Microeconomics 5: Intro to Uncertainty; Risk and Insurance

Question 1

What is uncertainty?

Answer 1

It is a rule or function consisting of outcomes or states of nature (from a list of outcomes)
and probabilities linked to those outcomes

Question 2

Describe what consumers’ choice is based on

Answer 2

Consumer’s choice is based on probability distribution:
 For each of the states of nature the rational representative consumer will have a contingency
plan or a contingent consumption plan.
 The representative consumer will have preferences over different contingent
consumption plans.
 We will model the choice of the representative consumer in the same way: the best
consumption plan he/she can afford.

Question 3

Describe variables which can take only two values, with
associated distribution of probabilities

Answer 3

We need to think in terms of probabilities:
 Suppose there are only two possible outcomes. We can then note:
1 > Pr 𝑋 , Pr 𝑌 > 0 and Pr 𝑋 + Pr 𝑌 = 1
Pr (𝑉 = 𝑣) = {Pr(𝑣bottom right1) , 𝑖𝑓 𝑉 = 𝑣1
{1 − Pr(𝑣bottom right1) , 𝑖𝑓 𝑉 = 𝑣2

Question 4

Using wealth as an example how can you define probability distribution of a factor?

Answer 4

We can define wealth in an uncertain (risky) situation: we can define the
expected value of wealth, if we know the probabilities distribution:
E[W] = Uppercase Epsilon with “n” on top and “𝑖=1” underneath 𝑝bottom right𝑖𝑤bottom right𝑖
 Where 𝑝bottom right𝑖 is the probability associated to wealth 𝑤bottom right𝑖 obtained in situation 𝑖.

Question 5

Describe what consumers’ utility will depend on in an uncertain environment

Answer 5

 In an uncertain environment, consumer’s utility will depend not only on the
consumption, but also on the probability distribution.
 Suppose two states of nature, first one with consumption 𝑐1 which occurs
with probability 𝜋1 and second one with consumption 𝑐2 which occurs with
probability 𝜋2.
 Consumer’s utility will be:
𝑈(𝑐bottom right1, 𝑐bottom right2 , 𝜋bottom right1, 𝜋bottom right2)