TRENT UNIVERSITY
DEPARTMENT OF ECONOMICS
ECON 3250H
ASSIGNMENT #1
Dr. M. Arvin XXXXXXXXXX2022
DATE GIVEN: Wednesday, September 22, 2021.
DUE DATE: Beginning of class on Wednesday, October 13, XXXXXXXXXXAs your course
outline states: “late penalty is 20% for each day or part thereof for which the assignment is
late.” You have three weeks to complete this assignment.
Please complete your assignment in ink or type it. Your assignment will not be marked
unless you are officially registered in this course.
XXXXXXXXXXSuppose the demand for housing D is given by the function
XXXXXXXXXX −−= rpD
where p is the price of housing and r is the mortgage interest rate. Treat r as
exogenous. The supply of housing is given by
__
SS = , where
__
S is
exogenous.
i) Solve for the equili
ium housing price and then by partially
differentiating your reduced form, ca
y out a comparative
static analysis with respect to the mortgage interest rate and
the housing supply. Explain (in plain English) why your
answers make sense and be sure to depict each change that
takes place in a simple (two-dimensional) diagram.
ii) Suppose the demand for housing is changed from above to a
general function
),( rpDD = 0,0 rP DD
The supply of housing is still the same. Again, conduct a
comparative static analysis with respect to the mortgage
interest rate and the housing supply.
XXXXXXXXXXA consumer spends time t searching for a good, the price of which is p(t).
Assume the longer the search goes, the lower price the consumer would
pay for the good. Furthermore, assume there are diminishing returns to
the search since it is harder to find even lower prices as the search
continues; that is: p″(t) > 0. Without search the consumer would pay the
cu
ent going price of the good p0 . While searching, the consumer loses
income at a constant rate w .
i) Find the condition for an optimal search time t, if q number
of units of the good are bought. Explain what your
condition is saying in plain English.
ii) Check to make sure your second-order condition is
satisfied.
iii) What is the impact of a change in the consumer’s wage rate
w on the optimal search time if nothing else changes?
Explain why your answer makes sense.
iv) What is the impact of a change in the number of units q on
the optimal search time if nothing else changes? Again,
provide the necessary intuition.
XXXXXXXXXXA closed economy is described by the following equations representing
the goods and money markets:
)(rII = 0rI
),( rySS = 0,0 ry SS
GG =
TT =
0,0),( =
d
y
ddd MMryMM
p
M
M s =
I is real investment, S is real savings, G is real government expenditure,
T is real taxation,
dM is real demand for money,
sM is real supply of
money, y is real income, r is real rate of interest, M is nominal
money supply, and P is the price level. A bar over a variable indicates
exogeneity.
i) What is the effect of an increase in the nominal money
supply on the equili
ium p and r ? Explain.
ii) Find the partial elasticities of equili
ium p and equili
ium
with respect to M .
iii) Explain your results in part ii) in plain English (here I am
looking for some sort of intuition on why you think your
esults make sense; simply writing a mathematical result in
English – i.e., stating that your result ca
ies a certain sign –
will receive little credit because that is not intuition).
XXXXXXXXXXSuppose a profit maximizing automobile manufacturer produces its output
in two plants, one in the U.S. and the other in Canada. The total costs of
producing in the two plants are identical, except that the output produced
in the U.S. is subject to a per unit tax, t. Suppose the two total cost
functions are
USUSUSUS tQQQTC +++= 12
2
XXXXXXXXXX/2 ++= CANCANCAN QQTC .
The firm’s demand function is P=26-QT , where QT is total output in U.S.
and Canada.
i) Find the first-order conditions for this problem.
ii) Find the reduced form solutions for optimum values of QUS
and QCAN .
iii) Show that the second-order condition for this problem is
satisfied.
iv) By partially differentiating your reduced form solutions,
describe (both mathematically and in words) the effect of a
change in per unit tax on optimum output in both countries.
v) Now find the same comparative static results by totally
differentiating your first-order conditions, rea
anging
them, writing them in a matrix form, etc.