# WU The Inflation Rate & Growth Rate of Real GDPare Constants Essay

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Macroeconomics B: Assignment 2
Similan Rujiwattanapong
Waseda University
January 21, 2022
 Your work must be submitted on the courses Moodle page by Friday 28th January 2022.
 Every group member must in principle submit the same copy of their joint work on Moodle.
 The first page should contain the names and student numbers of all group members.
 The main texts must be typed and not be handwritten (with the exception of diagrams).
 The answers should be no more than 20 pages. They should be in one single PDF file.
 To receive good marks, you must complete all exercises and answer all questions (read the questions carefully). Furthermore, your arguments must be complete and precise. For mathematical
questions, you must demonstrate how you obtain your results in each step. Be careful to label
every curve and axis, and use the notations as given in the questions.
1
Question 1
Consider an economy where the nominal interest rate (i), the inflation rate (?) and the growth rate of
real GDP (g) are constant unless otherwise stated.
(1.1) Interpret the following equation and argue why it must hold:
?Dt+1
=
Dt+1 ? Dt = Gt ? Tt + rDt
where Dt is the real government debt at time t, Gt is the real government expenditure at time t,
Tt is the real tax revenue at time t and r is the real interest rate.
Subsequently, show that the law of motion for the debt-to-GDP ratio (dt ?
?dt+1
=
Dt
Yt )
is
Gt ? Tt
+ (r ? g ) d t
Yt
(1.2) Assume that there is a primary budget deficit and that the real interest rate is strictly smaller than
the growth rate of real GDP. Illustrate the debt(-to-GDP ratio) dynamics in the (dt , ?dt+1 )-space.
In addition, calculate and interpret the debt-to-GDP ratio in the steady state/equilibrium.
(1.3) Now consider a scenario where the government increases its expenditure even further from its
position in (1.2) to attract/please the voters. Also assume the debt-to-GDP ratio is initially large
and above the steady-state debt-to-GDP ratio. This action from the government raises doubts
about its ability to repay its debt and, as a result, the interest rate on the government bonds
increases to the point where it is higher than the growth rate of real GDP. Illustrate and explain
the debt(-to-GDP ratio) dynamics in the (dt , ?dt+1 )-space. What happens to the growth rate of
the debt-to-GDP ratio?
1
(1.4) (This question continues from (1.3)) In response to this interest rate hike, the government tries to
stimulate the economy but they only manage to bring the growth rate of real GDP to be equal
to the real interest rate. Illustrate and explain what happens to the debt-to-GDP ratio in the
(dt , ?dt+1 )-space. Lastly, can the government stabilise the debt-to-GDP ratio in this scenario?
Explain.
2
Question 2
Consider a small open economy with a fixed exchange rate regime. It can be summarised by the
following system of equations:
= C (Y ? T, Y e ? T e , i ? ? e , A) + I (Y e , i ? ? e , K ) + G + NX (?, Y, Y ? )
Y
=
V (i )
ee
1 + i ? = (1 + i )
e
T = = T + ?Y
Y
M
P
Assume the exchange rate target (e? ) is credible, i.e. ee = e? = e, and that the economy is initially in
a short-run equilibrium where prices are fixed. T can be interpreted as a lump-sum tax and ? as an
income tax rate.
(2.1) Interpret the four equations and illustrate the model graphically. Is it possible for the central
bank to have full control over the domestic nominal interest rate in this setup? Explain carefully.
(2.2) Analyse graphically, verbally and mathematically the effects of a devaluation of the exchange
You can assume that the exchange rate target is always credible in this question (2.2).
(2.3) A currency devaluation comes with a risk of changes in the expected future exchange rate. Analyse graphically, verbally and mathematically the effects of an expected devaluation of a currency
in the future. Provide intuitions behind your answer. You can answer this question independently from the situation in (2.2). Hint: You need to consider how the UIP condition (along with
the variables inside this condition) may be affected in this scenario. Particularly, it will be useful
to recall which variable(s) are fixed.
(2.4) Compute mathematically the effect of an exogenous increase in government expenditure on real
GDP and compare its magnitude to that from a closed economy setup (assuming the same tax
system as in this question). Does the behaviour of the central bank in the closed economy setup