copyright © 2009 pearson addison-wesley. all rights reserved. chapter 10 the theory of economic...

Copyright © 2009 Pearson Addison-Wesley. All rights reserved.

Chapter 10

The Theory of Economic Growth

Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 10-2

Welfare Gains from Growth

• The profound importance of growth comes from the power of compound arithmetic.– Even small changes in growth rates make a huge

difference in the standard of living in the long run.

• Example: Korea and Philippines had the same level of real income per capita in 1965.– By 2004, Korea’s real income per capita was six times

that of the Philippines thanks to Korea’s rapid economic growth.


Great Questions of Economic Growth

• Economic Growth is the study of the causes and consequences of sustained growth in natural real GDP per person.

• What secrets did countries with rapid economic growth like Korea discover?

• Why is there a growing chasm between “rich” and “poor” countries?– “Rich” countries are from North America, much of Europe, Japan, some of

the successful Asian countries, and Australasia.

– “Poor” countries include much of the rest of the world except for “middle income” countries like most former members of the Soviet Bloc.

• What explains the ebb and flow of economic growth?


International Perspective: The Growth Experience of Seven Countries over the Last Century


International Perspective: The Growth Experience of Seven Countries over the Past Century


The Production Function

• Traditional growth theory divides output growth into two categories:– Growth of Factor Inputs that directly produce real GDP such as

capital (K) and labor (N).

– Growth in output relative to growth in factor inputs.

• The Production Function shows how much output (Y) can be produced by a given quantity of factor inputs and some autonomous growth factor, A:

Y = AF(K, N)

• In per capita terms, the production function becomes:

N

KfA

N

Y


Figure 10-1 A Production Function Relating per Person Output to per Person Capital Input


Solow’s Theory of Economic Growth

• We will first study an economy that has no technical change, implying that A is constant.

• The economy is in a Steady State when Y, K, and N are all growing at the same rate.– Implication: Y/K and K/N are both fixed in the steady state.

• Some new variables:– I = private investment– K = Capital stock– d = depreciation rate dK units of capital depreciate each yr– K1 = K0 + I – dK ∆K = I - dK or I = ∆K + dK– S = National saving (previously notated NS)– s = S/Y is the country’s saving rate– k, n, and y refer to the growth rates of K, N, and Y.


Derivation of the Steady State Condition

• At the steady state, ∆K/K = k = n.

• Investment adds to the capital stock (∆K) plus replaces worn out or depreciate capital (dK):

I = ∆K + dK = (∆K/K + d)K = (n + d)K

• Assuming NX = 0 S = I

• Using S = sY sY = (n + d)K

• Dividing through by N yields: N

Kdn

N

sY)(


Interpretation of Solow’s Result

• The LHS gives per person national savings.

• The RHS gives the amount of per person steady-state investment.

• Thus, in order for the economy to be at a steady state, the economy must save enough to pay for the investment required to replace worn out capital and to maintain per person capital.

N

Kdn

N

sY)(


Figure 10-2 Output, Saving, and Steady-State Investment per Person


What Affects the Solow Model?

• A higher saving rate leads to higher standard of living but not a permanent higher growth rate of output per person.

• A lower population growth rate leads to higher standard of living.

• A lower depreciation rate also leads to a higher standard of living.


Figure 10-3 Equilibrium of Saving and Investment in the Solow Growth Model


Figure 10-4 The Effect of a Higher Saving Rate on Capital and Income per Person


Two Types of Technological Change

• Growth in technology in all forms includes better schooling, improved organization, better health care, and the fruits of innovation and research.

• Technology that makes each worker more efficient is called Labor-Augmenting Technological Change.– Instead of counting the number of workers, we count

N = the Effective Labor Input

• Technology that shifts the per person production function is called Neutral Technological Change.– This is represented by the growth of the autonomous growth factor,

A, in the per person production function.


The “Solow Residual”

• The per person production function in terms of growth rates is given by: y – n = a + b(k – n)

(where b is the elasticity of output with respect to K)

• Solving for a yields the “Solow Residual”: a = (y – n) – b(k – n)• The Solow Residual is the amount that remains

after subtracting from the rate of real GDP growth all of the identifiable sources of economic growth. – a is also known as the growth in Multifactor

Productivity or Total Factor Productivity.


Puzzles for Solow’s Theory

• Conflict #1: Income per capita varies too much across countries.– The theory implies that a country that is 10 times richer

than a poor country must have vastly greater amounts of capital per worker (like 10,000 times the amount of K/N!)

• Conflict #2: Poor countries do not have a higher rate of return on capital.

• Conflict #3: Convergence has not been uniform.


Figure 10-5 A Production Function Relating per Person Output to per Person Capital Input


Human Capital and Solow Puzzles

• Human capital (H) is the value for a person or for society as a whole, of the extra future earnings made possible by education.– The new production function: Y = AF(K, H, N)

• Including human capital suggests that rich countries having 10 times the per person income of a poor nation need to have about 12.6 times the combined human and physical capital.

• Including human capital also removes the need for rich countries to have much lower returns on human and physical capital as compared to poor countries.


Endogenous Growth Theory

• Endogenous Growth Theory attempts to explain technical change as the outcome of market activity in response to economic incentives rather than just assuming that technical changes happens exogenously.– Some models have the key to growth being the

development of ideas for new goods, assuming monopoly power granted by patents and copyright.

– Other models look at the role of international trade in disseminating ideas.


Chapter Equations


Chapter Equations

( , ) (10.1)Y AF K N

(10.2)Y K

AfN N

(10.3)k n


Chapter Equations

(10.4)K

k nK

(10.5)K

I K dK d K n d KK

(10.6)S I


Chapter Equations

(10.7)sY n d K

(10.8)sY K

n dN N

(10.9)Y K

AfN N


Chapter Equations

General Form Numerical Example

( ) 0.25 (10.10)y n a b k n y n a k n

(10.11)a y n b k n


Chapter Equations

0.25


(10.12)b

Y N K N Y N K N

1 1 0.25


(10.13)b

K N Y N K N Y N

, , (10.14)Y AF K H N

copyright © 2009 pearson addison-wesley. all rights reserved. chapter 10 the theory of economic...

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