The following data give the dates of successive turning points in U. S. economic activity and the corresponding levels of real GDP at the time. Turning Point Date Real GDP (1996 $ billions) (A) July 1953 1992.2 (B) May 1954 1941.0 (C) Apr. 1957 2182.7 (D) Apr. 1958 2117.4 (E) Apr. 1960 2391.0 Which of the turning points are troughs? (A), (B), and (C) (C), (D), and (E) (A), (C), and (E) (B) and (D)

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?