ECN 134 SOLUTION KEY 1 1 i 06 and 10 Find P X 0 P Z 0 06 10 P Z 6 Turning to the normal tables we find that the probability associated with the critical value of 6 is 27 43 That is 27 43 of the time and thus approximately 13 years the return on corporate bonds was less than 0 ii 11 and 16 Find out what the rate of return is for the worst five years of the S P That is what was the rate of return for the worst 10 of the last 48 years We must solve for a 10 P X a P Z a 11 Turning to the 16 normal tables we find that the critical value leading to a 10 outcome is 1 28 Thus find a such that a 11 16 a 09 1 28 This tells us approximately that in the worst 5 years of the last 48 years the S P lost 9 or more 2 r 0 12 i NPV 75 000 140 000 1 r 5 75 000 79 439 76 4 439 76 ii Yes since Venkatesh can borrow against the return from selling the land iii Keeping future consumption unchanged means Venkatesh borrows against the entirety of his return i e he borrows 140 000 1 0 12 5 79 439 76 at t 0 So C0 Y0 75 000 79 439 76 Y0 4439 76 The e ect on C0 is 4439 76 NPV iv Venkatesh is willing to pay up to the PV of his returns on the land or 79 439 8 1 3 Work 39 39 PVW 39 39 1 r Law school 23 65 PVL 23 65 1 r Note that if the budget constraint is linear Hang Ro will allocate half of PV to each periods consumption Situation I r 30 Hence slope 1 r 1 3 and PVW 69 PVL 73 Her optimal consumption plan is Work C0 69 2 34 5 C1 34 5 1 3 44 9 Lending 39 34 5 4 5 Law C0 73 2 36 5 C1 36 5 1 3 47 5 Borrowing 36 5 23 13 5 Since the law school budget constraint is everywhere outside the work budget constraint Hang Ro will clearly choose Law school independent of her preference Situation II r 50 Hence slope 1 5 and PVW 65 PVL 66 3 i In this situation we need to know preferences If preferences were di erent she might choose L over W ii Work If borrowing was unrestricted then C0 65 2 32 5 C1 32 5 1 5 48 8 This point is in fact on the relevant portion of the constraint and Hang Ro will consume at 32 5 48 8 lending 39 5 32 5 6 5 and attain a utility level of 32 5 48 8 1586 Law If borrowing were unrestricted then C0 66 3 2 33 2 C1 33 2 1 5 49 8 Unfortunately this point is infeasible She will end up at the kink borrowing 3 at t 0 and consuming C0 26 C1 60 5 thus enjoying a utility of 26 60 5 1573 Now she is slightly better o working right away 2
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