Consider population of entrepreneurs, each endowed with a business that will be worth R if succesful or 0 if not. The businesses require no investment. Probability of success is either p ("good" entrepreneurs) or q ("bad"), where p > q. Population share of good entrepreneurs is , share of bad entrepreneurs is 1 The entrepreneurs are risk averse: their utility function u(wealth) is increasing and concave: u0 > 0; u00 < 0.

The businesses can be insured by a risk neutral, competitive outside company that oers payouts to entrepreneurs in case of failure in exchange for premium in case of success. The company is willing to insure any business up to any amount, as long as it is actuarially fair so that the insurer makes expected zero profit.

. What is the equilibrium insurance of a good entrepreneur if the insurer knows that the type is good? You may characterize the outcome in terms of post-insurace wealth of the borrower in each state (success and failure) RF G , RS G. Explain as sharply as you can. b. What is the insurance of a bad entrepreneur if insurer knows that the type is bad? Characterize as sharply as you can. Now assume information is asymmetric: the insurer does not observe entrepreneurs type. c. Explain as sharply as you can why there is no pooling equilibrium. (Pooling equilib- rium is one where both types obtain the same wealth allocation in both states)