Consider an individual who lives for two time periods. We will call these period 0 and period 1. In period 0. the individual can choose to attend school or work. In period 1. the individual works. If he does not attend school he period 0, he earns w_L("L" for "low") in both time periods. If he attends school, he pays the cost C in period 0 and earns w_H "(H" for "high) in period 1. The individual discounts period 1 earnings using the discount rate r. Assume the individual discounts period 1 goal is to maximize the present discounted value (PDV) of his earnings over these two periods. (a) Write an expression for the PDV of earnings for an individual who chooses to work in both periods. (b) Write a similar expression for an individual who attends school in period 0. (c) Write an inequality that if true would mean that the individual should go to school go period 0. (d) Explain how the decision to attend school is sensitive to changes in the model parameters: C, wH, wL, and r. (e) When w_L = $ 15,000, wH = $45,000, C = $10,000, and r = 25, what choice should the individual make? (f) If you knew that discount rates in the population we uniformly distributed over the interval [0, 1/2], what fraction of the population would attend school in period 0