(6 points rota!) Suppose an individual whojust graduated from high school has four periods in their working life [I = 1.2.3.4). In this economy. there are three career options; Option I Work for four periods. For each period. the salary is '1']. Option 2 Attend community college in the first period and work during the next three periods. It costs C1 in the rst period to attend community college. After graduation. the salary is Y: for each period I: 2.3.4. Option 3 Attend university in the first two periods and work during the third and fourth periods. Attending university costs (I; each period. Upon graduation. the salary is Y; each period t = 3.4. Denote the market interest rate in each period as r. a} (1.5 points) Write down the net present value of earnings for each of the three career options. Your answer should be expressed in terms of r. Y1. Y2. Y3, Cl. and C; Note: Do not use the approximation n'mnio covered in cioss. b) (2.5 points) Suppose F0. Y.=2t]. Y;=40. and Y3=90 For each career option. mathematically derive the range ofC. and C3 in which each career option is optimal. Graphically illustrate the combination of (C1. C2) in which each career option is optimal. Note: For tire graphic-oi iiiustron'on. pines Cr on the itorimnmi axis and C: on the vorticoi axis. Shade the region in which each career option is optimoi. c} (i point} Assume that in this economy. individuals face different values of (I. and C3. Suppose [C1 . C3) is uniformly distributed in the region {031. Cl 3 C1 5 100.0 5 C; E 100] (assume independence between C. and C2). W hat is the fraction of individuals who would choose option 1'? Briey explain. d) (i point} Now. suppose the government decides to provide a subsidy i) for university students. This lowers the per-period cost of attending university from Cgto Cg'b. Suppose the government sets F6. The remaining values for r. Y1. Y2. Y3, Cl. and C2 are the same as in part {b}. Mathematically derive the range of C1 and C; in which each career option is optimal. Graphically illustrate the combination of(Ct . C2) in which each career option is optimal. Assuming that the distribution of(C. . C2) is the same as in part (c). briey describe how the fraction ofindividuals who choose each option will change after the government subsidy