Game theory v. price theory

1. Game theory v. price theory

2. 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!

3. 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…

4. Assumptions of price theory • 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. • Complete markets: there are markets for all goods (and therefore no externalities). • Complete information: Buyers and sellers have no private information.

5. 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?

6. 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?

7. 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)

8. 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.

9. 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?

10. Expected value if $1000/$1500/ $2300/$4800 cars are all sold? • $1500 • $2000 • $2400 • $2800 • $3300 • $4200

11. 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!

12. 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?

13. Expected value if $1000/$1500/ $2300 cars are all sold? • $1000 • $1200 • $1400 • $1600 • $1800 • $2000

14. 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?

15. Expected value if $1000/$1500/ cars are all sold? • $1100 • $1250 • $1400

16. 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.

17. 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?

18. Who are the peaches and who are the lemons? • Peaches are $200, lemons are $4000. • Peaches are $4000, lemons are $200.

19. 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!

20. 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.

21. 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.

22. Assumptions of price theory • 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. • Complete markets: there are markets for all goods (and therefore no externalities). • Complete information: Buyers and sellers have no private information.