a) Is (A, B) a separating or pooling equilibrium? b) Suppose the economy has 90% low risk types and 10% high risk types. Draw the average zero profit line. c) What happens to the contract (A, B)? Explain why.
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- What is the outcome of the Stolper-Samuelson Theorem??? Account for lessons derived and offer appropriate policy recommendations.Consider two individuals whose utility function over wealth I is ?(?) = √?. Both people face a 10 percent chance of getting sick, and foreach the total cost of illness equals $50,000. Suppose person A has a total net worth of $100,000, and person B has a total net worth of $1,000,000. Both people have the option to buy an actuarially fair insurance contract that would fully insure them against the cost of the illness. a. Using expected utility calculations, show that person A would certainly buy full, actuarially fair insurance. b. Suppose an insurance company wants to maximize profits and wants to charge each customer the maximum price they are willing to pay. How much should the insurance company charge each client so that both buy the contract? c. What is surprising about your result in part b? What does this tell you about how insurance companies may be pricing health insurance contracts in the real world?5. A tax on healthy people. Consider the basic Rothschild-Stiglitz model with asymmetric information and robust and frail customers. a. Suppose the government imposes a Wellness Tax τ > 0, on robust and frail types but collects on this tax only when they are healthy (that is, there is no tax if they turn out to be sick). Will a separating equilibrium still be possible? Draw a version of the Rothschild-Stiglitz diagram to support your answer. b. Will a separating equilibrium be possible if the tax τ > 0, is imposed on all customers in both sick and healthy states? Again, support your answer graphically.
- Indicate whether the statement is true or false, and justify your answer.Under certain circumstances in the Rothschild–Stiglitz model, a separating equilibrium cannot exist.Consider a medieval Italian merchant who is a risk averse expected utility maximiser. Their wealth will beequal to y if their ship returns safely from Asia loaded with the finest silk. If the ship sinks, their incomewill be y − L. The chance of a safe return is 50%.(i) Draw and carefully label the merchant’s endowment point, their expected income, and their certainty equivalent income in a 2-dimensional state-contingent consumption space. Use the diagram to illustrate and explain how the merchant would benefit from buying insurancein a competitive insurance market. At which point a risk-neutral insurance firm would maximisetheir profits by offering the merchant full insurance?Consider the model of the market for lemons from Chapter 22. Suppose that there are two types of used cars — good ones and lemons — and that sellers know which type of car they have. Buyers do not know which type of car a seller has. The fraction of used cars of each type is 21 and buyers know this. Let’s suppose that a seller who has a good car values it at $10,000 and a seller with a lemon values the lemon at $5,000. A seller is willing to sell his car for any price greater than or equal to his value for the car; the seller is not willing to sell the car at a price below the value of the car. Buyers’ values for good cars and lemons are $14,000 and $8,000, respectively. As in Chapter 22 we will assume that buyers are risk-neutral; that is, they are willing to pay their expected value of a car. (a) Is there an equilibrium in the used-car market in which all types of cars are sold? Briefly explain.(b) Is there an equilibrium in the used-car market in which only lemons are sold? Briefly…
- What are the key assumptions and implications of the 'Lemon Model' in the context of adverse selection and its impact on markets?In Akerlof’s market for lemons model, suppose it is possible to certify cars, verifying that they are better than a particular quality q. Thus, a market for cars “at least as good as q” is possible. What price or prices are possible in this market? [Hint: sellers offer cars only if q ≤ quality ≤ p.] What quality maximizes the expected gains from trade?Suppose that an investor with $2 in capital has a logarithmic utility of wealth function: U 5 ln ( w ). The investor has the opportunity to buy into the gamble described in the St. Petersburg paradox. Assume that the investor can borrow without interest and that the gamble payoff is 2 i where i is the number of tosses or outcomes realized before the first head is realized. What is the investor’s current utility of wealth level? How much would the investor be willing to pay for the gamble described in the St. Petersburg paradox? How much would the investor be willing to pay for the gamble described in the St. Petersburg Paradox if his initial wealth level were $1000 rather than $2? What would be your answer to part b if the gamble payoff were to change to 2 2 i 2 1 where i is the number of tosses or outcomes realized before the first head is…
- Give an example, real or imaginary, of an adverse selection problem. Your example must clearly point out: what information is private/asymmetric (is it an attribute or an action?) which party has the private information when does the information asymmetry arise (before or after the contract/transaction?) what is the likely outcome and in which way it can be inefficientAn investor has a von Neumann-Morgenstern utility function, u(c)=-e^(-αc), where c represents consumption and α > 0. There are two equally probable states of nature, called 1 and 2, and two assets that can be acquired, each of which is attractive in a state of nature as follows: Each unit of asset 1 yields one unit of consumption in state 1 and nothing in state 2. Each unit of asset 2 yields nothing in state 1 and one unit of consumption in state 2. The price of each asset i is denoted by πi, which are normalized to π1 + π2 = 1. The investor has a monetary wealth of w units that must be distributed between the two assets. Denote xi the number of units of asset i that he acquires. Formulate the investor's expected utility maximization problem, subject to your budget constraint. Find the optimal quantities x of each asset i for this investor. How do these amounts of assets vary according to the α parameter? What is the economic interpretation of this relationship?Assume that, after the auto insurance mandate, 50% of purchasers of auto insurance were expected to be high-risk and 50% were assumed to be low-risk. Would both markets for insurance clear? Why or why not?