Economics 321 Problem Set #3 Rules: Please post your answers on Sakal. I. Life Cycle Model Michelle is a rising star in the world of TV news. She will make 10 units of income in her first year, then 20, then 40, and then 80, before retiring for the final year of her life. 1. What would Michelle desire to consume each year if she were a life cycle saver: (a) 30; (b) 35; (c) 10; (d) 40; What would Michelle actually consume each year, taking into account any liquidity con- straints she might face: 2. In year 1: (a) 20; (b) 10; (c . In year 2: (a) 10; (b) 15; (c . In year 3: (a) 30; (b) 40; (c) 0; (d) 15; . In year 4: (a) 10; (b) 20; (c) 40; (d) 80; 6. In year 5: (a) 0; (b) 40; (c) 20; (d) 10; Determine Michelle's actual consumption be if she received an unexpected inheritance from her parents of 10 units: 7. What is her consumption in year 1 assuming the inheritance comes m year 1: (a) 20; (b) 25; (c) 32; (d) 10; 8. What is her consumption in year 2 assuming the inheritance comes i year 2: (a) 20; (b) 30; (c) 40; (d) 32; 9. What is her consumption in year 3 assuming the inheritance comes in year 3: (a) 43.33; (b) 30; (c) 40; (d) 80; 10. What is her consumption in year 4 assuming the inheritance comes in year 4: (a) 80; (b) 10; () 27.3; (d) 45; 11. What is her consumption in year 5 assuming the inheritance comes in year 5: (a) 0; (b) 10; (c) 50; (d) 20; What would Michelle's actual consumption be if she knew for certain that she will receive an inheritance from her parents of 10 units in year 2: 12. Year 1: (a) 10; (b) 20; (c) 30; (d) 32; 13. Year 2: (a) 20; (b) 30; (c) 32; (d) 40; 14. Year 3: (a) 20; (b) 30; (c) 40; (d) 80; 15. Year 4: (a) 20; (b) 40; (c) 80; (d) 0; 16. Year 5: (a) 0; (b) 20; (c) 30; (d) 40; ' Lo 0: (d) 0; ; (d) 20; it Wt i st e O o= L2 . II. Risk aversion Investor A has utility function U = 1000W W?2, while investor B has utility U = 5W, where W is their wealth. They both are choosing among two investments and have $20 to invest. One is a savings certificate that guarantees their wealth to be $23 next year; the other is an investment in Spacely Sprockets in which her wealth has a 25% chance of resulting in a wealth of $92 and a 75% chance of leaving you with a wealth of 0. 17. What is your expected wealth if you invest in the savings certificate (a) 10; (b) 15; (c) 20; (d) 23; 18. What is your expected wealth if you invest in Spacely Sprockets: (a) 15; (b) 23; (c) 92; (d) 0; 19. What is A's expected utility from the savings certificate: (a) 19,732; (b) 1000; (c) 92; (d) 22,471 20. What is B's expected utility from the savings certificate: (a) 115; (b) 239; (c) 442; (d) 15; 21. What is A's expected utility from Spacely Sprockets: (a) 92; (b) 0.25; () 20,884; (d) 460; 22. What is B's expected utility from Spacely Sprockets: (a) 15; (b) 115; (c) 92; (d) 0.75; III. Mean-variance analysis Consider two stocks with the following return patterns over the last five years: 1 2 3 4 5 Fidelity 15 4 12 19 0 Dreyfus 10 6 5 11 8 23. What is the mean return on Fidelity: (a) 15; (b) 4; (c) 19; (d) 10; 24. What is the mean return on Dreyfus: (a) 8; (b) 9; () 11; (d) 0; 25. What is the variance of Fidelity returns: (a) 32; (b) 61.5; () 50; (d) 0; 26. What is the variance of Dreyfus returns: (a) 10; (b) 34.2; (c) 6.5; (d) -12; 27. What is their covariance between Fidelity and Dreyfus: (a) -27.5; (b) 10.75; (c) 19.2; (d) 7.34; Suppose your demand for risky assets 18 2 x Euxpected Return - 0.05 x Variance of Return, 28. How much would you be willing to pay for Fidelity: (a) 16.93; (b) 12.32; () 11.11; (d) -3.24; 29. How much would you be willing to pay for Dreyfus: (a) 12.33; (b) 21.9; (c) 19.72; (d) 15.67