Question

You rent a room with a nice ocean view in a house on Del Playa. Last week’s storms severely eroded
the sea cliffs and your friend (the engineering major) estimates that there is a 50% chance that they
will collapse and you will lose all of your possessions, valued at $100. You can sell off some of your
belongings to buy some insurance against this risk, for the price of p dollars for every dollar of insurance.

Now suppose that your utility of wealth is given by u(c) = c. Write your new MRS. How much
insurance would you buy if p = .4? If p = .6?

Could you explane in detail,Please? And could you also graph it?

thank you!

Answer 1

Let c_c denote your wealth if the cliffs collapse and c_nc denote your wealth if they do not collapse. The state contingent budget constraint is,

c_nc+ (p/1−p) c_c = 100

MRS = - c_nc /c_c = -1 as c_nc = c_c

MRS = −1. If p = .4, you spend all you money on insurances, meaning buy $250 of insurance (k = 250). If p = .6, you won’t buy any insurance (k = 0).

u(c) = c, implies you are risk neutral. This means that your consumption levels in the two states are perfect substitutes and you should try to maximize your expected consumption. Having $1 of insurance gives you an expected payout of $0.50, because there is a 50% chance of the collapse. When p = 0.4, it costs less than $0.50 to buy a dollar of insurance,you will buy as much as you can, because each dollar of insurance increases your expected c. Whereas, when p = 0.6, it costs more than $0.50, you won’t buy any, because each dollar of insurance lowers your expected c.