Study Guides
(238,408)

Canada
(115,131)

Simon Fraser University
(3,412)

Economics
(100)

ECON 305
(2)

Luba Patterson
(2)

Midterm

# Midterm 2B practice questions with solutions.docx

Unlock Document

Simon Fraser University

Economics

ECON 305

Luba Patterson

Winter

Description

Midterm -2B practice questions
The exam is out of 100 points.
Grading:
1. Omid
2. Sepideh
3. Emanuel
4. Bill
5. Edouard
1. Suppose Gilligan is on an island by himself and lives only for two periods. He has a
fruit tree that can produce y 10 units of fruit in period 1 andy 10 units of fruit
1 2
in period 2. The fruit rots each period if not consumed and cannot be saved. Gilligan
has a utility function given by
0.5
U(c 1c 2c c1 2
a) Given that Gilligan cannot trade with another person, what is his optimal
level of consumption of fruit in each of the two periods? How much should he
save in each period? (5 points)
Answer: Gilligan cannot save, so he should consume as much as possible of his
endowment each period. He will set
c 10
1
c 210
5 points for correct answer. 0 otherwise.
b) Now suppose Gilligan is visited by an explorer, Jack, who is willing to engage
in trade with Gilligan. Jack wants to lend to Gilligan in Period 1 at a gross
interest rate R, but wants to be able to borrow from Gilligan in Period 2.
Would Gilligan accept this deal? Why or why not? Explain in detail. (5 points)
Answer: You can easily see that Gilligan values consumption relatively more in
Period 1 than Period 2. This means he would want to borrow today and repay
tomorrow. This is what Jack is offering, so Gilligan should accept the deal.
5 points for correct answer (accept/reject deal + explanation. 2 points for
correct answer (accept/reject deal).
2. Anne has the following two-period utility function.
0.5
U(c 1c2) 2c1 c 2
Anne is considering going to university in Period 1. This will cost her an amount Q ,
which must be paid in Period 1. Anne cannot work while she is attending university.
After completing university, she will earn y 2 For what level of y2 is it worthwhile
for her to attend university? Assume that if she does not go to university, she will
earn y in each of Periods 1 and 2. Also assume that she can borrow at a gross
interest rate R.
(20 points)
Answer: Anne must compare the utility she gets from going to university and only
working in Period 2 to the utility she gets from working in both periods and earning
y each period.
If she goes to university, her utility can be solved for as
0.5 y2 c2
L 2c1 c2 Q c1
R R
0.5
c1:c1 0
c :1 0
2 R
y2 c2
:R Q c 1 R 0
Solving,
R
c 2 1
1 R 2
* 1
c2 y 2 R Q c 1 y 2 R RQ
1 0.5 1
U 2 2 y2 RQ
R R
2 y 1 RQ
R 2 R
1
y2 RQ
R
-5 points for finding c1 and c2 properly. Allow for part marks.
-3 additional points for plugging into U and finding the utility level.
If she works continuously, her utility level can be determined as follows: 0.5 y c 2
L 2c1 c2 y c 1
R R
c :c 0.5 0
1 1
c2:1 0
R
y c2
: y c 1 0
R R
Solving,
R
c 2 1
1 R2
c * y R(y c ) y R(y 1 )
2 1 R2
0.5
1 1
U 2 2 y R(y 2)
R R
2 1
y(1 R)
R R
1
y(1 R)
R
-5 points for finding c1 and c2 properly. Allow for part marks.
-3 additional points for plugging into U and finding the utility level.
She will go to university if
y 1 RQ y(1 R) 1
2 R R
y2 y(1 R) RQ
-4 points for comparing the utility levels and solving for y2.
3. Grace is deciding how much to work and consume today and tomorrow. She has
the following utility function:
U(c ,c ,n ,n ) ln(c) 3ln(1 n) ln(c 3ln(1 n)
1 2 1 2
Grace earns y z n (1 ) in Period 1 and y z n (1 ) in Period 2. That is,
1 1 1 1 2 2 2 2
she earns labour income, but must pay a fraction of it each period to the government
at a pre-specified tax rate.z1and z2 are exogenous productivity parameters. She
can also borrow and save in international financial markets at a gross interest rate
R. (30 points)
a) Write out Grace’s intertemporal budget constraint.
(5 points)
Answer: Grace’s budget constraint is given by
z n (1 ) z2 2(1 )2 c c 2
1 1 1 R 1 R
-5 points for correct answer.
-If they write in terms of y1 + y2/R, OK for now.
-2 points if they forget to divide through by R.
b) Write out Grace’s choice problem. (ie. What is she maximizing given certain
constraints, and what must she choose?)
Answer: Grace’s objective is to maximize her utility
U(c 1c 2n 1n 2 ln(c) 3ln(1 n) lnc) 3ln(1 n)
subject to the budget constraint:
z n (1 ) z 2 21 )2 c c2
1 1 1 R 1 R
by choosing optimal levels of consumption in periods 1 and 2, and labour
supplies in period 1 and 2.
-5 points for correct answer.
-If they write in terms of y1 + y2/R, OK for now.
-Deduct 1 point if they do not specify what Grace’s choice variables are.
-2 points if they only write out the utility function (and forget the budget
constraint).
c) Using a Langrangian, set up Grace’s optimization problem and take first
order conditions. (6 points) z 2 21 )2 c2
L ln(c)3ln(1n) lnc)3ln(1n) zn (11 1 1 c 1
R R
1
c1: 0
c1
c : 0
2 c R
2
3
n1: 1n z 11 )10
1
3 z 21 )2
n 2 0
1n 2 R
: z n (1 ) z2 2(1 2 c c20
1 1 1 R 1 R
-6 points for each of the lines (Lagrange equation and the 5 first order
conditions).
-Part marks OK and deductions for incorrect FOCs.
d) Find Grace’s intertemporal Euler equation for consumption. How will Grace’s
intertemporal decision be affected by an increase in the interest rate?
(4 points)
Answer: To find the Euler equation use the fir

More
Less
Related notes for ECON 305