Two options, X and Y, are available to solve an occurring problem. Option X provides a temporary solution for 5 years. It requires $1,000,000 initial investment, but results in a savings of $60,000 after six months and will be increased $25,000 each six months thereafter. Option Y provides a permanent solution. It requires $2,000,000 initial investment, but results in a savings of $120,000 every six months for an infinite amount of time. Assume the analysis period is infinitely long. Which option do you choose based on EUAW analysis at an interest rate of 10% compounded semiannually

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?