3. (20 points) Consider a model of annual employee earnings as a function of the age of each employee and other measures of productivity such as education. Earningsi=0+1Edui+2AAgei+3Ag ei2+ui, where Earnings si is the amount of money that individual i earns in a year measured by SGD, Edui is the year of education of i and Agei is the age of i measured by year. a. (4 points) What is the impact of a unit increase in Age i on average Earnings E i when A2ei=40 ? (Hint: take partial derivative first.) b. (6 points) As a young worker gets older, his or her earnings will typically increase. Beyond some point, however, an increase in age will not increase earnings by very much at all, and around retirement, we'd expect earnings to start to fall abruptly with age. Would you expect the signs of 2 and 3 to be positive or negative? c. (5 points) If a man decides to retire when his earnings start to fall with the increasing age, what is the best age for him to retire? d. (5 points) If we add an interactive term EduiAgei in the regression model, then we have Earningsi=0+ 1Edui+2AAgeei+3AAgeei2+4EduiA2ei+ui. What is the impact of Agei on the averaged Earnings Ein this model? i Suppose 4 is positive, can you give a brief analysis about 4 ?.

1. 3. (20 points) Consider a model of annual employee earnings as a function of the age of each
employee and other measures of productivity such as education. Earningsi=0+1Edui+2AAgei+3Ag
ei2+ui, where Earnings si is the amount of money that individual i earns in a year measured by
SGD, Edui is the year of education of i and Agei is the age of i measured by year. a. (4 points)
What is the impact of a unit increase in Age i on average Earnings E i when A2ei=40 ? (Hint: take
partial derivative first.) b. (6 points) As a young worker gets older, his or her earnings will typically
increase. Beyond some point, however, an increase in age will not increase earnings by very
much at all, and around retirement, we'd expect earnings to start to fall abruptly with age. Would
you expect the signs of 2 and 3 to be positive or negative? c. (5 points) If a man decides to retire
when his earnings start to fall with the increasing age, what is the best age for him to retire? d. (5
points) If we add an interactive term EduiAgei in the regression model, then we have Earningsi=0+
1Edui+2AAgeei+3AAgeei2+4EduiA2ei+ui. What is the impact of Agei on the averaged Earnings
Ein this model? i Suppose 4 is positive, can you give a brief analysis about 4 ?