There are two possible states of the world next year. If you keep your job, your income is equal to your labor market earnings E plus your non-labor income Y. You face a probability p of losing your job, and you are risk-averse. Your Bernoulli utility function is ln(C), where C is a composite consumption good. ?(1) Suppose that unemployment insurance is available in the private market, at price q per dollar of insurance.
(a) Consider a graph with “keep job payoff” on the horizontal axis, and “lose job payoff” on the vertical axis. What are the coordinates of your endowment point? What are the coordinates if you were to buy I units of insurance? Use these two points to derive the slope of the insurance line.
(b) Suppose that in the insurance market long-run, firms will enter until expected profits reduce to 0. Use this condition to derive a conclusion about the price of insurance q.
(c) Set up a maximization problem, solve, and use your solution in order to answer the following questions: If insurance is actuarially fair, how much insurance would you purchase? Is this result consistent with the Full Insurance Principle discussed in class?
(d) If insurance is more expensive than the “actuarially fair” price, will your chosen consumption bundle be to the southeast or the northwest of the 45 degree line? Prove this (and be able to do it on an exam).
(2) If your probability p of unemployment is 1%, then compute the amount of money you would spend on actuarially fair insurance, based on your answer to (1c), if your earnings are:
(a) $300 per week (b) $600 per week (c) $1200 per week (d) $1800 per week