ECON 500 Microeconomic Theory MARKET FAILURES Asymmetric Information Externalities Public Goods
Markets can and do fail to achieve the efficiency and welfare ideals that we have presented thus far. Asymmetric Information prevents the execution of simple efficient contracts between economic agents and leads to moral hazard and adverse selection problems. Externalities where actions of one economic agent affects the well-being of another agent in a way that is not priced through the market system leads to misallocation of resources. Public goods, because of their nonexclusivity and nonrivalry, cannot be efficiently provisioned through the market system because of free rider problem.
Asymmetric Information Markets may not be fully efficient in the presence of asymmetric information when one side has information that the other side does not. Market for insurance Market for credit Market for used cars Market for labor Similar problems also arise when one party to the transaction cannot monitor the actions of the other party that directly affects her well-being Manager-worker relationship CEO compensation Insurance
Contracts with more complex terms than simple per-unit prices may be needed to help solve problems raised by such asymmetric information. In a full-information environment, the principal could propose a contract to the agent that maximizes their joint surplus and captures all of this surplus for herself, leaving the agent with just enough surplus to make him indifferent between signing the contract or not. This outcome is called the first best, and the contract implementing this outcome is called the first-best contract. The outcome that maximizes the principal s surplus subject to the constraint that the principal is less well informed than the agent is called the second best, and the contract that implements this outcome is called the second-best contract.
Hidden Action Model Moral Hazard Imagine a firm with one representative owner and one manager Suppose the gross profit of the firm is where e is manager s effort and ε is a normally distributed random variable with mean 0 and variance σ 2 that affects gross profit and represents shocks outside of the manager s control. Manager s disutility of exerting effort c(e) is increasing and convex, i.e., c (e) > 0, c (e) > 0 Owners profit is the difference between gross profit and manager s salary
Hidden Action Model Moral Hazard Risk neutral owner wants to maximize expected net profit Risk averse manager s utility derived from her salary with constant absolute risk aversion parameter A is U(s) = -e -As - c(e) Manager maximizes the expected utility of from her salary
Optimal Salary Contract First Best with Observable Effort: The owner pays the manager a fixed salary s* if she exerts the first-best level of effort e* and nothing otherwise. For the manager to accept the contract, her expected utility must exceed what she would obtain from his next-best job offer (assumed to be 0) The lowest salary that satisfies this participation constraint is Owner s profit is which is maximized at the effort level satisfying
Optimal Salary Contract Second Best with Unobservable Effort: When salary cannot be conditioned on effort, with a constant salary s, the manager s expected utility would equals s c(e), which is maximized by choosing the lowest level of effort possible: e=0 Suppose the owner offers a salary that is linear in gross profit: The constant a can be interpreted as the base salary and b can be thought of as the incentive pay. We can analyze the relationship in three stages; the owner decides on a and b, the manager accepts or rejects the contract, and the manager decides on the level of effort.
Optimal Salary Contract Second Best with Unobservable Effort: Manager s expected utility from the linear salary is Manager will choose the level of effort that satisfies (IC) In the second stage, manager will accept the contract if (IR or PC) The owner can utilize the base salary to induce the manager to accept the contract, and use the incentive pay to induce her to exert the right effort.
Optimal Salary Contract Second Best with Unobservable Effort: In the first stage owner chooses a and b to maximize his expected surplus subject to the incentive compatibility and individual rationality constraints since both constraints will hold with equality, owner maximizes: Therefore the second best level of effort satisfies
Optimal Salary Contract Second Best with Unobservable Effort: The optimal effort in the second best case is less than the first best effort e** < e* When the owner cannot specify e in a contract, then he can induce effort only by tying the manager s pay to firm profit. However, doing so introduces variation into manager s pay for which the risk-averse manager must be paid a risk premium and this risk premium adds to the owner s cost of inducing effort. The fundamental tradeoff that appears in the presence of asymmetric information is between incentives and risk. As the manager becomes more risk averse, or as the variance of profit increases, the owner will need to reduce the dependence of manager s salary on gross profit which will in turn reduce her effort.
Hidden Type Model Adverse Selection Suppose a consumer of type θ: { θ H, θ L } obtains the surplus when she consumes q units of a good and pay a fixed tariff T. Her marginal benefit is decreasing in q and she can be of high type with probability β. Suppose the monopolist s profit is Π = T-cq
First Best Pricing with Observable Types Setting the consumer s outside option to 0, she will participate if Monopolist will then set the tariff as high as possible Monopolist s profit becomes: and is maximized at the quantity First best pricing offers each type consumer a quantity q H, q L that maximizes their surplus, and extracts that surplus with an appropriate tariff T H T L.
First Best Pricing with Observable Types ECON 500
Second Best Pricing with Unobservable Types If types are unobservable, the Monopolist cannot prevent high types from obtaining the contract intended for low types. In order to prevent this adverse selection, the tariff charged to high types needs to be reduced, and furthermore, the contract for the low types need to be distorted and made less desirable for high types. The second best contract is constructed by ensuring that both types participate voluntarily, and they obtain the contract intended for them. In other words, the monopoly should offer a menu of contracts that makes it undesirable for high types to pretend to be low types.
Second Best Pricing with Unobservable Types The monopolist s maximizes: subject to Note that only the first and the last constraints are binding
Second Best Pricing with Unobservable Types Using the binding constraints to solve for the tariffs we have: Monopolist s problem becomes an unconstrained maximization of with the FOCs:
Second Best Pricing with Unobservable Types ECON 500
Externalities Effects of an economic actor s actions on others in ways that are not reflected in market transactions. Interfirm Externalities: Suppose that the production of some good y depends not only on inputs but also on the production level of some other good x. As long as the cross partial with respect to x is different than zero externalities will be present.
Externalities Effects of an economic actor s actions on others in ways that are not reflected in market transactions. Externalities in Utility: Suppose that the utility function of some economic agent S depends not only on his consumption but also on the utility level of some other consumer J As long as the cross partial with respect to U J is different than zero externalities will be present.
Externalities is General Equilibrium The utility function of a representative consumer in an economy is Consumer has initial stocks of x and y (denoted by x* and y*) and can either consume these (x c, y c ) or use them as intermediary goods (x i, y i ) Good x is produced according to Good x is produced according to with g 1 > 0 and g 2 < 0 and
Externalities is General Equilibrium The Lagrangean of the society s utility maximization is with the FOCs:
Externalities is General Equilibrium Optimality in production requires and If the firms do not take externality into account more x is produced than the level that is optimal for the society.
Solutions to the Externality Problem Pigovian Tax: If firms are found to be disregarding the externality, a per unit tax that is precisely equal to the marginal harm that x causes to y production would restore the optimality condition
Solutions to the Externality Problem Tradable Pollution Rights Firm y decides on how many rights to sell to firm x by maximizing The FOC implies that the price for the pollution right will be
Solutions to the Externality Problem Tradable Pollution Rights If firm x has the right to pollute, it s gross profits are: Firm y s gross profits are This profit maximization will yield the same solution as the case where firm y owns the rights. Coase Theorem: As long as private property rights are well defined under zero transaction cost, regardless of their initial assignment, exchange will eliminate externalities and lead to efficient use of resources.
Public Goods A good is a (pure) public good if, once produced, no one can be excluded from benefiting from its availability and if the good is nonrival, i.e., the marginal cost of an additional consumer is zero.