Ch. 7 - Economic Growth I: Capital Accumulation and Population Growth

Question 1

Why does supply and demand play a central role in the Solow model?

Answer 1

By considering the supply and demand for goods, we can see what determines how much output is produced at any given time and how this output is allocated among alternative uses.

Question 2

What is the supply of goods based on in the Solow model?

Answer 2

The production function, which states that output depends on the capital stock and the labour force.
Y = F(K,L)

Question 3

What is an assumption about the production function used in the Solow model?

Answer 3

Constans returns to scale.

zY = F(zK, zL) for any positive number z

Question 4

What do production functions with C.R.S. allow us to analyze in the Solow model?

Answer 4

All quantities in the economy relative to the size of the labour force.
Set z=(1/L)
Y/L = F(K/L, 1)

Question 5

How do we re-write the production function in the Solow model once we’ve set z=(1/L)?

Answer 5

y = f(k)   where 
y = Y/L
k = K/L

Question 6

What is the slope of the production function designed to show in the Solow model?

Answer 6

MPK = f(k+1) - f(k)

Question 7

What is the Solow growth model designed to show?

Answer 7

How capital stock, growth in the labour force, and advances in technology interact in an economy, and how they affect a nation’s total output of goods and services.

Question 8

How does the slope of the production function in the Solow model illustrate diminishing marginal product of capital?

Answer 8

The slope represents MPK, the fact that the slope gets flatter as k increases represents dimininshing product of capital.

Question 9

What is the demand for goods based on in the Solow model?

Answer 9

From consumption and investment.
y = c + i where
y = output per worker
c = consumption per worker
i = investment per worker

Question 10

How can we express the consumption function considering that the Solow model assumes that each year people save a fraction s of their income and consume fraction (1 - s)?

Answer 10

c = (1 - s)y where

c = consumption
s =  saving rate where 0

Question 11

How can we see what the new consumption function, developed in the Solow model, implies for investment?

Answer 11

Substitute (1 - s)y for c in the national accounts identity (demand for goods in the Solow model).
y = (1 - s)y + i
Rearrange the terms to obtain
i = sy

Question 12

What does i = sy show?

Answer 12

That investment equals savings.

Question 13

Which 2 forces influence the capital stock?

Answer 13

• Investment

- Depreciation

Question 14

What is investment in the Solow model and what does directly influence?

Answer 14

Expenditure on new plant and equipment. It causes the capital stock to rise.

Question 15

How can we express investment per worker as a function of the capital stock per worker?

Answer 15

Since i = sy, and y = f(k),

i = sf(k)

Question 16

What is depreciation in the Solow model and what does directly influence?

Answer 16

The wearing out of old capital. It causes the capital stock to fall.

Question 17

How do we incorporate depreciation into the Solow model?

Answer 17

We assume that a certain fraction of the capital stock wears out each year.
δ = depreciation rate

Question 18

How do we express the impact of investment and depreciation on the capital stock in the Solow model?

Answer 18

Δk = i - δk
Δk = sf(k) - δk
Change in capital stock = Investment - Depreciation

Question 19

When does k* reach steady state?

Answer 19

When i = δk.

Question 20

What happens when i > δk?

Answer 20

Capital stock increases.

Question 21

What happens when i < δk?

Answer 21

Capital stock decreases.

Question 22

What are the 2 significant aspects of the steady-state level of capital?

Answer 22

• An economy at the steady state will stay there

- An economy not at the steady state will go there

Question 23

What does the steady state level of capital represent?

Answer 23

The long-run equilibrium level of capital of the economy.

Question 24

What is a direct result of growth in capital stock?

Answer 24

Growth in output

Question 25

Which equation allows you to quickly find the steady state of capital in the Solow model?

Answer 25

0 = sf(k)-δk
or equivalently
k/f(k) = s/δ

Question 26

What happens to an economy after its saving rate increases if it began at the steady state?

Answer 26

the sf(k) curve shifts upward.as s increases.
i, increase while δk* and k* remain the same, therefore i>δk. k* rises until the economy reaches the new steady state k* which has a higher capital stock and higher output.

Question 27

How does the Solow model show that the saving rate is a key determinant of the steady-state capital stock?

Answer 27

If s is high, k* and y will also be high in ss.

