please solve this question on a paper when you draw the graph for part b

(6 points total) Suppose an individual who just graduated from high school has four periods in their working life (t=1,2,3,4). In this economy, there are three career options: Option 1 Work for four periods. For each period, the salary is Y1. Option 2 Attend community college in the first period and work during the next three periods. It costs C1 in the first period to attend community college. After graduation, the salary is Y2 for each period t=2,3,4. Option 3 Attend university in the first two periods and work during the third and fourth periods. Attending university costs C2 each period. Upon graduation, the salary is Y3 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,C1, and C2. Note: Do not use the approximation formula covered in class. b) (2.5 points) Suppose r=0,Y1=20,Y2=40, and Y3=90. For each career option, mathematically derive the range of C1 and C2 in which each career option is optimal. Graphically illustrate the combination of (C1,C2) in which each career option is optimal. Note: For the graphical illustration, place C1 on the horizontal axis and C2 on the vertical axis. Shade the region in which each career option is optimal. c) (1 point) Assume that in this economy, individuals face different values of C1 and C2. Suppose (C1,C2) is uniformly distributed in the region {(C1,C2)0C1100,0C2100} (assume independence between C1 and C2 ). What is the fraction of individuals who would choose option 1 ? Briefly explain. d) (1 point) Now, suppose the government decides to provide a subsidy b for university students. This lowers the per-period cost of attending university from C2 to C2b. Suppose the government sets b=6. The remaining values for r,Y1,Y2,Y3,C1, and C2 are the same as in part (b). Mathematically derive the range of C1 and C2 in which each career option is optimal. Graphically illustrate the combination of (C1,C2) in which each career option is optimal. Assuming that the distribution of (C1,C2) is the same as in part (c), briefly describe how the fraction of individuals who choose each option will change after the government subsidy