L12 - Long-Run Economic Growth

Question 1

Why is economic growth important for poor countries?

Answer 1

In the poorest one-fifth of all countries,

• daily caloric intake is 1/3 lower than in the richest fifth
• the infant mortality rate is200 per 1000 births, compared to 4 per 1000 births in the richest fifth.
• In Pakistan, 85% of people live on less than $2/day
• •One-quarter of the poorest countries have had famines during the past 3 decades. (none of the richest countries had famines)

Source: The Elusive Quest for Growth, by William Easterly. (MIT Press, 2001)

The point: If we can learn how to help poor countries rise out of poverty (which long-run growth is really important for) , we will be making a huge difference in the lives of billions of people, as well as creating new markets for our exports

Question 2

Why growth matters?

Answer 2

• Anything that affects the long-run rate of economic growth – even by a tiny amount – will have huge effects on living standards in the long run.
• A government policy or economic reform that leads to a small change in the average long-run growth rate can have a huge impact on the standard of living in the long-run.

Question 3

How do you calculate discrete and continuous growth?

Answer 3

Discrete:

FV = PV (1 +r)^t

Continuous:

FV = PVe^rt

Question 4

How is Economic Size related to influence?

Answer 4

• Political influence on the world stage is correlated with economic power.
• Richer economies are more likely to have a say on world politics than poorer ones. Consider the G7 (G8 if Russia is included), that meets on a regular basis to discuss political and economic issues.
• This effect is even stronger at the international financial institutions such as the International Monetary Fund or the World Bank, where the number of votes of a given country is calculated by a formula that includes its economic size.
• Example: The US holds 17% of the total voting power at the IMF, which is sufficient for vetoing important changes.

Question 5

What are the lessons of growth theory?

Answer 5

growth can make a positive difference in the lives hundreds of millions of people

These lessons help us:

• understand why poor countries are poor
• design policies that
• can help them grow
• learn how our own growth rate is affected by shocks and government’s policies

Question 6

What is the Solow Model?

Answer 6

due to Robert Solow, won Nobel Prize for contributions to
the study of economic growth

a major paradigm:

• widely used in policymaking
• benchmark against which most recent growth theories are compared - if you restrict more reason models most of them collapse onto the Solow Model

•looks at the determinants of economic growth and the standard of living in the long run

Question 7

What are the main determinants of growth in the Solow Model?

Answer 7

K is no longer fixed:

• investment causes it to grow,
• depreciation causes it to shrink.

L is no longer fixed:

• population growth causes it to grow.

The consumption function is simpler.

No G or T (only to simplify presentation; we can still do fiscal policy experiments).

Question 8

What is the production function of the Solow Model?

Answer 8

constant returns to scale –> double in inputs, you double the outputs

f(k) is the “per worker production function,” it shows how much output one worker could produce using k units of capital.

Question 9

What does the production function of the Solow model look like on a graph?

Answer 9

Question 10

What is the national income identity?

Answer 10

Y = C + I –> (remember no, G)

S=I as it is assumed everything saved is used for investment purposes

In per worker terms:

y = c + i

where c = C/L and i = I/L

Question 11

What is the consumption function in the Solow model?

Answer 11

s = the saving rate

the fraction of income that is saved (s is an exogenous parameter)

Note: s is the only lower case variable that is not equal to its upper case version divided by L

Consumption function (per worker):

c = (1-s)y

Question 12

how is Saving and Investment related in the Solow Model?

Answer 12

saving (per worker) = y – c = y – (1–s)y = sy

•National income identity is y = c + i

Rearrange to get: i = y – c = sy

•Using the results above,
i = sy = sf(k)

The real interest rate r does not appear explicitly in any of the Solow model’s equations. This is to simplify the presentation. We can assume that investment still depends on r, which adjusts behind the scenes to keep investment = savings at all times (e.g., I=S).

Question 13

What does the Production and Savings function look like in the Solow Model?

Answer 13

Question 14

How do you calculate depreciation per worker?

Answer 14

The capital stock here refers to physical capital stock, such as plants or housing, and not to financial investments.

Question 15

How do you calculate capital accumulation?

Answer 15

Change in capital stock = investment - depreciation

Δk = i - 𝛿k

• if this is positive there is more investment than depreciation per workers so capital stock is growing

Since i = sf(k), this becomes:

Δk = sf(k)- 𝛿k –> equation of motion

Question 16

What is the law of motion of k?

Answer 16

Δk = sf(k)- 𝛿k

• the Solow model’s central equation
• Determines the behaviour of capital over time…which, in turn, determines the behaviour of all of the other endogenous variable because they all depend on k E.g.,

income per person: y = f(k)

consumption per person: c = (1–s) f(k)

Question 17

What is the steady state in the Solow model?

Answer 17

Δk = sf(k)- 𝛿k

If investment is just enough to cover depreciation
[sf(k) = 𝛿k],

then capital per worker will remain constant:
Δk = 0.

This constant value, denoted k*, is called the steady-state capital stock.

Question 18

What happens on the investment function when you are away from the steady-state?

Answer 18

As long as k < k*, investment will exceed depreciation,
and k will continue to grow toward k*.

• Each period Δk will be added in correspondence to the capital accumulation (this is the vertical gap between the investment function and depreciation)
• Each period you will move up the line till Δk=0 at k*

Question 19

What happens when there is an increase in the savings rate?

Answer 19

Here there is a prediction that:

•Higher s –> higher k*.

•And since y = f(k) ,
higher k* –> higher y* .

•Thus, the Solow model predicts that countries with higher rates of saving and investment will have higher levels of capital and income per worker in the long run.

• the problem with this is that in the real world a change in the savings rate does not influence GDP
• Therefore Solow introduces technology advancements to facilitate the growth of output per worker over time

Question 20

What is high investment associated with?

Answer 20

• high income per person, as the Solow model predicts
• This scatterplot shows the experience of 96 countries, each represented by a single point.
• The horizontal axis shows the country’s rate of investment;
• The vertical axis shows the country’s income per person.

Question 21

What does K(dot) mean?

Answer 21

Look up what K(dot) is ==> small change -> dk/dt

rn, it has become the convention in the economic growth literature to express the differential of a variable with respect to time by placing a dot above

K(dot)/K = the growth rate of K