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Practice problem--it's very helpful ~

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Department
Economics
Course Code
ECO359H5
Professor
Sun

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ECO359/2011UniversityofToronto
PracticeProblems  DepartmentofEconomics
1
ECO 359 Practice Problems 1 – Solution Guidelines
1.
(a) From your lecture notes: î:+;LN, hence +ÛLwFN. Note that the project will only be
carried out if r < 5 (else +ÛLr).
(b) The NPV of investing I units into the project is given by
028 L F+E
s
sEN:xF+t
;+ä
Verify that maximizing the above NPV indeed yields your answer in (a).
Maximizing NPV yields wF+
ÛLN, hence again: +ÛLwFN.
(c)
i. The constraint is ?5E?
6Lsw for ?5Qsr. Note that the budget line does not extend to
the right of the endowment (your cannot borrow with the storage technology).
ii. Assuming NRr, the budget constraint is
?5E?6
sENLsrE
w
sEN
If NOr, Chuck will only deal with the back to borrow, but will use the storage
technology to save. Hence, the budget constraint is:
?5E?
6LswBKN?5Osr
?5E?6
sENLsrE
w
sENáBKN?
5Rsr
iii. Chuck will invest +ÛLwFN units, and the budget constraint will then be given by
?5E?6
sENL:srF:wFN;;E
wEx
:wFN
;F:wFN;
6t
sEN :s;
I trust that you could do any simplifications of the above expression yourselves.
(d) Continue to assume that rONOw., hence the budget constraint that you derived in (c)(iii)
holds. Denote the RHS of (1) by M:
?5E?6
sENL:srF:wFN;;E
wEx
:wFN
;F:wFN;
6t
sEN /:t;
To solve for the optimal utility choice, we need to set MRS =slope of the budget line (=
“price ratio”) (recall from your micro course that at an interior optimum the indifference
curve is tangent to the budget line):
t?6
?5
LsEN\?
6L?5:sE;
t
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Description
ECO3592011 UniversityofToronto PracticeProblems DepartmentofEconomics ECO 359 Practice Problems 1 Solution Guidelines 1. (a) From your lecture notes: + L N, hence + L M . N. Note that the project will only be carried out if r < 5 (else +H). (b) The NPV of investing I units into the project is given by I & L .+ - :N . +J + I - N Verify that maximizing the above NPV indeed yields your answer in (a). Maximizing NPV yields M . + L N, hence again: + L M . N. (c) i. The constraint is # - ?$L IM for ? # IH. Note that the budget line does not extend to the right of the endowment (your cannot borrow with the storage technology). ii. Assuming N 4 H, the budget constraint is ? - ?$ L IH - M # I - N I - N If N O H, Chuck will only deal with the back to borrow, but will use the storage technology to save. Hence, the budget constraint is: ? - ? L IM*KN? O IH
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