On January 1, 2021, M Company granted 93,000 stock options to certain executives. The options are exercisable no sooner than December 31, 2023, and expire on January 1, 2027. Each option can be exercised to acquire one share of $1 par common stock for $12. An option-pricing model estimates the fair value of the options to be $4 on the date of grant. If unexpected turnover in 2022 caused the company to estimate that 10% of the options would be forfeited, what amount should M recognize as compensation expense for 2022

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?