Economic growth
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Economic Growth. Junhui Qian. Content. Overview Solow Model I ( a ccumulation of capital and population growth ) Solow Model II (considering technological progress) Endogenous growth models Economic growth accounting. The Importance of Economic Growth.

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Economic growth

Economic Growth

Junhui Qian

Intermediate Macroeconomics


Content

Content

  • Overview

  • Solow Model I (accumulation of capital and population growth )

  • Solow Model II (considering technological progress)

  • Endogenous growth models

  • Economic growth accounting

Intermediate Macroeconomics


The importance of economic growth

The Importance of Economic Growth

  • For poor countries, a stagnant economy means a persistent absolute poverty.

  • In relative terms, a slight but persistent difference in growth rate results in huge income gaps.

  • The following table illustrates how three different growth rates (from the same income per cap, 100 ) lead to starkly different outcomes.

Intermediate Macroeconomics


Growth performances of 143 economies

Growth Performances of 143 Economies

Intermediate Macroeconomics


Where economic growth comes from

Where Economic Growth Comes From

  • Increases in factor inputs

    • Capital

    • Labor

  • Technology progress

Intermediate Macroeconomics


Content1

Content

  • Overview

  • Solow Model I (accumulation of capital and population growth )

  • Solow Model II (considering technological progress)

  • Endogenous growth models

  • Economic growth accounting

Intermediate Macroeconomics


Solow model i

Solow Model I

  • The first Solow model characterizes the role of factor inputs in economic growth.

  • We assume:

    • Closed economy (), no government spending ().

    • Fixed production function, , a constant-return-to-scale technology.

    • The saving rate is constant:

    • Capital depreciates at constant rate .

    • Population grows at constant rate ,

Intermediate Macroeconomics


The per capita output

The Per Capita Output

  • Let and is the output per cap. And is the amount of capital per cap. We have

  • Define We have

  • f(k) isthe“per worker production function,” how much output one worker could produce using k units of capital. We assume

    Note that is the marginal product of capital (MPK).

  • We also assume:

Intermediate Macroeconomics


The per capita demand

The Per Capita Demand

  • Without government spending and net export, the demand for goods and services is composed of consumption () and investment ().

  • In per cap terms, we have

    where and

  • The per cap investment is a constant fraction of the out

Intermediate Macroeconomics


Accumulation of capital

Accumulation of Capital

  • Investment causes capital to rise and depreciation causes capital to wear out.

  • The aggregate capital accumulation is described by

  • Similarly, the evolution of the population is characterized by

  • Let , the capital per cap at time We then characterize the dynamics of capital accumulation by

    .

Intermediate Macroeconomics


Steady state level of capital

Steady-State Level of Capital

  • As capital accumulates, it will reach a point where new investment equals depreciation,

  • At this level of capital, , the economy reaches a steady state, where capital does not increase or decrease. We call the stead-state level of capital.

Intermediate Macroeconomics


A graphic illustration

A Graphic Illustration ()

Intermediate Macroeconomics


An example

An Example

  • Suppose . Then we have

  • Let Each year (), the capital stock changes by

    .

  • Solving , we obtain

Intermediate Macroeconomics


Approaching the steady state a numerical illustration

Approaching the Steady State: A Numerical Illustration

Assumptions: , s=0.3, ,

Intermediate Macroeconomics


Implications of solow model i

Implications of Solow Model I

  • If the economy is already at the steady state, per capita income () ceases to grow. However, the total income continues to grow as the population grows,

  • If the initial level of capital is below the steady-state level, there will be a convergence (or, catch-up) period to the steady-state level.

Intermediate Macroeconomics


The role of saving

The Role of Saving

  • To see the effect of a change in the saving rate, , we examine the equation characterizing the steady state,

  • Fix and , let . Using the implicit function theorem, we have

  • Due to the assumption , we must have , otherwise the curve cannot cross with the line . Hence must be positive.

  • An increase in saving rate would lead to a higher level of steady-state capital and income.

Intermediate Macroeconomics


A graphic illustration1

A Graphic Illustration ()

Intermediate Macroeconomics


The golden rule level of capital

The Golden-Rule Level of Capital

  • At steady states, the consumption is given by

  • The level of capital that corresponds to the maximum consumption, which we call the golden-rule level of capital, must satisfy the first-order condition:

  • At the golden-rule level, marginal product of capital (MPK) equals the depreciation rate plus the population growth rate.

Intermediate Macroeconomics


A graphic illustration2

A Graphic Illustration ()

Intermediate Macroeconomics


How the golden rule level of capital might b e achieved

How The Golden-Rule Level of Capital Might Be Achieved

  • Recall that the steady-state level of capital is a function of the saving rate, .We might adjust to achieve the golden-rule level of capital.

  • Suppose that . Since , we might increase the saving rate to achieve the golden-rule level.

  • If the initial level of capital is higher than the golden-rule level, then we might decrease the saving rate to achieve the golden-rule level.

Intermediate Macroeconomics


An example1

An Example

  • Suppose Then solving for the steady-state level

    we obtain the function .

  • Suppose we obtain the steady-state level of capital in this economy.

  • The golden-rule level, however, is obtained from

    which gives =25.

  • In this economy, the steady-state level of capital is too low. We might increase the saving rate to achieve the golden rule. Which saving rate corresponds to the golden rule?

  • We solve and obtain

Intermediate Macroeconomics


Approaching the golden rule

Approaching The Golden-Rule

Intermediate Macroeconomics


Dealing with too much capital

Dealing with Too Much Capital

Intermediate Macroeconomics


Case studies

Case Studies

  • The economic miracle of Japan and Germany since the end of the World War II.

