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EFIM20034
INTERMEDIATE MACROECONOMICS
May 2024 Examination Period
SECTION A
Instructions for this Section: Answer the TWO questions below
1. [33 marks] Consider an economy composed of two overlapping generations of households that live for two periods. Households work in both periods: in the first period, the household born at tsupplies, by choice, l1,t units of labour (0 < l1,t < 1); while in the second period they must supply one third of a unit of labour. Formally, the decision of the household at time t is to
subject to the following lifetime budget constraint
with Ut: lifetime utility of the household; rt+1: real interest rate at time t + 1; wt (wt+1): wage per unit of labour at t (t + 1); c1,t (c2,t+1): consumption at t (t + 1); w tl1,t: period t labour income (so wt(1 − l1,t) is the implicit value of period t leisure time); wt+1 3/1: period t + 1 labour income; and σ 1 and σ2 are consumption taxes on the (typical) goods and services bought when young and old, respectively.
(a) Without doing any calculations, use your knowledge of income and substitution effects to explain how optimal period t consumption c1,t might be affected by a rise in
(i) σ 1; (ii) σ2; (iii) rt+1; (iv) wt and (v) wt+1 . [10 marks]
It can be shown (but you are not being asked to show ithere) that optimal savings at(*)+1 and labour supply l 
t are given by, respectively,
(b) Look at equation (4).
(i) Does it surprise you that optimal labour supply l 
t depends the way it does on σ 1 ?
Explain your answer.
(ii) And why does l 
t not depend on σ2 ? Explain your answer. [4 marks]
(c) Now look at equation (3). Recalling, that the period t budget constraint of the household is at+1 = w tl1,t − (1 + σ1 )c1,t, and your answers to parts (a) and (b), explain why optimal savings at(*)+1 depends negatively on σ 1 . [4 marks]
Suppose that the economy is in the steady state, there is no technological progress nor pop- ulation growth. Output Yt is produced by perfectly competitive firms using physical capital Kt and labour Lt with the production function Yt = Kt2/1 . Physical capital depreciates com- pletely in one period. Labour is a homogeneous factor, so Lt = Nl 
t + N 
= N (l 
t where N stands for the number of individuals per generation. Given our assumption regard- ing capital depreciation, the respective rental rates of Kt and Lt are 1 + rt and wt.
(d) Use this new information to show that at(*)+1 – from equation (3) – can be rewritten as
follows:
with kt = Kt/Lt and kt+1 = Kt+1/Lt+1 capital per unit of labour variables. [4 marks]
(e) Now use the capital market equilibrium condition and the previous results to argue whether or not tax rates σ 1 and σ2 crowd-out capital accumulation in this economy. [4 marks]
(f) Finally, use the Lagrangian method to show that the constrained optimization problem of equations (1) and (2) results in the following optimal period t choice:
[7 marks]
2. [33 marks] Consider the following 3-equation two agent new Keynesian (TANK) model of an economy:
with xt the output gap at t; rt the real interest rate at t; πt the inflation rate at t; r(¯) a constant; π(¯) the inflation target; Et the expectations operator conditioned on time-t information (this includes the values of all variables and shocks up to time t).
Parameter θ is given by 
χ and Λ positive parameters.
There are two shocks in the model, a zero-mean cost-push shock u-t with no-persistence, and a zero-mean AR(1) demand shock gt with positive persistence. Formally, {u-t} ~IID(0, σ
) and
with {g-t} ~IID(0, σ
)
(a) Briefly explain how the TANK model differs from the representative agent new keynesian (RANK) model. [4 marks]
(b) Show that this TANK model can be reduced to a system of two difference equations in xt and πt and then check,using either of these, that the solutions for xt and πt are given by:
[10 marks]
(c) Without doing any calculations, explain how the solutions given in part (b) would change if the central bank conducted monetary policy according to the following rule instead of the one given above:
[4 marks]
(d) Assume the economy was in long-run equilibrium at time −1. Let Λ = 1/2 and r(¯) = 0.02. At time 0 the economy is hit by a pandemic which translates into a simultaneous negative demand shock g0 = −1 and a positive cost-push shock u(^)0 = 2.
Use the solutions in part (b) to show graphically (in an IS diagram and a Phillips Curve diagram) how these two combined shocks would affect the economy when χ = 1/2.
Briefly explain the intuition for why xt and πt respond the way they do. [9 marks]
(e) Now suppose the demand shock also has no persistence: gt = g-t , with {g-t} ~IID(0, σ
). It can be shown (but you are not being asked to show it) that the solution in part (b) for xt and πt changes to:
Assuming that χ = 3/2 and recalling that 
show whether xt and πt −
more volatile or less volatile in the TANK economy (where, recall, Λ = 1/2) than in the RANK economy (where Λ is equal to 0).
Hint: consider what happens to the variance of xt and πt − π(¯) in the two economies. [6 marks]
SECTION B
Instructions for this Section: Answer ONE of the THREE questions below
3. [34 marks] Consider an economy well described by the neoclassical growth model with a production function Y = K3/6 (AL)1/6 F2/6 that depends on three factors of production (inputs), K , L and F. The letter Y denotes output, K the capital stock, L the constant labour force, F constant (fixed) resources, and letter A (A > 0) is an index of productive efficiency which grows at a constant rate over time. Assume the economy is at the steady state.
How would you characterise the steady state of this economy? If it suddenly increased its saving rate, would it experience faster growth and rising standards of living? If so, why? And how does your answer depend on the time horizon? Explain all your answers.
4. [34 marks] “Here is the current situation in many developed countries:
First, people aged 65 and over now account for a quarter or more of the adult population, and their share of the population is still rising.
Second, most of the aged 65 to 75 are in good health and surveys show that many would be supportive of “truly lifelong” learning and employment policies.
Third, despite all the support offered to families, fertility decline is here to stay. Until recently, it was driven by families having fewer children than their parents, now the key dynamic is childlessness: children do not fit into many millenials’ life plans.
So, although it is not surprising that the long-term sustainability of these countries’ current pay-as-you-go state pension systems is being questioned, the path to sustainability is also pretty obvious.”
Do you agree with this view? Explain and discuss.
5. [34 marks] Economists argue that an important reason for the 2008-9 global financial crisis was what many consider as excessive debt accumulation in the period leading up to the crisis. Economists also note that during the crisis the UK stock market and UK house prices saw one of their biggest crashes in recorded history.
Given the information above, use consumption theory to explain why the UK households’ savings ratio increased significantly during the crisis (from about 3% pre-crisis to about 8% during the crisis) and then remained high for the next five years.