1. You have a job pays $x. You have been dreaming about opening up your own restaurant, but you know that restaurants in your town fail within the first year with 40% probability. You have studied the market and figure the average successful restaurant yields a net profit of $y > $r, but you are weary since you would earn $0 if the restaurant fails. a. What is your expected utility from opening the restaurant (for a general utility in U(c)? What is your expected utility from opening the restaurant if U(c) = @3/4? b. What if in the case your restaurant failed, instead of limited liability resulting in income of $0, you suffered a loss of -$z, which meant you would have to sell your house to pay the debts? What effect do you think the limited liability option has on the borrowing rate for the entrepreneur? In what ways does the limited liability option encourage entrepreneurship and in what ways does it discourage it? c. Suppose we are in the limited liability case so that income is zero if the business fails. If the wage from your job is $.r = 50, what does Sy have to be for you to be indifferent between keeping your job and starting the restaurant