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

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 expected utility, not expected income.

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

4. Uncertainty and Risky Behavior Risk Averter U Y 100200 U 100 U 200

5. Uncertainty and Risky Behavior Risk Averter U Y 100200 U 100 U 200 Here, utility is a function of income. But utility rises slower than income: MU is declining

6. Uncertainty and Risky Behavior Risk Averter U Y 100200 U 100 U 200 Why do I draw this red line? Patience

7. Uncertainty and Risky Behavior Risk Averter U Y 100200 U 100 U 200 Our individual is offered either $150k for sure or a 50-50 bet for $50k 150

8. Uncertainty and Risky Behavior Risk Averter U Y 100200 U 100 U 200 If he passes on the bet E(U) = U 150 150 U 150

9. Uncertainty and Risky Behavior Risk Averter U Y 100200 U 100 U 200 If he takes the bet E(U) = 0.5U 200 +0.5U 150 150 U 150

10. Uncertainty and Risky Behavior Risk Averter U Y 100200 U 100 U 200 E(U) is where the red line hits the expected income line 150 U 150

11. Uncertainty and Risky Behavior Risk Averter U Y 100200 U 100 U 200 150 U 150 Expected Utility Expected Income

12. Uncertainty and Risky Behavior Risk Averter U Y 100200 U 100 U 200 150 U 150 Expected Utility Expected Income The geometry requires that the utility from the bet be less than the utility from the sure thing.

13. Uncertainty and Risky Behavior Risk Averter U Y 100200 U 100 U 200 150 U 150 Expected Utility Expected Income Don’t take bet. Expected utility is less than utility without bet.

14. Uncertainty and Risky Behavior Risk Averter U Y 100200 U 100 U 200 150 U 150 Expected Utility Expected Income Don’t take bet. Expected utility is less than utility without bet. Person is risk averter; will not take fair bet.

15. Uncertainty and Risky Behavior A Digression An individual is offered a bet. –If he loses, he gets income of I L. –If he wins, he gets income of I W. –The probability of winning is p His expected income is (1-p)I L + pI W

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

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

18. Uncertainty and Risky Behavior A Digression U Y ILIL IWIW U Lose U Win Plot I L, I W, U(I W ), U(I L )

19. Uncertainty and Risky Behavior A Digression U Y ILIL IWIW U Lose U Win Draw the red line; connect the dots.

20. Uncertainty and Risky Behavior A Digression U Y ILIL IWIW U Lose U Win Find (1-p)I L + pI L

21. Uncertainty and Risky Behavior A Digression U Y ILIL IWIW U Lose U Win Find the Utility with the expected income U

22. Uncertainty and Risky Behavior A Digression U Y ILIL IWIW U Lose U Win Find the point where the blue income line hits the red line. U

23. Uncertainty and Risky Behavior A Digression U Y ILIL IWIW U Lose U Win Draw a line to the utility axis. This gives us Expected Utility U

24. Uncertainty and Risky Behavior A Digression U Y ILIL IWIW U Lose U Win Here, E(U) < U(Sure). Always true with diminishing MU U

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

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

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

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

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

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

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

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

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

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

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

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

37. Uncertainty and Risky Behavior 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

38. Uncertainty and Risky Behavior 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

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

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

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

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