Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

ECON 4016 Macro Theory > 2. Neoclassical Growth Model > Flashcards

2. Neoclassical Growth Model Flashcards

1
Q

How much does each person decide to work?

A

They don’t decide, everyone works one unit of labour in each time period t

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

How are firms illustrated in the model?

A

-Continuum of identical firms
-Firms have access to same technology that uses capital and labour as a single final good
-Perfectly competitive market

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Is the production function F(.) homogeneous?

A

Yes of degree one so has CRS

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What is the output per capita in efficiency units?

A

yt= Yt/AtLt= F(Kt/AtLt, 1)= f(kt)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

What is the capital per capita in efficiency units?

A

kt=Kt/AtLt

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

What can we say about the shape of the production function wrt capital?

A

Production is positive for any level of capital. Increasing capital increases production but does so at a decreasing rate. Concave shape

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Assumptions of feasibility condition

A

-Labour alt grows exogenously at rate n>=0
-the state of technology progresses at rate gamma >=0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

What is rho?

A

The subjective discount rate

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

What is sigma?

A

The Constant Inter-temporal Elasticity of Substitution (CIES)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

What is the marginal utility of consumption like as t increases? Give the expression which shows this

A

Strictly positive but decreasing

u’(c(hat)t=c(hat)^(-1/sigma)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Second welfare theorem

A

Any efficient allocation can be achieved by a competitive equilibrium -> the solution to the social planner problem is identical to the competitive equilibrium

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

What does the Euler equation show?

A

The growth rate of consumption measured as consumption per efficiency units of labour

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

in the limit, ie when time goes towards infinity what is the optimal value of capital according to the transversality condition?

A

Zero

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

When do individuals postpone consumption?

A

When the market interest rate is greater than the subjective discount rate

When alpha x kt^(alpha-1) - delta> rho

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

What does the amount which individuals postpone consumption depend on?

A

The intertemporal elasticity of substitution ó

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What is the definition for the balanced growth path?

A

An equilibrium such that for all t, change in capital and consumption in efficiency units is zero

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

Rational expectations principle

A

Rational agents choose initial consumption on the stable path

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

What is the balance growth path solution?

A

The unique stable saddle path converging to the balanced growth path

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

When the economy is in a steady state is there growth?

A

Yes the economy grows at rate of technological progress (gamma) in per capita terms and grows at gamma plus population growth (n) for the whole economy. In efficiency units it isn’t growing

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

Why do economies in transition to steady state grow quicker

A

They grow at exogenous rate of technological progress (gamma) but are also boosted by increase in capital accumulation as they move towards the steady state

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

How can technological progress or total factor productivity be measured?

A

In logs as
change in TFPt= change in log(Yt) - alpha x log( kt) - (1- alpha) x log(Lt)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

How does the population grow?

A

Population grows geometrically at rate n>=0.

Lt= L0e^(nt)

23
Q

Give the equation which shows how the representative firm produces the final good using a neoclassical technology

A

Yt= F(Kt, AtLt)

24
Q

How does the state of technology evolve?

A

According to

At=A0e^(gamma t)

25
Q

How can production be employed?

A

Production Y can be employed for consumption C or investment I
A feasible allocation is Yt=Ct+It

26
Q

Law of motion for capital given by the differential equation

A

K(dot)t = It- delta x Kt

Delta>0 is the capital depreciation rate
K(dot)t is net investment
K0 is given

27
Q

What does a dot over a variable mean?

A

It means the change in that variable over time

K(dot)t = Kt+1 - Kt

28
Q

Give the feasibility condition in efficiency units

A

A path {kt,ct} subject to

k(dot)t=kt^alpha - ct - (delta + n + gamma)kt

29
Q

What is c(hat)t equal to?

A

c(hat)t= Ct/Lt denotes per capita consumption at t

30
Q

What does the representative household maximise?

