Macroeconomic Analysis 3 Hours

There are FOUR QUESTIONS. Answer any THREE questions. Each question carries an

equal weight. If you attempt more questions than are indicated on the rubric you should

clearly indicate which answers you wish to be marked. Data provided: None. Do not

exceed 3750 words. Do not copy material from lecture notes or handouts, no points will

be awarded for copied material.

ECN6520 1 Turn Over

ECN6520

1 An infinitely-lived household’s lifetime utility can be expressed as follows:

U0 =

X1

t=0

t ln (ct

n

t )

where ct is consumption and nt are hours worked. is a parameter determining

the curvature of the utility function. The parameter determining the dis-utility of

labour is

. The representative household produces goods, yt , using a constant

elasticity of substitution (CES) technology in hours worked and the capital stock:

yt =

kk

t + n(ztnt) 1

k , n and are parameters of the production function. Total factor productivity

(TFP), zt evolves as follows: ln zt = ln zt1 + t where t is an iid shock with

a zero mean. The capital stock, kt is pre-determined in period t and evolves as

follows:

kt+1 = yt ct + (1 )kt

The firm belongs to the household, which chooses consumption, hours as well as

next period’s capital stock.

(a) Set up the Lagrangian function and derive the first-order conditions for ct ,

nt and kt+1. (20 marks)

(b) Consider the first-order conditions for nt and kt+1, under which parameter

restriction is the CES production function equivalent to the Cobb-Douglas

production function that you are familiar with? (20 marks)

(c) Use the first-order conditions for ct and nt to analyse the effect of an

exogenous increase in consumption (assume that household wealth has

risen) on the supply of labour. (20 marks)

(d) In your own words, explain how TFP shocks (shocks to zt) can lead to

business cycles. (40 marks)

ECN6520 2 Continued

ECN6520

2 A firm, existing for two periods, produces output using capital and labour. The

firm’s production at any time i can be described by a simple production function

zik

i n1

i . The firm faces the following profit function expressed in real terms:

z1k

1 n1

1 +k1k2+(s1+d1)a0s1a1w1n1+

z2k

2 n1

2 + k2 + (s2 + d2)a1 w2n2

1 + r

ai , si and di denote the quantity and price of shares as well as dividend payments

of shares held by the firm in period i in real terms. n and k denote labour input

and capital stock, respectively. The firm has to borrow to invest in new capital

stock. The amount it can borrow is constrained by the value of its stock holdings:

(k2 k1) = Rs1a1

where R < 1 is a parameter that limits investment spending to a fraction of the

firm’s stock holdings.

(a) Set up the constrained optimisation problem and derive the first-order conditions

for n1; n2; k2 and a1. (10 marks)

(b) Using the first-order conditions for k2 and a1, show that a binding borrowing

constraint will reduce the capital stock in the second period. (45 marks)

(c) Assume that the economy is hit by a shock that reduces the second period

real share price, s2. In your own words, describe the financial accelerator

mechanism that can be triggered by such a decline in asset prices. (45

marks)

ECN6520 3 Turn Over

ECN6520

3 Assume an economy where households receive utility from consumption of goods

and from holding real money balances:

u

ct ;

Mt

Pt

Households maximise utility subject to the following inter-temporal budget constraint:

Ptct + Bt +Mt + Stat = Yt +Mt1 + (1 + it1)Bt1 + (St + Dt)at1

Where Yt in nominal GDP, Ptct is nominal consumption, it is the nominal interest

rate, Bt is the level of bond holdings, St is the share price, at the stock of shares

purchased by the household in period t, Dt is a dividend payment and Mt is the

money stock held by agents at the end of period t.

(a) Set up the intertemporal Lagrangian and derive the first-order conditions

with respect to ct , at , Bt and Mt . (10 marks)

(b) Assume that the utility function takes the form:

uct ;Mt Pt= ln ct +11

Mt

Pt

1

and use this function along with the first-order conditions to derive an

expression for real money demand as a function of consumption. (45

marks)

(c) Carefully explain what is meant by money neutrality. Why might money

not be neutral? (45 marks)

ECN6520 4 Continued

ECN6520

4 Assume an economy where households receive utility from consumption of goods

and disutility from hours worked. Households maximise expected utility:

U0 =X1t=0t ln

ct

n!

t

!

where the parameter ! > 1. Households maximise expected utility subject to an

infinite sequence of flow budget constraints:

X1

t=0

t (Ptwtnt + (St + Dt)at1 +Mt1 + (1 + it1)Bt1) =

X1

t=0

t (Ptct + Stat +Mt + Bt)

In addition, households face a cash-in-advance constraint on the purchases of

consumption goods and shares.

X1

t=0

tMt =

X1

t=0

t (Ptct + Stat)

Ptct is nominal consumption, (1+it) is the nominal interest rate on bonds bonds,

Bt is the level of bond holdings, St is the share price, at the stock of shares

purchased by the household in period t, Dt is a dividend payment and Mt is the

money stock held by agents at the end of period t. wtnt denotes the household’s

labour income.

(a) Set up the intertemporal Lagrangian and derive the first-order conditions

with respect to ct , nt , at , Bt and Mt . (10 marks)

(b) Carefully analyse why the price of shares can be affected by the level of the

nominal interest rate in this model. (40 marks)

(c) Show how the presence of a cash-in-advance constraint distorts the

consumption-labour decision. What can monetary policy do to eliminate

this distortion? (50 marks)

End of Question Paper

ECN6520 5

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