Why can a pooling equilibrium be sustained in Spence’s signaling model but not in the Rothschild-Stiglitz screening model? Explain why in both models, the “good” type (high productivity in Spence, or low risk in Rothschild-Stiglitz) lose out in a separating equilibrium.
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Why can a pooling equilibrium be sustained in Spence’s signaling model but not in the Rothschild-Stiglitz screening model? Explain why in both models, the “good” type (high productivity in Spence, or low risk in Rothschild-Stiglitz) lose out in a separating equilibrium.
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- Indicate whether the statement is true, false, or unclear, and justify your answer.Although a firm prediction of Akerlof’s model, the adverse selection death spiral has never been observed in practice.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?One major premise of the Rothschild-Stiglitz (RS) model is that there is a perfectly competitive market for health insurance. Suppose instead that the market is not perfectly competitive, and in fact competitor firms have a hard time entering the market. Could a pooling equilibrium occur in this case? What is it about competition that prevents pooling in the RS model? No formal proof is necessary, but do make your reasoning clear. Evaluate the following statement: competition in health insurance markets is harmful.
- Consider the following claim: “If a decision maker prefers one given lottery that yields $x with probability 1 over another given lottery whose expected return is $x, then we can fully characterize the agent's risk attitude. That is, this information comparing two given lotteries is enough to determine if the decision maker is risk averse, risk loving or risk neutral.” If this claim is TRUE, then provide a proof. If it is FALSE, then prove your argument by providing an explanation.Which of the following statements is FALSE regarding the concept of "adverse selection"? Multiple Choice Adverse selection describes a situation where an individual's demand for insurance is positively correlated with the individual's risk of loss. Adverse selection occurs when someone increases their exposure to risk when insured. This can happen, for example, when a person takes more risks because someone else bears the cost of those risks. The relationship between smoking status and mortality provides a good illustration for adverse selection, especially in the case in which a life insurance company did not vary its premiums according to smoking status of its customers. To counter the effects of adverse selection, insurers may offer premiums that are proportional to a customer's risk.Consider a variant of the benchmark model of adverse selection. The types of workers (θ) are uniformly drawn from the unit interval [0,1]. A θ-type worker can produce θ units of some product if he is hired by firms. (Workers are the only input in the production.) The price of the product is normalised as 1. Before entering the labor market, workers decide whether to secure some certificate at a cost c ∈ (0, 1) or not. The certificate can fully reveal a worker’s type and he then decides whether to show it to firms or not. If a θ-type worker decides to quit the labor market, he can earn θ/4 from self-employment. Find the competitive equilibrium. (Hint, if a θ-type worker obtains the certificate and shows it to firms, he will receive a wage of θ from the market. For sure, he can also decide to join the labor market without obtaining or showing the certificate.)
- 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 the St. Petersburg Paradox problem first discussed by Daniel Bernoulli in 1738. The game consists of tossing a coin. The player gets a payoff of 2^n where n is the number of times the coin is tossed to get the first head. So, if the sequence of tosses yields TTTH, you get a payoff of 2^4 this payoff occurs with probability (1/2^4). Compute the expected value of playing this game. Next, assume that utility U is a function of wealth X given by U = X.5 and that X = $1,000,000. In this part of the question, assume that the game ends if the first head has not occurred after 40 tosses of the coin. In that case, the payoff is 240 and the game is over. What is the expected payout of this game? Finally, what is the most you would pay to play the game if you require that your expected utility after playing the game must be equal to your utility before playing the game? Use the Goal Seek function (found in Data, What-If Analysis) in Excel.Debt as a means of mitigating the common-pool problem. (Chari and Cole, 1993.) Consider the same setup as in Problem 12.15. Suppose, however, that there is an initial level of debt, D. The government budget constraint is therefore (a) How does an increase in D affect the Nash equilibrium level of G?(b) Explain intuitively why your results in part (a) and in Problem 12.15 suggest that in a two-period model in which the representatives choose D after the first-period value of G is determined, the representatives would choose D > 0.(c) Do you think that in a two-period model where the representatives choose D before the first-period value of G is determined, the representatives would choose D > 0? Explain intuitively.
- 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?Consider the following utility functions for wealth w: (i) u(w) = 3w, (ii) u(w) = w^1/3, (iii) u(w) = w + sqrt(w), (iv) u(w) = w*sqrt(w). Which of these is most risk-averse (has the highest Arrow-Pratt coefficient of absolute risk aversion) at w = 1?A. (i)B. (ii)C. (iii)D. (iv)You are one of five risk-neutral bidders participating in an independent private values auction. Each bidder perceives that all other bidders’ valuations for the item are evenly distributed between $10,000 and $30,000. For each of the following auction types, determine your optimal bidding strategy if you value the item at $22,000. a. First-price, sealed-bid auction. b. Dutch auction. c. Second-price, sealed-bid auction. d. English auction.
