please answer question thorough.

Problem 1: Human Capital Investment (30 pts) From class, we have the human capital investment decision expressed in the equation below. The worker makes the decision to invest at time t = (). If she chooses to invest, she will pay for her investment at = 0. The worker will attend college if and only if T W, H Z L>Hy+C (Human Capital Investment) r (14+7r)t where t indicates year from 1 to T (the last period of work), W} represents the earnings at year if the worker is a college graduate, H; represents the earnings at year if the worker is not a college graduate, and r represents the interest rate. Hg represents the earnings at year t = 0 if the worker is not a college graduate, and Cj represents the direct monetary costs of investment at t = 0. For all calculations below, round your answers to the nearest hundredth. Suppose that the worker's earnings if she did not invest are $40 in time 0, $45 in time 1, $50 in time 2, and $55 in time 3. Suppose that the worker's earnings if she did invest are $60 in time 1, $70 in time 2, and $80 in time 3. Suppose also that the cost of schooling is Cjy = 10. The worker discounts the future at a rate of r = 0.10. a. Set up the equation based on the values given above. Plug in the values for each term. You do not have to solve the equation at this point. (4 pts) b. Now, solve the equation you set up in part a. Will the worker choose to invest in human capital? (2 pts) Now, suppose the worker discounts the future at a rate of r = 0.01. c. Solve the human capital investment equation. Will the worker choose to invest in human capital now that her discount rate r decreased? (4 pts) d. Would a decrease in r make her more or less likely to invest? Explain the economic intuition behind your answer. (3 pts) e. Suppose that all values except for Cy return to the values in part a-b. What is the monetary cost Cj that would make the worker still invest in human capital? Note: This will be a range. (4 pts) f. Suppose that all values except for H; return to the values in parts a-b. The rate of discounting the future is r = 0.10. Suppose that the worker will earn the same amount each year if she did not invest in human capital: H; = H for all t. What is the level of earnings from not investing, H;, that would make the worker invest in human capital? Hint: This will be a range. Write your answer for H in terms of the other variables before plugging in for values. This will make it easier to solve the rest of this question. (5 pts) g. Suppose now that everything is the same as in part f, except r = 0.01. Solve for H such that the worker would choose to invest in human capital. (5 pts) h. How does a decrease in r change the level of earnings from investing that would make the worker invest? State the economic intuition behind your answer. (3 pts)