Lottery jackpots are often paid out over 20 or more years, but the winner can often choose to take a lump sum instead. For some, the cash option is a lot better. In January 2007, an 84 year old retired electrician and WWII veteran in Missouri won the $254 million Powerball jackpot. He was given the option of receiving the jackpot as $8.467 million immediately and $8.467 million per year for the next 29 years, or $120.504 million immediately. What discount rate does this option imply?

3. saving two consumers, larry and jeff, have utility functions defined over the two periods of their lives: middle age (period zero) and retirement (period 1). they have the same income in period 0 of m dollars and they will not earn income in period 1. the interest rate they face is r. larry’s and jeff’s utility functions are as follow. = 0.5 + 0.5 and = 0.5 + 0.5 for each person is between zero and one and represents each consumer’s temporal discount econ 340: intermediate microeconomics. ben van kammen: purdue university. rate. a. write the budget constraint that applies to both jeff and larry in terms of consumption in each period and ), interest rate, and m. b. what is larry’s and what is jeff’s marginal rate of intertemporal substitution? c. what is the slope of the budget constraint? d. write each consumer’s condition for lifetime utility maximization. e. re-arrange the conditions from part (d) to solve for the ratio, . f. if > which consumer will save more of his middle age income? g. if > 1 1+ , in which period will larry consume more: = 0 or = 1?