Uncertainty. The St. Petersburg Paradox. Managerial Economics MBACatólica

Transcription

1 Fernando Branco Fall Quarter Session 9 Part II Uncertainty Most managerial decisions are taken under uncertainty. Some markets trade on the basis of uncertainty (e.g., insurance, stock market). How do we evaluate alternatives with uncertain outcomes? The St. Petersburg Paradox. The St. Petersburg Paradox How much are you willing to pay for the following business: A coin is tossed until it comes up heads for the first time; If the coin is tossed n times, you will receive 0.5 n. The mean-variance approach. Risk aversion. 1

2 Managerial decisions with risk-averse customers How to induce customer switching to a new product? There is an additional value from belonging to a chain or being certified. Insuranse is valuable. It pays to diversify ( put the eggs in separate baskets ). Strategic use of consumer search. Decisions by risk-averse managers Choosing among risky projects: Project Boom (0.9) Recession (0.1) Mean Variance Bologna -$10.000,00 $12.000,00 -$7.800,00 $6.600,00 Caviar $20.000,00 -$8.000,00 $17.200,00 $8.400,00 Joint $10.000,00 $4.000,00 $9.400,00 $1.800,00 T-bill $3.000,00 $3.000,00 $3.000,00 $0,00 Uncertainty and asymmetric information Uncertainty often comes with asymmetric information: A seller and a buyer have distinct information sets; An employer and a worker have private information on the value of a labor contract. Problems of asymmetric information: Moral hazard; Adverse selection. Dealing with asymmteric information: Incentives, signaling and screening. 2

3 A leading example from insurance Why should the costs of an insurer, that increases the average coverage of a given insurance from 50% to 60%, increase more than 20%? Because, there will be more accidents! Adverse selection: more high risk customers will be attracted; Moral hazard: all customers will be less careful in avoiding accidents. Moral hazard and incentives Agents act in their own interest. Taking incentives into consideration is crucial when dealing with asymmetric information. An important moral hazard problem is related with managerial compensation. The Principal-agent problem Often the owner is not directly managing the firm. The owner wants the manager to work in the owner s interest. The manager wants to work in hisown interest. Incentives should be aligned. 3

4 Dealing with the owner-manager principal-agent problem Incentive contracts (e.g., stock options). External incentives: Reputation and competition for managers Take-overs. Dealing with the manager-worker Principal-agent problem Profit-sharing Revenue-sharing Piece rates Adverse selection: Why is insider trading bad? The existence of asymmetric information may severely hurt the role of markets. How much do you pay for a pot of coins? Why should insider trading be forbidden? Adverse selection in a competitive market. 4

5 Example: The market form lemons What is a lemon? Used cars may be of high quality (H) or low quality (L). There are 100 used cars. The owners valuations are: S v =1000 = 2000 S L v H The 200 potential buyers valuations are: D v =1200 = 2400 D L Everybody is risk neutral. v H Market for lemons: Symmetric information What is the market equilibrium if everybody knows the quality of each car? All cars are traded: the high quality at a price of 2400, the low quality at a price of What is the market equilibrium if no one knows the quality of each car (and there are 50 of each type)? All cars are traded at a price of Market for lemons: Informed sellers (I) What is the market equilibrium if owners know the quality of their cars, but buyers do not? Supply: 0 if p < 1000 Q S ( p) = 50 if 1000 p < if 2000 p Demand: Q 200 if p 1200 D ( p) = 0 if < p 5

6 Market for lemons: Informed sellers (II) In equilibrium, only low quality cars are traded, and at a price of The information asymmetry prevents the high quality cars from being traded. Signaling The informed party may want to signal the quality of the cars. Example: Provide a warranty if the car breaks down. Signaling may allow for the identification of the high quality cars. But, still, that has a cost! Warranties for the used cars (I) All cars last up to 2 years. The probability of lasting 1 year only is: 2/3 for low quality cars and 1/3 for high quality cars. Cars that last 1 year value 0; while cars that last 2 years value 3000 for owners and 3600 for potential buyers. The owners of high quality cars may want to offer a warranty on the value of 3900! 6

7 Warranties for the used cars (II) Buyers infer that a car with a warranty is of high quality. Buyers are willing to pay up to 3700 for a car with a warranty but only up to 1200 for a car without it. The owners of high quality cars need to receive at least 3300 to sell it with a warranty but only 2000 to sell it without the warranty. The owners of low quality cars need to receive at least 3800 to sell it with a warranty but only 1000 to sell it without the warranty. Warranties for the used cars (III) There is the following equilibrium: Cars without warranties are sold at Cars with warranties are sold at Conclusion: All cars are sold; The asymmetry of information impose the cost of issuing the warranty on the owners of good cars. 7