Question 3: Suppose an individual has the following utility over consumption: u(x) = x
1
2 . The
individual currently earns $2,500 per month, which is spent to finance consumption. Suppose the
individual is ofered a job with a new internet company. The new position will pay the individual
$6,400 per month, but there is a risk that the company will fail. In the event of a failure, an event
which happens with probability q, the individual will lose her job and fnd herself earning only $400
per month.
a) Write the equation for the individual's expected utility if she takes the internet frm job. Plot
both endowments in state-space and draw a hypothetical indifference curve.
b) Calculate the value of q such that the individual is indifferent between the two jobs. That is, find
the value of q such that the current job is the certainty equivalent of the internet job. Suppose
the probability of failure q is equal to 25%. Which occupation will the individual choose?
c) Suppose the individual chooses the internet job and the probability of failure is 25%. In addi-
tion, suppose she can purchase private unemployment insurance which yields a dollars worth of
consumption in the event of the internet company's failure at a cost of p. Write out and plot the
equation for the individual's budget line yielding the combinations afordable state contingent
consumption bundles. Find the individual's optimal insurance purchase for the price p.
d) If insurance were actuarially fair, what would be the price of insurance? What level of insurance
would the individual purchase in this case?
I wanted to ask about how to proceed for part c.
He gets 400 if the new company fails.
NOw how do i treat p here:
What i thought was,
In case of unemployment
he will pay p and get good worth 1 $
SO if he pays 400 he get goods worth 100/p
is this approach correct, i m stuck