Topic 3 - Growth Theories

Question 1

Y

Answer 1

total output

Question 2

K

Answer 2

capital stock

Question 3

L

Answer 3

labour, number of workers

Question 4

A, alpha

Answer 4

technology parameters

Question 5

t

Answer 5

time

Question 6

Production Function

Answer 6

Yt = F(Kt, Lt)

Question 7

Cobb-Douglas production function

Answer 7

Yt = A (Kt^a) (Lt^(1-a)) where 0 <= a <= 1

Question 8

What does alpha refer to in the Cobb-Douglas (CD) specification?

Answer 8

Output elasticity with respect to capital; factor share of capital; diminishing returns to scale parameter

Question 9

CRS

Answer 9

Constant Returns to Scale Technology; i.e. if you double the size of inputs, you double the size of outputs

Question 10

For any constant z, provide the formula for CD production function:

Answer 10

For any z,: zY = F(zK, zL)

Question 11

Proof of CD production function

Answer 11

F(zK, zL) = A(zK)^a(zL)^(1-a)
= Az^a(K)^a (z^(1-a))(L)^(1-a)
= Az(a+1-a) K^a L^(1-a)
= zA K^a L^(1-a)
= zF(K, L)
= zY

Question 12

National Income Accounting formula

Answer 12

Yt = Ct + It + Gt + NXt

Question 13

Total output in terms of consumption and savings

Answer 13

Yt = Ct + St

Question 14

Key assumptions of Solow Model

Answer 14

1. Technology is exogenous
2. Total savings are a constant share of s of income, i.e. S = sY
3. Output is produce according to CRS technology

Question 15

Simplifying assumptions of Solow Model

Answer 15

1. No trade = NX = 0
2. No government expenditures G = 0
3. Population (hence labour) grows at a constant rate n

Question 16

Depreciation

Answer 16

0 <= delta <= 1

Question 17

Capital stock at time t+1 (equation, and rearranged in terms of It)

Answer 17

The capital stock at time t + investment at time t - the depreciation of capital stock at time t. I.e.

Kt+1 = Kt + It - delta *Kt

Kt+1 = It + (1-delta)Kt

It = Kt+1 - (1-delta)Kt

Question 18

Suppose z = 1/L, give the formula for average labour productivity (productivity per unit of labour) in terms of Yt

Answer 18

Yt/Lt = F(Kt/Lt, Lt/Lt)

Question 19

Output per unit of labour

Answer 19

Yt/Lt

Question 20

Capital per unit of labour

Answer 20

Kt/Lt

Question 21

If yt = Yt/Lt and kt = Kt/Lt, then…

Answer 21

yt = f(kt) = Akt^a

Question 22

Formula for total capital accumulation

Answer 22

𝐾𝑡+1 = 𝑠𝑌𝑡 + 1 − 𝛿 𝐾𝑡

Question 23

Formula for capital accumulation per worker

Answer 23

(1 + 𝑛)𝑘𝑡+1= 𝑠𝑦𝑡 + 1 − 𝛿 𝑘𝑡

Question 24

What is the formula for equilibrium?

Answer 24

(1 + 𝑛) 𝑘𝑡+1 = 𝑠𝐴𝑘𝑡^𝛼 + (1 − 𝛿 )𝑘𝑡

Question 25

Describe the steady state of equilibrium

Answer 25

𝑦∗, 𝑘∗ such that:
𝑘𝑡+1 = 𝑘𝑡 = 𝑘∗
𝑦𝑡+1 = 𝑦𝑡 = 𝑦∗

Question 26

Formula for equilibrium when k < k*

Answer 26

(1 + 𝑛) < 𝑠𝐴 𝑘 𝛼 + (1 − 𝛿) 𝑘