ECO359/2011UniversityofToronto

PracticeProblems DepartmentofEconomics

1

ECO 359 Practice Problems 1

1. Consider the situation of Chuck Noland who is stranded on an island: Chuck has to decide on

his consumption today, ?5and next year, ?6. Today (PLs) he has income S5Lsr coconuts,

next year (PLt) is cyclically bad and he has only S6Lwcoconuts. His utility function is

7:?5á?

6;L?

5

6?6. Once every year he gets a visitor from the Wilson Bank Inc. who allows

him to lend or borrow money at interest rate N.

In addition to putting money to the bank or borrowing money from it, he can invest some of

his income in his coconut plant which will give him a marginal rate of return î:+;LwF+,

where + is the amount he invests in the plant.

(a) Which level of investment will he choose?

(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).

(c) You will now be asked to describe Chuck's budget constraint. Do this in three steps:

i. Draw Chuck's budget constraint assuming there is no investment opportunity and no

Wilson Bank, but a costless storage facility. What is each period's budget constraint

expressed mathematically?

ii. Now draw a new picture in which you include the budget line from (i) and add the

budget line resulting if there bank borrowing and lending but no investment opportunity.

What is the combined budget constraint for both periods together expressed

mathematically?

iii. Assume that rONOw. Repeat (ii) but now include the investment project. What is the

combined budget now if expressed mathematically? (Hint: Use the Fisher Separation

theorem and the NPV formula given to you in part (b)!)

(d) Continue to assume that rONOw. Compute Chuck's optimal utility choice as a function

of N. (Hint: Recall from your micro courses that the relevant optimality condition is

/45L price ratio.

Multiple Choice Questions. The following questions are a collection of "true-false" or Multiple

Choice questions. You should be prepared to explain your answer briefly.

1. Which of the following statement(s) are true concerning Fisher separation?

(a) Investors can delegate decisions to managers irrespective of their preferences.

(b) The manager will never choose negative NPV projects.

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