THE ECONOMIC IN THE VERY LONG RUN - …web.uvic.ca/~aahoque/Fall 2012 UVic/Chapter 7.pdfTHE ECONOMIC IN THE VERY LONG RUN Chapter 7 ... Nigeria Vietnam India China Mexico Russia Germany

THE ECONOMIC IN THE VERY LONG RUN

Chapter 7

Economic Growth I

October 31, 2012

2 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012

Outline

1. Stylized Facts of Economic Growth

2. Basic Solow Growth Model (CLOSED ECONOMY)

3. How a country’s standards of living depends on its

saving and population growth rates

4. Golden Rule Level of Capital


1. Stylized Facts of Economic Growth

Objective: A model of economic growth

Economic growth of what?

Our focus: income approach – the growth rate of output (GDP) per person (per capita)

More precisely, growth of the natural rate of output in per capita or per person terms — a better measure of well-being.


Figure: International Differences in the Standards of Living, Year 2004 (in US $)

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

Nigeria Vietnam India China Mexico Russia Germany Japan Canada USA


Stylized Facts1

1. Wide and steady income disparity across countries 2. Evidence of increasing disparity across countries

3. Almost all countries exhibit some growth As wealthy countries have grown so have poorer

countries – no absolute poverty trap.

4. Wide distribution of growth rates

1 Parente and Prescott(1993)


Some countries have taken off, others have not — why?

(1) and (2) — cross country differences in the level of GDP per person

(3) and (4) — cross country differences in the growth rates of GDP per person.

Objective is to explain these differences.

!! We won’t be able to do everything with the Solow growth model but we make a decent start.


Why Growth Matters?


Economic growth raises living standards and reduces poverty….



2. The Solow Model

A dynamic model of output growth and capital accumulation.

Due to Robert Solow2, won Nobel Prize for contributions to

the study of economic growth

A major paradigm:

o widely used in policy making

o benchmark against which most recent growth

theories are compared

looks at the determinants of economic growth and the

standard of living in the long run

2 Solow, R. (1956), “A contribution to the Theory of Economic Growth,” Quarterly Journal of Economics


Assumptions:

a) K is no longer fixed

- investment causes it to grow

- depreciation causes it to shrink

b) L is no longer fixed

- population growth causes it to grow

c) The consumption function is simpler

d) No G or T (only to simplify presentation; we can still do

fiscal policy experiments)


The Supply of and Demand for Goods

Supply of Goods: the production function In aggregate terms:

Define:

Assume constant returns to scale

Let

. Then

or,

or,


For example, if

then,

Graphically, production per worker is pictured as:

Slope of the production

function is:

and exhibits diminishing

returns


Demand for Goods

Closed economy, no government spending so output is either consumed or invested. All variables expressed in per person terms; i.e., divided by the size of the labour force L.

Consumption per person:

Where, s is an exogenous parameter of the model

As before, the real interest rate adjusts so that AS = AD:

In other words, investment per person, i, is a constant share s of output per person:


Growth of Capital Stock and the Steady State

Output and investment in diagram


Investment increases the stock of capital per person, k. Depreciation (wearing out of capital) reduces the stock of k at a constant rate. Together, these are modelled as:

Solow model’s central equation

Where,


A Steady State (SS) is defined as:

From the above, this means our steady state is described as,

or,

When this condition holds,

Where, is the steady state level of capital per person


The Model can be represented in a single diagram combining

output and investment, and depreciation diagrams:


At steady state, and . We get,

SS output per person

SS investment per person

SS consumption per person

Adjustment to steady state: If then ; investment exceeds depreciation; and is growing and we move toward . Output is also growing. If then ; capital per person is declining and we move toward . Output is contracting.


The steady state represents the long-run equilibrium of the economy


A Numerical Example

Production function:

So, output per person: Given, initial capital per person, . Solve for the SS values We know, in the SS

or,


Plug in all values and formula, we get

That is,

So, the SS output per person,

The SS investment per person, =0.9

The SS consumption,

The SS depreciation,

Thus,



Savings, Growth and Steady State Output

Our simple model makes the following predictions:

• A higher saving rate, s, leads to a higher SS capital stock

per person and a higher level of SS output.

• A higher s leads to higher economic growth but only

temporarily.

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

Note the difference between level and growth


At A and B, output growth is zero: . From A to B due to an

increase in saving: and until the new SS is achieved.


Golden Rule Level of Capital

What is the best steady state capital stock? As s increases, and increase. Does this imply that s = 1 is optimal? Clearly, the answer is NO. Although is as large as possible, nothing is available for consumption! An optimal level of steady state capital, :

one that provides the highest level of steady state consumption per person.


Let be the steady state level of capital that provides this

optimal level of consumption.

In steady state,

or,

Since in steady state,

is biggest where the slope of the production

function equals the slope of the depreciation line: MPK=



If we are at a below then the marginal product of

capita exceeds the depreciation rate.

What this means is that if we were to increase steady state capital by one unit of capital, the gain in output (MPK) exceeds the additional required investment to maintain the capital stock, .

As a result, there is some left over for additional consumption.

Mathematically, we choose to maximize:

The solution to this problem is,

or,


Transition to the Golden Rule SS The economy does NOT have a tendency to move toward the Golden Rule steady state. Achieving the Golden Rule requires that policymakers adjust s. This adjustment leads to a new steady state with higher consumption. If

and the s is reduced to achieve :



If and the s is increased to achieve

:


Welfare Implications If we simply compare different steady states, then everyone is

better off at than they are at any other level of .

However, if we think about moving the economy from one SS to

another (by changing the s), then the welfare implications are

not so straightforward.

If and the s is reduced to achieve

:

current generation consumes more and so is better off;

future generations consume more and so are better off.

all generations are better off.


If and the s is increased to achieve

:

current generation consumes less and so is worse off;

future generations consume more and so are better off.

Not all generations are better off.

Importantly, those who are worse off also are those that can

influence the current saving decisions. So it seems unlikely

that, if an economy is below , it will achieve it.


Solow Growth Model with Population Growth

The model is exactly as before but we now assume that the labour force (population) is growing at a rate n.

n is a number like 0.03 or 3 percent, and is exogenous

Previously we saw, , with no population growth.

If : capital per person shrinks by rate .

Now, labour growth at rate n also causes capital per person to shrink, at a rate n. e.g. i is zero — then K is changing due to depreciation:


or,

And, labor growth:

We know,

, and is changing:


So, without investment,

Of course, if investment per person is not zero then it is adding

to the per person capital stock:

( + n)k = break-even investment:

the amount of investment necessary to keep k constant.

Break-even investment includes: k to replace capital as it wears out n k to equip new workers with capital

(Otherwise, k would fall as the existing capital stock would be spread more thinly over a larger population of workers.)


Now, the steady state is:

Actual investment = break-even investment

Result: population growth lowers the SS level of capital

and output per person (for a given saving rate and depreciation rate)


Point A: The SS level of for high population growth;

Point B: The SS level of for low population growth.


Intuition:

A high capital stock has a high steady state replacement cost;

this gets higher with higher population growth.

In steady state:

are growing at the rate of population growth

No growth in standard of living

Golden rule is now,

Same logic as before


Solow model predicts

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

Thus, the Solow model predicts that countries with higher

population growth rates will have lower levels of capital

and income per worker in the long run.


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THE ECONOMIC IN THE VERY LONG RUN - …web.uvic.ca/~aahoque/Fall 2012 UVic/Chapter 7.pdfTHE ECONOMIC IN THE VERY LONG RUN Chapter 7 ... Nigeria Vietnam India China Mexico Russia Germany