A

The discounted flow of utility of all members. This is equal to the integral of

u(c(hat)t) x Lte^(-rhot)

Where rho is the subjective discount rate

31
Q

What is the CIES and the equation it is involved in?

A

The constant intertemporal elasticity of substitution.

u(c(hat)t)= (c(hat)t^(1-1/sigma))/(1-1/sigma)

32
Q

What does the social planner solve for a given k0?

A

Max the integral of
(ct^(1-1/sigma))/(1-1/sigma) x e^(-rho(hat)t
Subject to
k(dot)t=kt^alpha - ct -(delta+n+gamma)kt

The social planner chooses, among all feasible allocations, the one that maximises the welfare of the representative household. To solve this problem we apply control theory, ct is a control and kt is a state variable

33
Q

In the Hamiltonian what does lambda t measure?

A

It measures the marginal value of capital

34
Q

In the Hamiltonian what makes the objective bounded?

A

The assumption that rho(hat)>0

35
Q

What is growth rate in the economy driven by?

A

The returns to capital

36
Q

How does the neoclassical growth model perform in line with the Kaldor facts?

A

The neoclassical growth model satisfies all of the Kaldor facts

37
Q

What is the ultimate engine of growth?

A

Technological progress

38
Q

What is the “measure of our ignorance”

A

The increase in output that can’t be explained by the rise in the production factors

39
Q

What is the technology to produce output in efficiency units?

A

y=k^alpha

40
Q

What is the marginal product of capital in efficiency units?

A

dy/dk= alpha x k^(alpha-1)

41
Q

What do individuals do when kt<k*?

A

rt > rho

Individuals save to increase k

42
Q

What does it mean when sigma is equal to zero and infinity?

A

When ó=0 there are perfect compliments
When ó= infinity the function becomes linear and there are perfect substitutes

43
Q

What is the case of u(c)=ln c

A

The case of CIES with ó=1

44
Q

Why can’t co be above the saddle path?

A

ct will grow but kt will start declining at some point to reach zero on a finite time. It can’t be optimal for consumers to eat the capital stock on a finite period and pay the cost of having a zero consumption forever

45
Q

Why can’t co be below the saddle path?

A

Then kt will always be growing while ct will start declining at some point converging to zero in the far future

46
Q

What is the golden rule of growth?

A

BGP consumption can be derived from feasibility condition under k(dot)=0.

c=k^alpha -(delta + n + gamma)k

Consumption is at a max when k^alpha is equal to the brackets. This gives a value k* which is the unique stock of capital in efficiency units.

47
Q

What is rho(hat) equal to?

A

rho(hat)= rho- n- (1-1/ó)gamma

48
Q

How do we get from the FOCs to the Euler equation?

A

Take logs and then differentiate the FOC for c wrt to time. Sub this result into the FOC for k

49
Q

Give the transversality condition

A

In the limit as t goes to infinity,

kt x lambda t x e^-rho(hat)t =0

Note that lambda t= ct^(-1/ó)

50
Q

Give the 5 Kaldor facts and their respective values according to the NGM

A
  1. Output per capita Yt/Lt=Atk*^alpha grows a constant rate gamma
  2. The capital to output ratio is constant: Y/K=k*^(alpha-1)
  3. The capital and labour shares are alpha and 1-alpha
  4. The return to capital is constant r* = alpha x k*^(alpha-1) - delta
  5. Real wages wt= (1-alpha)k*^alpha x At
51
Q

Why might the NGM not be useful?

A

Because of features of technological progress in the long run. Technology is exogenous which isn’t realistic. In reality countries experience technological progress at different rates and this impacts their growth rate

52
Q

How can income per capita be written in the NGM?

A

Yt/Lt= At^(1-alpha) x (Kt/Lt)^alpha

gy= alpha x gk + (1-alpha)gamma

53
Q

What is a typical value for alpha?

A

1/3

ECON 4016 Macro Theory (8 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions