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ECON 2450 Department of Economics
Intermediate Macroeconomic Theory II York University
Instructor: Sharif F. Khan Summer 2 2013
Suggested Solutions to Assignment 2 (OPTIONAL)
Total Marks: 25
Read each part of the question very carefully. Show all the steps of your calculations to
get full marks.
B1. (5 marks)
Consider two hypothetical countries: Home and Foreign. Home makes ordinary
soap bars that are sold for 5 dollars each. Foreign makes deluxe soap bars that are
sold for 100 yens each. The real exchange rate between Home and Foreign is a half
of the deluxe soap bar per ordinary soap bar.
(i) What is the nominal exchange rate between the Home dollar and the
Foreign yen?
The price level in Home is H = 5 dollars per ordinary soap bar. The price level
in Foreign is P= 100 yens per deluxe soap bar. The real exchange rate, e, is ½ of a
deluxe soap bar per ordinary soap bar.
(i) The general formula for the real exchange rate is
e P
e = nom (1)
PF
Eq. (1) can be also written as
eP F
ebom = (2)
PH
Using Eq. (2),
enom= ((1/2 deluxe soap bar per ordinary soap bar) x 100 yens per deluxe soap bar) / 5
dollars per ordinary soap bar = 10 yens per dollar.
Page 1 of 7 Pages (ii) During the following year, Home has 10% domestic inflation and Foreign
has 20% domestic inflation. The real exchange rate remains unchanged. At
the end of the year, what has happened to the nominal exchange rate? Which
country has had a nominal appreciation? Which has a nominal depreciation?
Inflation in Home is H = 10%. Inflation in Foreign Fs π = 20%. The real exchange rate is
constant.
We can write Eq. (2) in the percentage change form as
∆enom ∆e ∆PF ∆P ∆e
= + − = +π Fπ H (3)
enom e P F P e
So, ∆enom = 0+0.20−0.10 = 0.10 .
e
nom
Therefore, the nominal exchange rate (yens per dollar) has increased by 10%. The Home
dollar has appreciated, the Foreign yen has depreciated.
B2. (20 marks)
Consider the following Keynesian small open economy:
d
Desired Consumption: C = 200+0.6 Y −T −200r
d
Desired Investment: I = 300−300r
Government Purchases: G =152
Taxes: T = 20+ 0.2Y
Net Exports: NX =170 −0.08Y − 0.5e
Real exchange rate: e = 230
Real Money Demand: L = 0.5Y − 200r
Money Supply M = 924
Full-employment output: Y =1000
Net Factor Payments: NFP = 0
In this economy, the real interest rate does not deviate from the foreign interest rate.
a) Derive the equation for the IS curve as a function of Y and e.
The equation for the IS curve is derived from the goods market equilibrium condition for
an open economy, which is
S − I d= CA = NX + NFP = NX (because, NFP=0). (1)
Page 2 of 7 Pages d d
S = Y+NFP - C - G = Y+0 – {200 + 0.6[Y – (20 + 0.2Y)] – 200r} –152
= 0.52Y – 340 +200r
So, S = 0.52Y – 340 +200r (2)
It is given that NX =170 −0.08Y − 0.5e and I = 300−300r .
Substituting the functional forms of S , I , and NX into Eq. (1),
0.52Y – 340 + 200r – (300 – 300r) = 170 – 0.08Y –0.5e.
Rearranging terms and simplifying gives the IS curve:
500r = 810 – 0.5e – 0.6Y
810 5 6
or, r = − e − Y (4) [IS curve]
500 5000 5000
b) Derive the equation for the LM curve as a function of Y, M and P.
The equation for the LM curve is derived from the assets market equilibrium condition
for an open economy, which is
M/P = L (5)
Substituting the given functional form of L into Eq. (5),
M/P = 0.5Y – 200r
or, 200r = -M/P +0.5Y
M 5
or, r = − + Y (6) [LM curve]
200P 2000
c) What are the general equilibrium (that is, long-run) values of output, the real
interest rate, real exchange rate, consumption, investment, net exports, and
the price level? Illustrate the general equilibrium values of output and the
real interest rate in the IS-LM-FE diagram.
In the general equilibrium, output equals to its full-employment level, which is 1000.
The given general equilibrium value of real exchange rate, e = 230.
With e = 230 and Y = 1000, the IS curve (Eq. (4)) gives
r = 810 − 5 (230 −) 6 1000 = )0.19
500 5000 5000
Page 3 of 7 Pages So, the general equilibrium value of the real interest rate is 19%.
With r = 0.19 and Y = 1000, the LM curve (Eq. (6)) gives
924 5
0.19 = − + 1000 )
200P 2000
924
⇒ = 2.5−0.19
200P
924

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