Adverse Selection The adverse selection problem Overview Key concepts (1) Key concepts (2)

Adverse Selection The adverse selection problem Overview Key concepts (1) Key concepts (2) www.phwiki.com

Adverse Selection The adverse selection problem Overview Key concepts (1) Key concepts (2)

Sumner, Mark, Contributing Editor has reference to this Academic Journal, PHwiki organized this Journal Adverse Selection MICROECONOMICS Principles in addition to Analysis Frank Cowell May 2004 Almost essential Risk Risk-taking Prerequisites The adverse selection problem A key aspect of hidden in as long as mation In as long as mation relates to personal characteristics. Hidden in as long as mation about actions is dealt with under “moral hazard.” Focus on the heterogeneity of agents on one side of the market. Elementary model of a single seller with multiple buyers Jump to “Moral Hazard” Overview Principles Monopoly problem Insurance Adverse selection Background in addition to outline

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Key concepts (1) Contract: An agreement to provide specified good or service in exchange as long as specified payment Type of contract will depend on in as long as mation available. Fee schedule: Set-up involving a menu of contracts One party draws up the menu. Allows some selection by other party Again the type of fee schedule will depend on in as long as mation available Types: Assume that hidden in as long as mation is well structured General shape of (e.g.) agents’ preferences is common knowledge But there is heterogeneity as to (e.g.) intensity of preference Correspond to different types of agents Key concepts (2) Adverse selection: individuals faced with a contract can choose to accept or reject . Multiple contracts aimed at different types Then some individuals may choose the “wrong” one. Screening: Knowing this, other side of market seeks to respond. Draw up contracts so that the various groups self-select the “right” ones. “Adverse selection” in addition to “Screening” are effectively equivalent labels. Based on concept of Bayesian Nash equilibrium Follow through a simplified version of the game Screening: extensive- as long as m game 0 [LOW] [HIGH] 1-p p f f b [NO] [OFFER] [accept] [NO] [OFFER] a [reject] [accept] [reject] “Nature” chooses a person’s type Probabilities are common knowledge Firm may offer a contract, not knowing the type Consumer chooses whether to accept contract

Outline of the approach Begin with monopolist serving a market heterogeneous customers differ in terms of taste as long as the product other differences (income) are unimportant Easy to see what is going on Main points can be established from case of just two customer types Lessons from this are easily transferred to other contexts. Examine these later Overview Principles Monopoly problem Insurance Adverse selection A fee schedule to maximise profits from consumers with known tastes Exploitation: full in as long as mation Effect of hidden in as long as mation “Second-best” solution Model structure Monopoly produces good 1 using good 2 as input. Constant marginal cost Zero fixed cost Good 1 cannot be resold. The monopoly sells to heterogeneous customers The firm wants to set up a system of payment. A fee schedule Some customer in as long as mation might be concealed. Imagine this in as long as mation in the as long as m of a parameter Knowledge of each customer’s parameter value would help the firm exploit the customer. Some fee schedules

Alternative fee schedules x1 Fee Revenue A straight unit price Two-part tariff Multi-part tariff 1 2 3 1. F(x1) = px1 2. F(x1) = F0 + px1 3. F(x1) = F0 + p x1, x1 x1 = F0 + p x1+ p [x1 x1], x1 > x1 x1 Single customer type Suppose there is just one type of customer Income is y. Utility is given by U(x1, x2) = x2 + y(x1) where y(0) = 0. Zero income effect as long as good 1 Welfare can be measured by consumer surplus Reservation utility level is u = U(y, 0) = y Firm maximises profits subject to reservation constraint. Monopoly position means firm can appropriate the surplus. Can do this by imposing two-part tariff: Fixed charge F0 . Price p = c. A two-part tariff F0 x1 F(x1) p

Exploitative contract x2 F0 x1 y Income Preferences Budget set arising from exploitative contract Fixed charge Optimal consumption Reservation utility By not participating consumer can get utility level u =U(0, y) Reservation indifference curve is given by U(x1, x2) = u u Heterogeneous consumers Two groups: a-types in addition to b-types Groups differ in their incomes in addition to in their tastes. Each group is internally homogeneous Introduce the single-crossing condition: imposes regularity on indifference curves; makes it possible to compare the groups easy to introduce “tailor-made” fee schedules Two sets of preferences Ua(x1a, x2a) = x2a + ta y(x1a) a-type indifference curves b-type indifference curves Single-crossing condition is satisfied Ub(x1b, x2b) = x2b + tb y(x1b) h=a h=b

Full-in as long as mation contracts Assume that there is full in as long as mation about both types of consumer. The firm knows The preferences of both Alf in addition to Bill The incomes of both Alf in addition to Bill There as long as e Uses this in as long as mation to design two-part tariffs Tailor-made as long as each type of consumer. Forces each down to the reservation utility levels ua in addition to ub Outcome can be illustrated as follows. Exploitation of two groups ya yb Alf Bill Income of Alf in addition to Bill Preferences of Alf in addition to Bill Budget sets arising from exploitative contracts Fixed charges Optimal consumptions ua ub Overview Principles Monopoly problem Insurance Adverse selection Key issues of the adverse-selection problem Exploitation: full in as long as mation Effect of hidden in as long as mation “Second-best” solution

