consider a modified scenario where a potential worker invests in years of education. Each year of education costs a motivated worker $10,000 in terms of disutility and an unmotivated worker $20,000 in terms of disutility. The motivated worker is paid $900,000 in terms of present value of lifetime income while the unmotivated worker is paid $750,000, just like the previous problem. Each potential worker is motivated with probability 0.5. Assume that workers decide the number of years of schooling they invest in before joining school.

a. What is the cost of t years of education to a motivated and unmotivated worker?

b. Find the separating equilibrium.

c. In the separating equilibrium you just found, what is the minimum number of years of education would the motivated worker invest in? What about the unmotivated worker?