Question 3. [13 points] Use the Rothschild/Stiglitz insurance model to determine the equilibrium contract in the following situations. Individuals have initial wealth W. o If an individual falls ill, he always purchases one treatment. The price of the treatment is P. There are two risk types. For high risk individuals, the probability of falling ill is p_high; for low risk individuals, the probability of falling ill is p_low. We have p_high> p_low. * The insurance market is competitive, so we only will observe contracts that break even. Note: Please draw corresponding graphs for each situation. Each graph should include (1) the no insurance point, (2) individuals' indifference curves for each risk group, and (3) breakeven lines for insurers when offering contracts to each risk group. In your answer, please label the optimal contract for each risk group. a) [Experience Rating] Suppose \"experience rating\" is allowed, meaning that insurers know the risk type of each individual and can offer each risk group a different contract. i. Show graphically that when offered policies along the corresponding breakeven line (i.e. insurers offer policies along the breakeven line for high/low risks to high/low risk individuals), which plan would be chosen by the low risk? Which plan would be chosen by the high risk? (3 points) ii. Which risk type end up with plans with higher premium, the high risk or the low risk? (1 point) iii. Are these plans full insurance plans, i.e., plans with no out-of-pocket cost? (1 point) iv. What is the fairness issue of the \"experience rating\" equilibrium (i.e., insurers offering different insurance plans to different risk types)? (1 point) b) Suppose \"experience rating\" is abandoned (i.e., insurers cannot detect, in advance, which buyers are which, or offer different contracts to different risk types). This means insurers have to offer the same set of contracts to both risk groups. i. [Adverse Selection] Suppose insurers are forced to offer both optimal contracts you found in a) to both risk groups. Which plan will the high risk will choose? Please show it graphically. (2 points) Can insurers breakeven in this situation? (1 point) ii. [Cream Skimming] Now suppose insurers are allowed to offer whatever policies they find profitable. Show that insurers could offer a set of contracts to both risk groups and the two risk groups could identify themselves by choosing different insurance policies. (3points) Can the low risk individuals get full insurance in this situation? (1 point)