  • The economic miracle of China since 1978.

  • Why East-Asian economies grew so fast?

Intermediate Macroeconomics


The effect of population growth

The Effect of Population Growth

  • To see the effect of a change in , we still examine the equation characterizing the steady state,

  • Fix and , let . Using the implicit function theorem, we have

  • Hence higher population growth leads to lower steady-state capital per cap.

Intermediate Macroeconomics


A graphic illustration3

A Graphic Illustration

Intermediate Macroeconomics


Case study population growth v s per capita income

Case Study: Population Growth v.s. Per Capita Income

Intermediate Macroeconomics


Content2

Content

  • Overview

  • Solow Model I (accumulation of capital and population growth )

  • Solow Model II (considering technological progress)

  • Endogenous growth models

  • Economic growth accounting

Intermediate Macroeconomics


Solow model ii

Solow Model II

  • The first Solow model fails to allow sustainable growth in per capita output/income.

  • The second Solow model introduce technological progress as the engine for sustainable growth.

  • We assume:

    • Closed economy (), no government spending ().

    • Labor-augmenting production function, , where

      • is a constant-return-to-scale function,

      • is technology level, which grows at a constant rate and

      • denotes population, which grows at a constant rate .

    • The saving rate is constant:

    • Capital depreciates at constant rate .

Intermediate Macroeconomics


Output per effective worker

Output Per Effective Worker

  • Let and is called the output per effective worker. And is the amount of capital per effective worker. We have

  • As in the first Solow model, we define and write

  • f(k) isthe“per effective worker production function,” how much output one effective worker could produce using k units of capital. We assume

    Note that is the marginal product of capital (MPK).

  • We also assume:

Intermediate Macroeconomics


The accumulation of capital

The Accumulation of Capital

  • Note that And as previously, we have

  • The the dynamics of capital accumulation is characterized by

    .

Intermediate Macroeconomics


The steady state

The Steady State

  • The steady state capital per effective worker, , is then characterized by the following equation,

  • At steady state, the capital per effective worker is a constant,

  • We have the following implications:

    • Total output, , grows at the constant rate

    • Per capita output, , grows at the constant rate .

  • Thus the Solow Model II, incorporating the factor of technological progress, is able to explain sustained growth in per capita terms.

Intermediate Macroeconomics


Exercises

Exercises

  • What would be the impact of an increase in saving rate on the steady-state capital per capita?

  • What would be the Golden-rule level of capital per effective worker?

Intermediate Macroeconomics


Real wage and real rental price of capital

Real Wage and Real Rental Price of Capital

  • Recall that in a competitive economy, the real wage equals marginal product of labor () and the real rental price of capital equals the marginal product of capital ():

  • Hence the Solow Model II implies that the real wage grows with the technological progress and that the real return to capital remains constant.

Intermediate Macroeconomics


Content3

Content

  • Overview

  • Solow Model I (accumulation of capital and population growth )

  • Solow Model II (considering technological progress)

  • Endogenous growth models

  • Economic growth accounting

Intermediate Macroeconomics


What endogenous models do

What Endogenous Models Do

  • In the Solow model, technological progress is assumed.

  • Endogenous models treat the technology progress as an outcome of economic activities, or in other words, as an endogenous process.

  • In this part of the lecture, we introduce two simple endogenous models.

    • A basic model

    • Two-sector model

Intermediate Macroeconomics


A basic model

A Basic Model

  • The basic model assumes

    • Constant population.

    • A linear technology,

      where is output, is capital stock that includes “knowledge”, and is a constant.

    • The capital accumulation follows

  • It is obvious that

Intermediate Macroeconomics


The implication

The Implication

  • As long as , sustained growth is achieved. The sustained growth depends on high saving and investment.

  • This is possible because this model enjoys the constant return to capital, while the Solow model assumes diminishing return to capital.

  • The capital stock in this model should be understood to include “knowledge”.

Intermediate Macroeconomics


A two sector model

A Two-Sector Model

  • The two-sector model assumes

  • Production function in manufacturing

    where is the fraction of the labor force in universities.

  • Production function in research universities

    where is describes how the growth in knowledge depends on the fraction of labor force in universities.

  • Capital accumulation

Intermediate Macroeconomics


Exercise

Exercise

  • Solve this two-sector model and obtain the stead state.

  • Does this model exhibits constant return to capital?

  • Does this model allows sustained growth?

Intermediate Macroeconomics


Content4

Content

  • Overview

  • Solow Model I (accumulation of capital and population growth )

  • Solow Model II (considering technological progress)

  • Endogenous growth models

  • Economic growth accounting

Intermediate Macroeconomics


Accounting for economic growth

Accounting for Economic Growth

  • Where does economic growth come from?

    • Increases in the factors of production

      • Capital (K)

      • Labor (L)

    • Technological progress

  • How much does each element contribute to economic growth?

Intermediate Macroeconomics


Increases in factors

Increases in Factors

  • We first assume that growth comes from increases in factors only.

  • Assume , which is to say that technology does not change over time.We obtain:

  • Dividing the equation by , we have

    where is capital’s share and is labor’s share.

Intermediate Macroeconomics


Technological progress

Technological Progress

  • Assume , where is called total factor productivity. measures current level of technology.

  • Similar derivation yields the equation of growth accounting:

  • ,which is called the Solow residual, measures technological progress. It is the changes in output that cannot be explained by changes in inputs.


Case study source of growth in us

Case Study: Source of Growth in US

Intermediate Macroeconomics


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