Macroeconomics B: Assignment 2 2022
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Macroeconomics B: Assignment 2
2022
1 Question 1
Consider an economy where the nominal interest rate (i), the inflation rate (π) 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:
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 
is
(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?
(1.4) (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:
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 τ 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 rate. Provide intuitions behind your answer. Lastly, how does the value of τ affect your answer? 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. Anal- yse 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 indepen- dently 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 matter for your answer? Explain.
2022-01-25