WEEK 4 - Economic Growth I (Basic Solow model)

Question 1

What is the importance of growth for poor countries?

Answer 1

-Standard of living
(Daily caloric intake 1/3 lower than in richest fifth)
-the infant mortality rate is 200 per 1000 births, compared to 4 per 1000 births in the richest fifth

Question 2

What does the Solow Model look at?

Answer 2

The determinants of econ growth and standards of living in LR

Question 3

What are some elements of Solow’s model that differ from traditional growth models?

Answer 3

1. K no longer fixed
   (Depreciation shrinks it, Investment causes it to grow)
2. L no longer fixed
   (Pop growth causes it to grow)
3. Consumption function simpler
4. No G or T

Question 4

What is the basic Solow production function?

Answer 4

Y = F(K,L)

Where:
y = Y/L = Output per worker
k = K/L = Capital per worker

Question 5

How do we derive a production function that expresses output per worker as a function of capital pr worker?

Answer 5

1. Assume constant returns to scale (noted as z):
   zY = F(zK,zL) for any z>0
2. Put z = 1/L then,
   Y/L = F(K/L, 1)
   y = F (k,1)
   y = f (k) (per worker production function)

SEE GRAPH IN NOTES

Question 6

What is the national income identity in the Solow Model?

Answer 6

Y = C+I

In per worker terms:
y = c + i

Where:
c = C/L and i = I/L

Question 7

How do we define the savings rate?

Answer 7

As the fraction of income that’s saved (s)

Question 8

What is the Solow Consumption function (per worker)?

Answer 8

c = (1 - s)y

Question 9

How do we find the savings and investment function for the Solow Model?

Answer 9

1. Savings (per worker) = y - c
   = y - (1-s)y
   = sy
2. National income identity is y = c + i
   Rearrange to get: i = y - c = sy

Which gives us:
i = sy = sf(k)

Question 10

Output, Consumption and Investment graph

Answer 10

SEE IN NOTES

Question 11

How do we identify depreciation?

Answer 11

δ = The rate of depreciation
= The fraction of the capital stock that wears out each period

(capital stock = Physical Capital Stock)

SEE GRAPH IN NOTES

Question 12

What alters the level of capital stock?

Answer 12

Investment increases it

Depreciation decreases it

Question 13

How do you identify the change in capital stock /capital accumulation?

Answer 13

ΔK = i - δ
(Change in capital stock = investment - depreciation)

Since i = sf(k) this becomes,
ΔK = sf(k) - δk

Question 14

What is known as the law of motion of k (central equation of Solow)?

Answer 14

ΔK = sf(k) - δk
(Determines behaviour of capital over time)
So, it determines behaviour of all other endogenous variables because they all depend on k

Question 15

What is known as the steady state?

Answer 15

ΔK = sf(k) - δk

If investment is just enough to cover depreciation
(sf(k) = δk) then capital per worker will remain constant

SEE GRAPH IN NOTES

Question 16

What do we denote the steady state by?

Answer 16

k* - called the steady state capital stock

Question 17

How does an economy move towards the steady state?

Answer 17

SEE NOTES

Question 18

What is the overall statement about moving towards the steady state?

Answer 18

As long as k

Question 19

How do you numerically identify the steady state?

Answer 19

1. Production function (aggergate):
   Y = F(K,L) = Sq root of KxL = K1/2 L1/2
2. To derive per worker production function, divide through by L:
   Y/L = K1/2 L1/2 / L = (K/L)1/2
3. Then sub y=Y/L and k = K/L to get:
   y = f(k) = k 1/2

Question 20

How do you calculate for the steady state?

Answer 20

Use equation of motion (ΔK = sf(k) - δk )
e.g. s = 0.3 δ = 0.1 y= k1/2

1. Set ΔK to 0
   leaving us with just sf(k) - δk
2. Using assumed values
   0.3 Sq root K = 0.1k
   3 = k/Sq root K = Sq root of k

Giving us k* = 9 and y* = Sq root k* = 3

Finally, c=(1-s)y = 0.7 x 3 = 2.1

Question 21

What does an increase in the savings rate do?

Answer 21

Raises investment since in the model all that isn’t consumed is saved and what is saved is then invested.

Causing k to grow toward a new steady state

Question 22

What does the Solow Model predict?

Answer 22

Higher s = Higher k*
and since y = f(k)
higher k* = Higher y*

Thus, solow model predicts that countries with higher rates of saving and investment will have higher lvls of capital and income per worker in LR

Question 23

What is the golden rule of capital stock?

Answer 23

The steady state value of k that maximises consumption

Question 24

How do we find the golden rule of capital stock?

Answer 24

K*gold

1. Express c* in terms of k*

c* = y* - i*
= f(k) - i
= f(k) - δk

Because in general i = ΔK + δk
In steady state i* = δk because ΔK = 0

SEE GRAPH IN NOTES

Question 25

What are some important elements about the Golden rule steady state?

Answer 25

It is not a tendency for the economy to move to the golden rule steady state
- Achieving golden rule requires that policymakers adjust s

Question 26

What must happen to an economy if they have more or less capital than the golden rule level?

Answer 26

• More capital than golden rule lvl (k* > kgold):
  Increasing c requires fall in s

(Golden rule, consumption higher at all points in time)

• Less capital than golden rule (k< kgold):
  Increasing c* requires increase in s (savings)

(Future generations enjoy higher consumption, but the current one experiences an initial drop in consumption.)

Question 27

How do we calculate population growth?

Answer 27

ΔL/L = n

n is rate of population growth

Question 28

What is break even investment?

Answer 28

Amount of investment necessary to keep k constant

Question 29

How do you calculate break even investment?

Answer 29

(δ+n)k

Question 30

What does break even investment include?

Answer 30

δk to replace capital as it wears out
nk to equip new workers with capital (otherwise k would fall as existing capital stock would be spread more thinly over larger population of workers)

Question 31

What is the law of motion for k considering population growth? (per worker terms)

Answer 31

Δk = sf(k) - (δ+n)k
(Actual Investment - Break even investment)

SEE DIAGRAM IN NOTES

Question 32

What is the impact of population growth?

Answer 32

Increase in n causes increase in break even investment leading to a lower steady state lvl of k

SEE GRAPH IN NOTES

Question 33

What is the logic behind increased population growth?

Answer 33

Higher n = Lower k*
And since y = f(k),
lower k* = lower y*

Thus, the Solow model predicts that in the long run countries with higher population growth rates will have lower levels of capital and income per worker

Question 34

What is the golden rule with population growth?

Answer 34

To find Golden rule capital stock again express c* in terms of k:
c = y* - i*
= f(k) - (δ+n)k

Therefore,c* maximised when:
MPK = δ +n
or equivalently,
MPK - δ = n

Question 35

What is the Malthusian Model to population growth?

Answer 35

Predicts population growth will outstrip the Earth’s ability to produce food, leading to the impoverishment of humanity.

Since Malthus, world population has increased sixfold, yet living standards are higher than ever.
Malthus neglected the effects of technological progress.

Question 36

What is the Kremerian Model to population growth?

Answer 36

Posits that population growth contributes to economic growth.
More people = more geniuses, scientists & engineers, so faster technological progress.