The Present value of an infinite stream of dollar payments of $z (that starts next year) is $z/I when the nominal interest rate, I, is constant. This formula gives the price of a consol -a bond paying a fixed nominal payment each year, forever. It is also a good approximation for the present discounted value of a stream of constant payments over long but not infinite periods, as long as i is constant 1.1. Suppose i-1096. Let $z-100, what is the present value of the consol? 12. ifi-10%, what is the expected present discounted value of a bond that pays $z over the next 10 years? 20 years? 30 years? (Hint: Use the formula from Chapter 14, but remember to adjust for the first payment. 1.3. Repeat the calculations in (1.1) and (1.2) for i-2% and 1-5%.

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?