Explain Each Step Throughly-----
Sharon spends period 1 in school and period 2 working.
In period 1 her utility function is given by U1(S,F) = 300*min[S,F] where S represents studying and F represents fun.
In period 2 her utility function is given by U2(L,c) = l(c-120), where represents leisure and c represents consumption. Sharon’s consumption is determined by her wage and the number of hours she works, c=wL. You can assume l+ L = 24 and pc = 1.
Here is the catch: w = 2S. Your parents may have mentioned this. The more time spent studying, the higher the wage you might reasonably expect.
Ultimately, we are going to want to figure out the choice of S that maximizes Sharon’s lifetime utility, where UL = U1 + U2, but we will proceed step-by-step.
(a) Find Sharon’s maximum first period utility. Consider only period 1 for now.
(b) Find Sharon’s optimal consumption and leisure as a function of w. Consider only period 2 for now.
(c) Now let us consider how w=2S links the 2 periods. Explain why Sharon would never choose S<12. One sentence is all you need.
(d) Find U1 + U2 if S=12. (Yes, you have already pretty much done the work.)
(e) Can Sharon beat your answer in part d by studying more? For full credit, find the level of S that maximizes U1+U2.