Lecture 1- Year 1 Recap

Question 1

How do we write out ‘A implies B’ and what does this mean?

Answer 1

A⇒B, means the set of states where A is a subset of B so if B occurs A has to also occur.

Question 2

X=3 is a sufficient condition for x^2=9 explain this

Answer 2

If we mix the two scenarios A and B with a third one the preference ordering of the two lotteries does not depend on the third.

Question 3

If A and B are equivalent how would we write this out?

Answer 3

A

Question 4

Using an example explain what the contrapositive is

Answer 4

The contrapositive is the logical twin of a statement, for example if A ⇒ B the contrapositive would be A’⇒B’

Question 5

What does upside down A and inverted E mean in negation

Answer 5

Upside down A: Means ‘for all’ or ‘for every’

For the inverted E it means ‘there exists’

Question 6

What is completeness?

Answer 6

Consumers are able to compare and rank bundles, they are able to state whether A>B or B>A

Question 7

What is transitivity?

Answer 7

Assume transitive preferences if a>b b>c and a>c

Question 8

What is monotonicity?

Answer 8

Consider 2 scenarios A and B. A would be preferred over B if it assigns a higher probability of getting a higher score. This is the idea that more is better so you would want the outcome that gives you more.

Question 9

What is continuity?

Answer 9

For any two lotteries small changes in probabilities does not change the ordering between lotteries.

Question 10

What is independence?

Answer 10

If we mix the two scenarios A and B with a third one the preference ordering of the two lotteries does not depend on the third.

Question 11

What are the three steps in solving an optimisation problem

Answer 11

1. Find the MRS
2. Set the MRS=Price ratio
3. Plug the equation into the BC and solve for X1 and X2