2. Probability assigned to each state
3. Probability laws satisfied

Question 3

What is the basic prospect set up?

Answer 3

P = (π, y) = (π₁, π₂, .., π_s, y₁, y₂, .., y_s)

Question 4

What are the Von Neumann & Morgenstern Axoims?

Answer 4

1. Ordering - complete & transitive preferences
2. Preferences increase with probability - prospect preferred if higher prob of good state
3. Equivalent Standard Prospect - certain level of income such that y¹ ~ P₀¹
4. Rational equivalence - Complexity of compund prospect doesnt matter
5. Context Independence - using 3 and 4 to derive the expected utility fn.

Question 5

Explain the ordering axiom of VN & M

Answer 5

Preferences are complete and transitive

Question 6

What is an equivalent standard prospect?

Answer 6

• The value of money that makes an individual indifferent between taking the money or playing the prospect.
• y_u > y¹ > y_L
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Question 7

Explain Rational Equivalence

Answer 7

• In compound prospects, agents only look at probability of final outcome
• complexity doesnt matter

Question 8

Show the derivation for Context independence

Answer 8