Demand For Insurance - DONE

Question 1

State contingent budget constraint

Answer 1

Takes into account different possible outcomes (hence why it is contingent on the state of nature)

Question 2

How to express the state-contingent budget constraint and its components:

Answer 2

Accident (a) or no accident (na)

Probability of a is πa probability of na is πna

Ca is consumption value in a, Cna is value in na

L is loss of wealth

Y is cost of insurance per wealth unit

M is wealth.

K is amount of insurance bought.

Question 3

State contingent budget constraints:
When no accident (for Cna)

Answer 3

Cna= M - yK

Question 4

When accident has occured

Answer 4

Ca= m - L + (1-y)K

Question 5

Now we have Cna and Ca initial expressions, what can we do?

Answer 5

Rearrange last expression to find K, and sub the K back into the Cna expression (first one)

Cna = m-y (Ca - m + L)/(1-y)

Or express as
Cna = (m-yL)/(1-y) - y/1-y Ca

Better when doing graphically as -y/1-y is slope

Question 6

So these were consumption with insurance bought.

If no insurance, what is expression for Ca and Cna

Answer 6

Ca = m - L (since accident occured so we have a loss L)

Cna = m (no loss since no accident)

Question 7

What is important about the diagram

Answer 7

Bold part highlights where insurance is being bought

Faint part shows no insurance being bought as no accident.

Question 8

How are indifference curves different now we have uncertainty?

Answer 8

They represent expected utility now.

Question 9

How to find MRS for indifference curves

Answer 9

-πα MU(Ca)
/
πna MU(Cna)

a is accident occurring
Na is not occurring
π is probability of the state occuring

Question 10

So now we have the state-contingent budget constraint and expected utility indifference curves.

How to find the optimal contingent consumption bundle

Answer 10

Y/1-y =
πα MU(Ca)
/
πna MU(Cna)

Slope of budget constraint = MRS (slope of IC)
Where the indifference curve and budget constraint meet tangent