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Uncertainty and Risky Behavior

Uncertainty and Risky Behavior. The Economics of Uncertainty. Utility is a function of income. The higher the level of income, the higher the level of utility. Decisions are based on expected utility, not expected income. Income and Utility. U. U. U.

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Uncertainty and Risky Behavior

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  1. Uncertainty and Risky Behavior Lectures in Microeconomics-Charles W. Upton

  2. The Economics of Uncertainty • Utility is a function of income. • The higher the level of income, the higher the level of utility. • Decisions are based on expectedutility, not expected income. Uncertainty and Risky Behavior

  3. Income and Utility U U U Rises more than proportionally: MU Increasing Rises in proportionMU Constant Rises less than proportionally:MU Declining I I I Uncertainty and Risky Behavior

  4. Risk Averter U U200 U100 Y 100 200 Uncertainty and Risky Behavior

  5. Risk Averter U Here, utility is a function of income. But utility rises slower than income: MU is declining U200 U100 Y 100 200 Uncertainty and Risky Behavior

  6. Risk Averter U Why do I draw this red line? Patience U200 U100 Y 100 200 Uncertainty and Risky Behavior

  7. Risk Averter U Our individual is offered either $150k for sure or a 50-50 bet for $50k U200 U100 Y 150 100 200 Uncertainty and Risky Behavior

  8. Risk Averter U If he passes on the bet E(U) = U150 U200 U150 U100 Y 150 100 200 Uncertainty and Risky Behavior

  9. Risk Averter U If he takes the bet E(U) = 0.5U200 +0.5U150 U200 U150 U100 Y 150 100 200 Uncertainty and Risky Behavior

  10. Risk Averter U E(U) is where the red line hits the expected income line U200 U150 U100 Y 150 100 200 Uncertainty and Risky Behavior

  11. Risk Averter U U200 U150 Expected Utility U100 Expected Income Y 150 100 200 Uncertainty and Risky Behavior

  12. Risk Averter U The geometry requires that the utility from the bet be less than the utility from the sure thing. U200 U150 Expected Utility U100 Expected Income Y 150 100 200 Uncertainty and Risky Behavior

  13. Risk Averter U Don’t take bet. Expected utility is less than utility without bet. U200 U150 Expected Utility U100 Expected Income Y 150 100 200 Uncertainty and Risky Behavior

  14. Risk Averter U Don’t take bet. Expected utility is less than utility without bet. U200 U150 Expected Utility Person is risk averter; will not take fair bet. U100 Expected Income Y 150 100 200 Uncertainty and Risky Behavior

  15. A Digression • An individual is offered a bet. • If he loses, he gets income of IL. • If he wins, he gets income of IW. • The probability of winning is p • His expected income is (1-p)IL + pIW Uncertainty and Risky Behavior

  16. A Digression • An individual is offered a bet. • If he loses, he gets income of IL. • If he wins, he gets income of IW. • The probability of winning is p • His expected income is (1-p)IL + pIW U((1-p)IL + pIW ))or (1-p)U(IL) + pU(IW)? Uncertainty and Risky Behavior

  17. A Digression • An individual is offered a bet. • If he loses, he gets income of IL. • If he wins, he gets income of IW. • The probability of winning is p • His expected income is (1-p)IL + pIW If he is offered his choice between the bet or his expected income, which should he take? Uncertainty and Risky Behavior

  18. A Digression U Plot IL, IW,U(IW), U(IL) UWin ULose Y IL IW Uncertainty and Risky Behavior

  19. A Digression U Draw the red line; connect the dots. UWin ULose Y IL IW Uncertainty and Risky Behavior

  20. A Digression U Find (1-p)IL + pIL UWin ULose Y IL IW Uncertainty and Risky Behavior

  21. A Digression U Find the Utility with the expected income UWin U ULose Y IL IW Uncertainty and Risky Behavior

  22. A Digression U Find the point where the blue income line hits the red line. UWin U ULose Y IL IW Uncertainty and Risky Behavior

  23. A Digression U Draw a line to the utility axis. This gives us Expected Utility UWin U ULose Y IL IW Uncertainty and Risky Behavior

  24. A Digression U Here, E(U) < U(Sure). Always true with diminishing MU UWin U ULose Y IL IW Uncertainty and Risky Behavior

  25. Risk Neutrality U Utility rises in proportion to income U200 U100 Y 200 100 Uncertainty and Risky Behavior

  26. Risk Neutrality U Find expected income, draw the red line U200 U100 Y 150 200 100 Uncertainty and Risky Behavior

  27. Risk Neutrality U Draw the green dot; find expected utility U200 U150=E(U) U100 Y 150 200 100 Uncertainty and Risky Behavior

  28. Risk Neutrality U Expected utility and utility from the sure thing are the same. U200 U150=E(U) U100 Y 150 200 100 Uncertainty and Risky Behavior

  29. Risk Neutrality U Expected utility and utility from the sure thing are the same. U200 U150=E(U) Person is risk neutral. He is indifferent to fair bet. U100 Y 150 200 100 Uncertainty and Risky Behavior

  30. Risk Taker U The last case: utility rises faster than income, MU is increasing U200 U100 Y 200 100 Uncertainty and Risky Behavior

  31. Risk Taker U Draw the red line U200 U100 Y 200 100 Uncertainty and Risky Behavior

  32. Risk Taker U Find Expected Income and Utility from the sure thing. U200 U150 U100 Y 200 100 150 Uncertainty and Risky Behavior

  33. Risk Taker U Draw the green dot and find E(U) from the bet. U200 E(U) U150 U100 Y 200 100 150 Uncertainty and Risky Behavior

  34. Risk Taker U Expected utility exceeds utility from the sure thing. U200 E(U) U150 U100 Y 200 100 150 Uncertainty and Risky Behavior

  35. Risk Taker U Expected utility exceeds utility from the sure thing. This individual is a risk-taker. He will take the gamble. U200 E(U) U150 U100 Y 200 100 150 Uncertainty and Risky Behavior

  36. The Three Cases • When utility rises less than income, we say the individual is a risk averter. • That is, he will avoid fair bets Uncertainty and Risky Behavior

  37. The Three Cases • When utility rises less than income, we say the individual is a risk averter. • When utility rises faster than income, the individual is a risk-taker. • He will take fair bets Uncertainty and Risky Behavior

  38. The Three Cases • When utility rises less than income, we say the individual is a risk averter. • When utility rises faster than income, the individual is a risk-taker. • When utility is proportional to income, the individual is risk-neutral • He is indifferent to fair bets Uncertainty and Risky Behavior

  39. The Three Cases • Which one is most likely? Uncertainty and Risky Behavior

  40. The Three Cases • Which one is most likely? • Some are risk takers, some are risk averters, and some are risk neutral. Uncertainty and Risky Behavior

  41. The Three Cases • Which one is most likely? • Some are risk takers, some are risk averters, and some are risk neutral. • Butmost people are risk averters. Uncertainty and Risky Behavior

  42. End ©2003 Charles W. Upton Uncertainty and Risky Behavior

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