ECO359/2011UniversityofToronto

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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