A researcher estimated the following regression models:

Ln Ym = 30,000 + 2,000S

Ln Yf = 30,000 + 1,250S

Where Ln Ym is the Ln (or base e logarithm) of annual wage of males and Ln Yf is the annual wage of females, and S is the number of years of education (schooling). Suppose that the average annual wage of males is $50,000, the annual wage of females is $40,000, the average years of education is 10 for males and 8 for females. Show your work.

a) Decompose the difference in the annual wages between males and females into a part that is due to differences in schooling;

b) and a part that is due to "discrimination" in the returns to schooling.

c) State why this estimate of discrimination may be too high, and too low.