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. Earnings, Bo + B Edu; + Age; +B3Age? + ui, = where Earnings, is the amount of money that individual i earns in a year measured by SGD, Edu, is the year of education of i and Age, is the age of i measured by year. a. (4 points) What is the impact of a unit increase in Age, on average Earningsi when Age; = 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 3 and B3 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 Edu, Age, in the regression model, then we have Earnings, Bo + B Edu; + Age; + B3Age? +BEdu Age; + u. What is the impact of Age, on the averaged Earnings, in this model? Suppose 4 is positive, can you give a brief analysis about 4?