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Lecture 8

Lecture 8. Extra office hours . Wednesday 2013/6/18, 1 -3pm . Price Theory. Risk and Uncertainty Chapter 18. Introduction. States of the world can be considered as different goods States can be traded. How? As there is trade, there is a price. What’s the price?. Introduction.

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Lecture 8

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  1. Lecture 8

  2. Extra office hours Wednesday 2013/6/18, 1-3pm.

  3. Price Theory Risk and Uncertainty Chapter 18

  4. Introduction • States of the world can be considered as different goods • States can be traded. How? • As there is trade, there is a price. What’s the price?

  5. Introduction • Key elements: a complete set of states, and a probability distribution across these states. • Expected value: the average value of all the states, weighted by the corresponding probabilities. • Graphically, we can use iso-expected value lines.

  6. Opportunities • Budget line and prices • Fair odds • Reflect true probabilities of various states of world • Expected value of betting same as expected value of not betting • Individual offered fair odds • Budget line coincides with expected value line

  7. Introduction • How to measure the risk of a stochastic variable (or a risk asset, or a gamble…)? • You need a variation index, such as variance or standard deviation. • Note that these measures are different from risk-attitude measures.

  8. Section 18.1 Attitudes toward risk

  9. Risk attitudes and utility functions • Define utility U as a function of wealth (W) • If U is concave (U’’<0), the individual is considered risk-averse • If linear (U’’=0) , then risk-neutral • If convex (U’’>0), risk-loving

  10. Preferences Under Uncertainty • Think of a lottery. • Win $90 with probability 1/2 and win $0 with probability 1/2. • U($90) = 12, U($0) = 2. • Expected utility is

  11. Preferences Under Uncertainty • Think of a lottery. • Win $90 with probability 1/2 and win $0 with probability 1/2. • U($90) = 12, U($0) = 2. • Expected utility is

  12. Preferences Under Uncertainty • Think of a lottery. • Win $90 with probability 1/2 and win $0 with probability 1/2. • Expected money value of the lottery is

  13. Preferences Under Uncertainty • EU = 7 and EM = $45. • U($45) > 7  $45 for sure is preferred to the lottery risk-aversion. • U($45) < 7  the lottery is preferred to $45 for sure risk-loving. • U($45) = 7  the lottery is preferred equally to $45 for sure risk-neutrality.

  14. Preferences Under Uncertainty 12 EU=7 2 $0 $45 $90 Wealth

  15. Preferences Under Uncertainty U($45) > EU  risk-aversion. 12 U($45) EU=7 2 $0 $45 $90 Wealth

  16. Preferences Under Uncertainty U($45) > EU  risk-aversion. 12 MU declines as wealth rises. U($45) EU=7 2 $0 $45 $90 Wealth

  17. Preferences Under Uncertainty 12 EU=7 2 $0 $45 $90 Wealth

  18. Preferences Under Uncertainty U($45) < EU  risk-loving. 12 EU=7 U($45) 2 $0 $45 $90 Wealth

  19. Preferences Under Uncertainty U($45) < EU  risk-loving. 12 MU rises as wealth rises. EU=7 U($45) 2 $0 $45 $90 Wealth

  20. Preferences Under Uncertainty 12 EU=7 2 $0 $45 $90 Wealth

  21. Preferences Under Uncertainty U($45) = EU  risk-neutrality. 12 U($45)=EU=7 2 $0 $45 $90 Wealth

  22. Preferences Under Uncertainty U($45) = EU  risk-neutrality. 12 MU constant as wealth rises. U($45)=EU=7 2 $0 $45 $90 Wealth

  23. Preferences Under Uncertainty • For risk-neutral individuals, state-contingent consumption plans that give equal expected utility are equally preferred.

  24. Preferences Under Uncertainty Cna Indifference curvesEU1 < EU2 < EU3 EU3 EU2 EU1 Ca

  25. Preferences Under Uncertainty • What is the MRS of an indifference curve? • Get consumption c1 with prob. 1 andc2 with prob. 2 (1 + 2 = 1). • EU = 1U(c1) + 2U(c2). • For constant EU, dEU = 0.

  26. Preferences Under Uncertainty

  27. Preferences Under Uncertainty

  28. Preferences Under Uncertainty

  29. Preferences Under Uncertainty

  30. Preferences Under Uncertainty

  31. Preferences Under Uncertainty Cna Indifference curvesEU1 < EU2 < EU3 EU3 EU2 EU1 Ca

  32. Choice Under Uncertainty • Q: How is a rational choice made under uncertainty? • A: Choose the most preferred affordable state-contingent consumption plan.

  33. Measures of risk-aversion • Absolute risk aversion • Relative risk aversion

  34. Implications • Considering forming a portfolio with one risky asset and one risk-free asset. • If the person experiences an increase in wealth, he/she will choose to increase (or keep unchanged, or decrease) the number of dollarsof the risky asset held in the portfolio if absolute risk aversion is decreasing (or constant, or increasing). • Thus economists avoid using utility functions, such as the quadratic, which exhibit increasing absolute risk aversion, because they have an unrealistic behavioral implication.

  35. Implications • Similarly, if the person experiences an increase in wealth, he/she will choose to increase (or keep unchanged, or decrease) the fraction of the portfolio held in the risky asset if relative risk aversion is decreasing (or constant, or increasing).

  36. Risk attitude and wealth

  37. Individuals vsentrepreneurs • In general, individuals are more risk-averse than businesses • Possibly because businesses know better about risk diversification. • Budget constraint is less a concern for businesses.

  38. Risk and Society • Societies’ desire for risk neutrality in some instances • Individual entrepreneurial endeavors promote risk aversion • Underinvest in risky projects • Provides corporations with a good buffer

  39. Market for Insurance • Transfer of risk from one party to another – transferring risks from RA agents to RN or RL ones increases efficiency. • Imperfect information • Moral hazard • Adverse selection

  40. An example of moral hazard • The prevailing health insurance programs in Taiwan provide compensations to women who have a hysterectomy before age 45. • This design leads to a typical phenomenon of moral hazard, creating a spike in the number of hysterectomies before insurants reaching age 45.

  41. Frequency by date

  42. Frequency by quarter

  43. Market for Insurance • Uninsurable risks • A risk that cannot be diversified • Eg. Group risk • Eg. Health risk • Eg. Profit or income

  44. Section 18.3 Futures markets

  45. Futures Markets • Futures contract • Deliver specified good at specified future date at specified price • Futures market • Market for futures contracts • Spot market • Market for goods for immediate delivery • Spot price • Price in spot market

  46. Speculation • Speculator • Attempts to earn profits in futures market • Predicts future changes in supply or demand • Speculation and welfare • Guess future correctly • Earn profit • Increase social welfare

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