Consider an economy with two agents where agents A and B where both have the same risk attitude given by u(x)=ln(x). Suppose in state 1, only agent A has a job that earns $3 and B does not earn anything. In state 2, only B works and earns $2. Solve for the equilibrium in this economy when mutual insurance is feasible. Assume both states are equally likely.
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- Consider the following competitive market for insurance. There are two states of the world: good G and bad B. Consumers have wealth £500. If the bad state occurs their wealth is reduced by £200. Consumers are expected utility maximisers, with common utility func- tion u(x) = Vx. There are two types of consumers: high risk types H and low risk types L. Consumers know their own types, but firms cannot distinguish between different types of consumers. The probabilities that H and L types find themselves in the bad state are Pu = 0.5 and p = 0.4. It is estimated that 70% of the population are low risk. Firms are expected profit maximisers that offer consumers state-contingent contractsc = (cg, Cg) in exchange for their endowment e = (eg, eg). Determine the equilibrium set of contracts.Suppose your preferences can characterized by the simple utility function U = √C, where C is consumption. You enjoy rock climbing, where you have a 10% chance of get- ting injured and losing $50,000. Your income (and therefore consumption) in the uninjured state is $90,000. What is the most you are willing to pay for an insurance policy? What is the fee for a fair insurance?Suppose Xavier has tickets to the Super Bowl, but is terribly ill with a noncontagious infection. How would a decision maker perform his economic calculation on whether to attend the game, based on the traditional model of risk behavior?
- Bob's farm harvests corns worth 106 thousand dollars (and nothing else). In each year, there is a 24% chance that a storm will attack and leaves him with only 26 thousand dollars worth of the corns. Bob's preferences over wealth are represented by U = ln w . What is the maximum that Bob is willing to pay for full insurance (in unit of thousand dollars)? (Round answers to 2 decimal places).Suppose an individual is looking to build a house in a plain that is prone to flooding. Because of the risk of damage due to flooding, the buyer's top dollar for building the house is only $290,000. Suppose the cost of building a house in this area is $330,000. A wealth-creating transaction is not possible since the seller's bottom line (or the cost of building the house) is (LESS THAN, EQUAL TO, GREATER THAN) the buyer's top dollar. The difference between the cost of building the house minus the buyer's top dollar is $_______. Suppose the government subsidizes flood insurance for homes in the flood plain. Because of this, the buyer has access to very cheap insurance, worth an expected $70,000. Without such a subsidy, the high likelihood of flood results in extremely high rates for flood insurance. With this subsidy, the individual (IS, IS NOT) incentivized to build a house in the flood plain..A seller has an indivisible asset to sell. Her reservation value for the asset is s, which she knows privately. A potential buyer thinks that the assetís value to him is b, which he privately knows. Assume that s and b are independently and uniformly drawn from [0, 1]. If the seller sells the asset to the buyer for a price of p, the seller's payoff is p-s and the buyer's payoffis b-p. Suppose simultaneously the buyer makes an offer p1 and the seller makes an offer p2. A transaction occurs if p1>=p2, and the transaction price is 1/2 (p1 + p2). Is the following strategy profile a Bayesian Nash equilibrium: the buyer chooses p1 = 1/2 if b>=1/2 and he chooses p1=0 if b<1/2; the seller chooses p2=1/2 if s<1/2 and she chooses p2=1 if s>1/2. Why or why not? Can there be a Bayesian Nash Equilibrium in which the transaction price is .9 whenever there is a transaction? Why or why not?
- Abigail is a consumer whose utility is a function of her total wealth W. u(W ) = log W. Suppose that Abigail begins with initial wealth of A = 100 but will suffer a serious illness with probability π = 0.15 which will require extensive treatment costing L = 80. To hedge against this risk, Abigail considers buying a health insurance policy. She may buy as much insurance I as she wishes at a cost of p per dollar of coverage, so her payoffs in each state are Healthy Ill Probability 0.85 0.15 No Insurance 100 20 Claim 0 I Premium −pI −pI a) Now suppose that the insurance company raises premiums to p = 0.2 so that they are no longer actuarially fair. Find Abigail’s expected wealth E[W ] and expected utility E[u(W )]. b) How much insurance should Abigail buy now?Now agent C can produce private information about the true realization x at t=1 at the cost γ=4. Suppose lA=lB=φA=φB=1 and x is either 40 or 100 with equal probability and w=70. - Suppose that φB=0.4 (and not φB=1). What is the maximum amount LB that agent B can borrow with probability 1? What is the haircut for agent A in equilibrium?Consider a health insurance market. The market has many insurers so that each insurance company offers insurance at the fair insurance premium. Each consumer has utility function, and has an initial wealth of $200. Consumers have access to a (magical) gym that reduces their probability of needing to go to the doctor from 90% to 10%. A gym membership costs $6. A trip to the doctor costs $120. Suppose insurance companies charge the fair insurance premium which assumes all consumers go to the gym. This fair insurance premium is $? and the insurance company makes a profit of $? per consumer. Suppose insurance companies continue to charge the fair insurance premium that assumes all consumers go to the gym, but now charges a copay of $15 for a doctor's visit. The insurance company now makes a profit of $ per consumer. By implementing a copay, the insurance company the problem.
- Shane just bought a house worth $360,000 in an area that is known for floods. A flood occurs with a 5% chance and if it occurs, his home is ✓ for reduced in value to $202,500. Shane has utility function given by U(X)=√√X. He would be willing to pay a maximum of flood insurance. The fair insurance premium for flood insurance is Shane's risk premium is Suppose, instead, that Shane's utility function is given by U(X) = X². Then, the maximum he would be willing to pay for flood insurance isDraw a utility function over income u(I) that describes a man who is a risk lover when his income is low but risk averse when his income is high. 1.) Using the 3-point curved line drawing tool, draw the low income portion of his utility function. Label it U₁. 2.) Using the 3-point curved line drawing tool, draw the high income portion of his utility function. Label it UH. Carefully follow the instructions above, and only draw the required objects. C 500- 450- 400- 350- 300- 250- 200- 150- 100- 50- 0 Utility 20,000 40,000 60,000 80,000 100,000 IncomeExercise 5: Insurance Consider two individuals, Dave and Eva. Both Dave and Eva have initial wealth 810,000 and face a 40% chance of losing L = 450, 000. Dave has von Neumann-Morgenstern utility function up(x) = x and Eva has von Neumann-Morgenstern utility function ug (x) = VT. 1. What do you know about Dave's and Eva's risk preferences? 2. What is the most Dave would be willing to pay for complete insurance against the loss? 3. What is the most Eva would be willing to pay for complete insurance against the loss? Suppose they are each able choose insurance with any coverage level z [0, 1] (i.e. 0 0. 6. Is Eva's optimal choice full insurance, i.e. z = 1?