Concealed in as long as mation Now suppose personal in as long as mation is private Can’t observe a customer’s taste characteristic Can’t implement a fee-schedule conditioned on taste Possibility of severe loss of profit to the firm. The reason is that some individuals may masquerade: High-valuation consumers can claim the contract appropriate to low-valuation consumers Imitate the behaviour of low-valuation consumers Enjoy a surplus by “hiding” amongst the others Will this lead to an inefficient outcome Bill’s incentive to masquerade yb Bill’s income in addition to preferences Contract intended as long as b-type Contract intended as long as a-type Bill would be better off with an a-type contract To masquerade as an a-type Bill mimics Alf’s consumption Now try cutting the fixed charge on a b-contract Bill finds the new b-contract at least as good as an a-contract Insight from the masquerade A “pooling contract” is not optimal By cutting F0 as long as b-types sufficiently: the b-types are at least as well off as if they had masqueraded as a-types the firm makes higher profits there is allocative efficiency But this new situation is not a solution: shows that masquerading is suboptimal illustrates how to introduce incentive-compatibility but we have not examined profit maximisation. Requires separate modelling

Overview Principles Monopoly problem Insurance Adverse selection First look at a design problem Exploitation: full in as long as mation Effect of hidden in as long as mation “Second-best” solution More on masquerading Now consider profit maximisation Build in in as long as mational constraints Will act as additional side constraint on the optimisation problem Because of this usually called a “second-best” approach Another way of seeing that a pooling contracts not optimal Let us examine the elements of an approach. Elements of the approach Choose F( ) to maximise profits Subject to Participation constraint Incentive-compatibility constraint The participation constraint is just as be as long as e Can opt out in addition to not consume at all Incentive compatibility encapsulates the in as long as mation problem Individuals know that tastes cannot be observed So they can select a contract “meant as long as ” someone else They will do so if it results in a utility gain Run through logic of solution

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Logic of the solution: (1) In principle we have a profit-maximisation problem subject to four constraints: Low valuation a-types’ participation constraint High valuation b-types’ participation constraint a-types’ incentive compatibility: must get as much utility as they would from a b-type contract. b-types’ incentive compatibility: must get as much utility as they would from an a-type contract. But a-types have no incentive to masquerade They would lose from a b-type contract So a-type incentive-compatibility constraint is redundant Can show this as long as mally Also b-types cannot be as long as ced on to reservation utility level ub. We’ve seen what happens: they would grab an a-type contract So b-types’ participation constraint is redundant So the problem can be simplified . Logic of the solution: (2) In practice we have a profit-maximisation problem subject to two constraints: a-types’ participation constraint b-types’ incentive compatibility: must get as much utility as they would from an a-type contract. a-types can be kept on reservation utility level ua There is an infinity of fee schedules that will do this. b-types must be prevented from masquerading. Do this by distorting upwards the unit price as long as the a-types Force the b-types down to the indifference curve they could attain with an a-type contract. Maximise profit from them by charging price=MC. Check this in a diagram Second-best contracts ya yb Alf Bill Income in addition to preferences Budget sets as long as full-in as long as mation case The a-type contract b’s utility with an a-type contract ua The b-type contract

Second-best contracts (2) ya yb Income in addition to preferences as long as the two types The a-type contract b’s utility with an a-type contract ua The b-type contract x1 Implementing the contract with a multipart tariff. An a-type is as long as ced down on to the reservation indifference curve. The attainable set constructed by the firm A b-type gets the utility possible by masquerading as an a-type. Multipart tariff has kink at x1. Second-best contracts (3) Multipart tariff: firm’s viewpoint An a-type choice A b-type choice The cost function x1 F(x1) C(x1) F( ) C( ) Profit on each a-type Profit on each b-type Pa Pb Second best: principles b-types have to be made as well off as they could get by masquerading So they have to keep some surplus Full surplus can be extracted from a-types High valuation b-type contract involves price = MC “No Distortion at the Top” Low-valuation a-types face higher price, lower fixed charge than under full in as long as mation they consume less than under full in as long as mation This acts to dissuade b-types.

Separating equilibrium xBLUE xRED Endowment & indiff curves 0 Pure a-type, b-type contracts b-type would like a pure a-type contract Then b-types take efficient contract Restrict a-types in their coverage P0 a-type’s in addition to b-type’s preferred prospects to (Pa ,Pb) A pooled contract preferred by both a-types in addition to b-type Pb Pa ~ Proposed separating contract might be dominated by a pooling contract. This could happen if g were large enough ~ P ^ Insurance model: assessment Why is the insurance case specially difficult Note the special role of parameters pa, pb. As “type indicators” – shift the indifference curves. As weights in the evaluation of profits. The population composition affects profitability Directly: expected profit on each contract written Indirectly: through the masquerading process As be as long as e, no pooling equilibrium But may not be a separating equilibrium What next Consider other fundamental models of in as long as mation Signalling models also hidden personal characteristics but where the in as long as med party moves first. Moral hazard hidden in as long as mation about individual actions

Sumner, Mark Contributing Editor

Sumner, Mark is from United States and they belong to DAILY KOS and they are from  Emeryville, United States got related to this Particular Journal. and Sumner, Mark deal with the subjects like Opinion/Commentary

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