Game theory v. price theory

Game theory Focus: strategic interactions between individuals. Tools: Game trees, payoff matrices, etc. Outcomes: In many cases the predicted outcomes are Pareto inefficient. But remember the Coase Theorem!

Price theory Focus: market interactions between many individuals. Tools: supply and demand curves Outcomes: In many cases the predicted outcomes are Pareto efficient. (This is the working of the invisible hand.) But remember the underlying assumptions and what can go wrong…

Assumptions of price theory 1.Each buyer and seller is small relative to the size of the market as a whole, and so each buyer and seller is a price-taker who takes the market price as given. 2.Complete markets: there are markets for all goods (and therefore no externalities). 3.Complete information: Buyers and sellers have no private information.

Price-taking assumption Each buyer and seller is small relative to the size of the market as a whole, and so each buyer and seller is a price-taker who takes the market price as given. If this assumption is not met, some buyers and/or sellers have market power, e.g., monopoly, monopsony, duopoly, etc. Resulting inefficiencies?

Complete markets assumption Complete markets: there are markets for all goods (and therefore no externalities). If this assumption is not met, there are externalities, either positive or negative. Resulting inefficiencies?

Complete information assumption Complete information: Buyers and sellers have no private information. If this assumption is not met, there can be asymmetric information. Resulting inefficiencies? Example: the market for lemons (from Akerlof’s Nobel Prize-winning paper)

The market for lemons Consider a used car market in which sellers know the quality of their car, but buyers cannot tell if a given car is a peach or a lemon. What is the effect of this asymmetric information on the market? Until Akerlof’s paper, economists thought that there was no major effect.

A numerical example Imagine that sellers’ cars are equally divided among 4 values: $4800 (the peaches), $2300, $1500, and $1000 (the lemons). Buyers cannot distinguish between them, so they’re only willing to pay the average value (i.e., expected value) for a used car. What is the expected value if all 4 types of cars are sold?

Expected value if $1000/$1500/ $2300/$4800 cars are all sold? 1.$ $ $ $ $ $4200

A numerical example Sellers’ cars are equally divided among 4 values: $4800 (the peaches), $2300, $1500, and $1000 (the lemons). If all 4 types of cars are sold, buyers are only willing to pay the average value (i.e., expected value) for a used car: $2400. But sellers of $4800 cars (the peaches) won’t sell for this amount!

A numerical example We can’t have a market where all 4 types of cars are sold, but maybe we can have a market where 3 types are sold: $2300, $1500, and $1000 (the lemons). Again, buyers are only willing to pay the average value (i.e., expected value). What is that value if cars are equally divided between these 3 types?

Expected value if $1000/$1500/ $2300 cars are all sold? 1.$ $ $ $ $ $2000

A numerical example We can’t have a market where even 3 types of cars are sold, but maybe we can have a market where 2 types are sold: $1500, and $1000 (the lemons). Again, buyers are only willing to pay the average value (i.e., expected value). What is that value if cars are equally divided between these 2 types?

Expected value if $1000/$1500/ cars are all sold? 1.$ $ $1400

The market for lemons In the numerical example, we have complete unraveling and only the worst- quality cars (the lemons) are sold. This is called adverse selection because the cars that are sold appear to be selected adversely. A more important example of adverse selection: health insurance.

A numerical example Imagine that consumers’ likely health care expenditures are equally divided among 4 values: $200, $2700, $3500, and $4000. Insurance companies cannot distinguish between them, so in order to avoid losing money they have to charge at least the average cost for health insurance. Who are the peaches and who are the lemons?

1.Peaches are $200, lemons are $ Peaches are $4000, lemons are $200.

A numerical example Consumers’ likely health care expenditures are equally divided among 4 values: $200, $2700, $3500, and $4000. If all 4 types of consumers buy health insurance, companies have to charge at least the average cost, ¼(200)+¼(2700) +¼(3500)+¼(4000) = $2600. But the peaches won’t pay that much!

A numerical example So maybe we can have a market where 3 types buy insurance: $2700, $3500, and $4000. Again, insurance companies have to charge at least the average cost, which is 1/3(2700)+1/3(3500)+1/3(4000)=3400. Again, the low cost buyers will choose to self-insure.

A numerical example We can’t have a market where even 3 types of consumers buy insurance, but maybe we can have a market with 2 types are sold: $3500 and $4000 (the lemons). But insurance companies must charge at least the average cost ($3750) and at this price the lower-cost consumers will self- insure, leaving only the lemons.

Assumptions of price theory 1.Each buyer and seller is small relative to the size of the market as a whole, and so each buyer and seller is a price-taker who takes the market price as given. 2.Complete markets: there are markets for all goods (and therefore no externalities). 3.Complete information: Buyers and sellers have no private information.