Chat with AIExam 22: Asymmetric Information in Competitive Markets
Suppose ordinarily half your class would get an A and half would get a B,with A students having a 25% chance of getting an A and B students having a 25% of getting an A.It costs $100 to persuade the instructor to raise a B grade to an A.A student is willing to pay $40 to insure she will get her usual grade and $70 to insure she will get a higher grade than usual.
a.If all students buy insurance that guarantees them an A,what is the zero profit price for an insurance company that offers A insurance.
b.Will grade insurance be sold in equilibrium?
c.Who would buy insurance and at what price if the insurance companies could tell what type of student each student is?
d.Is either the result in (b)or (c)efficient?
(37) 
Verifieda.0.25(0.5)100+0.75(0.5)100=$50.
b.A students will pay a maximum of $40 to insure their usual grade -- so they are not willing to pay the zero profit price that assumes everyone buys insurance.If only B students buy the insurance,the zero-profit price is 0.75(100)=$75.But B-students are only willing to pay $70 for A-insurance.So no insurance will be sold in equilibrium.
c.A students would be offered A-insurance at a price of $25 -- and would buy it at that price.B students would be offered A-insurance at the price of $75 and would not buy it.
d.The result in (c)is efficient -- A students have an expected cost of $25 and an expected benefit of $40 -- so surplus is created when insurance is sold to them at $25.B students have an expected cost of $75 but an expected benefit of only $70 -- so it would be inefficient for them to be insured.
Suppose ordinarily half your class would get an A and half would get a B,with A students having a 25% chance of getting an A and B students having a 25% of getting an A.It costs $100 to persuade the instructor to raise a B grade to an A.A student is willing to pay $40 to insure she will get her usual grade and $70 to insure she will get a higher grade than usual.
a.Who would buy insurance and at what price in a competitive equilibrium?
b.Suppose it costs $5 to truthfully signal your type and $10 to falsely signal what type of student you are,and if an insurance company receives no signal,it will interpret this as a signal that you are a B student.What would be the competitive outcome now?
c.Suppose a new teacher comes in -- and this teacher is willing to change a grade for just $60.How does your answer to (a)change?
d.How would your answer to (b)change?
e.Can you change something in the problem that would result in only A-students buying insurance?
(27) Verifieda.The zero profit price if all students buy insurance would be $50 -- which A students aren't willing to pay.The zero profit price if only B students buy is $75 -- which B students won't pay.So no one is insured in the competitive equilibrium.
b.B students would be willing to falsely signal that they are A students in order to buy insurance at the zero profit price where everyone buys ($40)-- but A students aren't willing to buy at that price.And if only B students end up buying the insurance,the zero profit price has to rise to $75 -- in which case B students are not willing to signal.So no insurance is sold.
c.The zero profit price when everyone buys insurance is now $30 -- which both A and B-students are willing to pay.Thus,everyone buys insurance at a price of $30.
d.So long as everyone buys the insurance,the price will remain at $30.Now,however,it costs A students $35 to get that insurance (because of the $5 signaling fee)-- but that still results in surplus of $5 for A students.B students would effectively now pay $40 for A-insurance -- and they are willing to pay as much as $70.Thus,the equilibrium remains that everyone buys insurance at the price of $30.
e.There are a number of variables that could be changed: We could reduce the willingness of B students to pay for a higher grade; or we could increase the signaling cost for revealing false information.
Explain the following statement: "In health insurance markets,moral hazard implies individuals will consume too much health care,whereas adverse selection implies too little health care will be consumed."
(35) VerifiedMoral hazard implies that those who are insured no longer face the marginal cost of medical procedures -- and,as a result,will consume beyond the point where marginal cost is equal to marginal benefit.Adverse selection implies that some individuals will have no insurance -- healthy individuals who choose not to pay the pooling equilibrium price,and lower income individuals who cannot afford to pay the price that will be high given that healthy individuals opt out.The uninsured would then consume too little medical care relative to the efficient amount.
If firms successfully gather information about consumers before offering them insurance,and if this leads to a separating equilibrium,efficiency is restored.
(34) A pooling equilibrium in insurance markets is inefficient because everyone buys too little insurance (relative to the efficient amount).
(39) If a pooling equilibrium exists in an insurance market,no separating equilibrium can exist.
(39) In the presence of adverse selection (due to high and low cost consumers),firms will employ screens to get information about consumers so long as this leads to a more efficient competitive equilibrium.
(36) Adverse selection in insurance markets results in missing markets because people engage in riskier behavior once they are insured.
(33) In a competitive market with high cost and low cost consumers (where firms are unable to tell consumer types apart),any screening costs incurred by firms will be passed on to low cost consumer but not to high cost consumers.
(28) Whenever there is adverse selection without signaling or screening,there will be a missing market.
(41) Expected utility theory predicts that individuals will fully insure in actuarily fair markets so long as their tastes are state-independent.How might adverse selection result in some individuals under-insuring?
(39) Consider two types of rules that might govern an otherwise unregulated health insurance market: (1)Insurance companies can price-discriminate against the sick and old; (2)insurance companies cannot price discriminate against the sick and old.Explain why,in equilibrium,insurance may be very expensive for the sick and old regardless of which case we find ourselves in.
(37) In a competitive separating equilibrium,low cost consumers of insurance will not fully insure because insurance rates offered to them are not actuarily fair.
(42) Suppose a competitive market with adverse selection has settled into a pooling equilibrium where everyone is offered the same price.If firms then screen consumers,the outcome may and may not be more efficient.
(36) In equilibrium,consumers will incur costs to signal their type (in markets with adverse selection)only if this results in a price that is lower than the pooling equilibrium price.
(31) Whether or not a pooling equilibrium exists in a competitive market with adverse selection depends on what fraction of consumers is of the high cost type and what fraction is of the low cost type.
(38) Regardless of whether or not screening or signaling occurs in markets with adverse selection,the equilibrium will always be less efficient than an equilibrium in the same competitive market if there were no asymmetric information.
(27) Whether or not a separating equilibrium exists in a competitive market with adverse selection depends on what fraction of consumers is of the high cost type and what fraction is of the low cost type.
(42) Whenever there is adverse selection,there will be missing market.
(40) Suppose a competitive market with adverse selection has settled into a pooling equilibrium where everyone is offered the same price.If full markets are re-established through signals,the new equilibrium will be more efficient than the original pooling equilibrium.
(41) 
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