If s is low, k* and y will also be low in ss.

Question 28

What does the Solow model say about the relationship between saving and economic growth?

Answer 28

Higher s leads to faster growth in the Solow model but only temporarily (until it reaches a new steady state).
Maintaining a high s will also maintain a high k* and y, but it will not maintain a high growth rate forever.

Question 29

What is said to have a growth effect?

Answer 29

Policies that alter the steady-state growth rate of income per person.

Question 30

What is said to have a level effect and why?

Answer 30

A higher s because only the level of income per person - not it’s growth rate - is influenced by the s in the steady-state.

Question 31

What is the Golden Rule level of capital?

Answer 31

The steady-state value of k that maximizes consumption.

Question 32

How can we find steady-state consumption per worker?

Answer 32

c* = f(k) - δk

Because capital stock is not changing in the steady-state, investment is equal to depreciation. substituting f(k) for y and δk for i in the national accounts identity c = y - i

Question 33

What does the equation c* = f(k) - δk suggest? What is it telling us?

Answer 33

According to this equation, steady-state consumption is what’s left of steady-state output after paying for steady-state depreciation.
On the one hand, more capital means more output, on the other hand, it also means more capital must be used to replace capital that is wearing out.

Question 34

How is steady-state consumption depicted on a graph showing steady-state output and steady-state depreciation/investment as a function of steady-state capital stock?

Answer 34

Steady-state consumption is the gap between output and depreciation.

Question 35

What happens if we increase capital stock, mathematically and graphically, if it’s below the Golden Rule level in the Solow model?

Answer 35

An increase in the k raises f(k) more than δk so c* rises.
The production function is steeper than the δk* line, so the gap between the two curves - which equals consumption - grows as k* rises.

Question 36

What happens if we increase capital stock, mathematically and graphically, if it’s above the Golden Rule level in the Solow model?

Answer 36

An increase in the k raises f(k) less than δk so c* decreases.
The production function is flatter than the δk* line, so the gap between the two curves - which equals consumption - shrinks as k* rises.

Question 37

How can we tell graphically when we’ve reached the Golden Rule level of capital?

Answer 37

At the Golden Rule level of capital, the production functions and the δk* line have the same slope, and consumption is at its greatest level.

Question 38

How does a policy maker maximize the wellbeing of the individuals who make up the society?

Answer 38

By implementing policies which will eventually maximize consumption (reach the Golen Rule level).

Question 39

How can we find the Golden Rule level of capital mathematically?

Answer 39

When MPK = δ or MPK - δ = 0

Because MPK is the slope of the production function and δ is the slope of depreciation.

Question 40

What happens to c* if we increase capital when MPK>δ?

Answer 40

If MPK>δ, increases in k increase c, so k must be below the Golden Rule

Question 41

What happens to c* if we increase capital when MPK

Answer 41

If MPK

Question 42

Why is it that the economy doesn’t automatically gravitate toward the Golden Rule steady-state?

Answer 42

Because if we want any particular steady-state capital stock, such as the Golden Rule, we need a particular saving rate to support it.

Question 43

Why is it more convenient to use the MPK-δ=0 identity than comparing steady-state levels of consumption?

Answer 43

Because it’s relatively straightforward to estimate the MPK. By contrast, the second method requires estimates of steady-state levels of consumption at many different saving rates; such information is hard to obtain.

Question 44

How should policymakers push the economy toward the Golden Rule level if it’s starting with too much capital?

Answer 44

The policymakers should pursue policies aimed at reducing the rate of saving in order to reduce the capital stock.

Question 45

How should policymakers push the economy toward the Golden Rule level if it’s starting with too little capital?

Answer 45

The policymakers should pursue policies aimed at increasing the rate of saving in order to increase the capital stock.

Question 46

What is the contrast between the cases of going toward the Golden Rule level when starting with too little vs too much capital?

Answer 46

When the economy begins above the Golden Rule, reaching the Golden Rule produces higher consumption at all points in time.
When the economy begins below the Golden Rule, reaching the Golden Rule requires initially reducing consumption to increase consumption in the future.

Question 47

When deciding whether to try to reach the Golden Rule steady-state, what do policymakers have to take into account?

Answer 47

When choosing whether to increase capital accumulation, the policymaker faces a tradeoff among the welfare of different generations.