1. Growth Theories “Frame of Reference” Lecture 1 of Eco 317
J.D. Han at King’s
“Frame of Reference”

2. General Neo-Classcial Model
Harrod-Domar Model
Solow Model
Endogenous Growth Model
Human Capital
Others
Lewis Model
Rostow Model

3. Neo-Classical Economics
Microeconomics that you have learned
Aggregate Demand does not matter for long-run growth of income
Macroeconomic Policies of Government (controlling Money Supply, Government Expenditures )do not matter for Y in the long-run – “You cannot pull yourself up by your own bootstrap”

4. 1. Neo-classical Mode = Supply Side Economics
Economic growth
= Growth of Income
= Growth of aggregate output comes from
an increase in labour L;
an increas in capital K; and/or
improvement of technology T

5. In General ‘production function’ Y = f (K, L; T) Growth function
dY = f (dK, dL; dT)

6. Specific Formula of Production Function
Most Widely Used Production Fn is
“Cobb-Douglas Production Function”:
Y = A K a L 1-a
, and a<1
*Realistic and Convenient Features of C-D function:
Diminishing Marginal Return
Constant Return to Scale

7. *Why are the two features realistic in Economics?
Diminishing Marginal Returns(DMR)
eg) Y = F(K,L ) = F(5, 5) = F(10, 5)
Decreasing Marginal Productivity of Capital or Labor
dY/dK = MPk, d MPk/ dk <0 or dY2/d2K <0
dY/dL = MPL, d MPL / dL <0
Constant Return to Scale (CRS)
If Y = F (K, L) is true, Y = F (2K, 2L) = 2 F (K, L) is attainable.
You do not have to take DRS 1.5 Y = F (2K, 2L)

8. **Diminishing Marginal Returns as a Fact of Life
Biological growth- “S curve”(upper part)
Stages of Acceleration (Youth) and Deceleration (Maturity)
Convergence
Production Function
Stages of Increasing Marginal Return and Decreasing Marginal Return
inflection point between IMR and DMR
Why is IMR no substantive issue?
Returns to Education/Efforts

9. 2. Harrod-Domar Model
Income Growth Rate = Saving Rate x Efficiency of Capital
dY/Y = S/Y x dY/dK
( as S = I = dK )
= Saving Ratio x Marginal Product of Capital

10. 2. Harrod-Domar Model
Income Growth Rate = Saving Rate x Efficiency of Capital
dY/Y = dY/dK x dK/Y
( as S = I = dK )
= dY/dK x S/Y
= Marginal Product(ivity) of Capital x Savings Ratio

11. = S/Y
dK/dY
= Average Propensity to Save
Incremetal Capital Output Requirement

12. In general, eventually, the more amount of capital, the Marginal Productivity of capital decreases – “Convergence”
Recall: In the latter part of the S curve, the MP of capital is a decreasing function of capital –“Decreasing Marginal Returns” or “Law of Diminishing Marginal Return”
This happens as the size of capital grows in the natural course of economic growth.
It is a formidable task to keep the weighted average Marginal Product of Capital constant or even Increasing for the entire economy.

13. Implications of the H-D model
-The key to economic growth is to expand the level of investment: capital accumulation or ‘Mobilization of capital’
-Equally important is the productivity of capital: the higher the marginal product(ivity) of capital, the better, or the lower the required incremental capital-output ratio, the better.

14. Limitation of the Harrod-Domar Model
difficult to stimulate the level of domestic savings particularly in the case of developing countries
One way of supplementing the low domestic savings would be foreign savings/investment:
However, borrowing from overseas causes debt repayment problems later.
The law of diminishing returns would suggest that as investment increases the marginal productivity of the capital will diminish, and the capital to output ratio rise. Fighting this natural law is a formidable task.
In a word, the model does not give any easy recipe for a success of economic development while it can explain the surface of the given economic growth.

15. How to enhance Efficiency of Capital: Higher MP of Capital, or lower ICOR
1) Through Technological advances or Technical innovations –
This can happen to any economic system: Market(economy) can take care of this while government may promote it too.
2) Though resource allocation by ‘visible hands’, government, channeling capital into ‘efficient areas’ –
- A specific Economic System/Institution
key words) Centrally planned economy; Economic Planning; Resource Allocation Planning; Industrial Policy; Promotion of National Strategic Industries; Key Industry

16. * Technical Innovation
Illusive
Difficult to measure
Hard to explain causes and impacts
- Refer to “Growth Accounting” later.

17. *To spark Growth, we may need Institutions
Institution (as opposed to Market Economy)
covers Government; Economic System; Value System(ethics,religion)
- Mechanism to ‘Mobilize Capital’? How to increase Saving Rate?
- Mechanism to raise the Efficiency of Capital?

18. *East Asian Government’s Role for Promotion of Economic Growth
Government Policies are needed to 1) encourage/force savings;
2)and/or to enhance efficiency of capital by allocating scarce capital primarily to strategic area of industry.

19. * Case Studies of Government’s Forced Savings and Resource Allocation
Successes
-Japan
by Kozo Yamamura’s paper reports that during the take-off stage of economic growth of Japan, the capital output ratio fell significantly due to Innovations(?) and Government’s Industrial Policy”
-Korea
Promotion of chae-bol(s)
Strategic industries of Ship-building, Cars, Semi-conductors, IT Industries, etc.

20. 2) Debacles
Some countries have succeeded in mobilization of capital, but failed in the efficient use of capital.
Stalinist Economy
North Korea
Great Leap Movement in China

21. 3. Solow Model

22. 1) Per-capital Income Production function: Y = F(K, L)
In “per worker” terms: y = f(k)
Relationship between variables:

23. From the above we can get:
Per-person or per-capita income level (y) depends on each worker’s capital equipment(k).
y=f(k) shows DMR.
Can you draw the graph with y and k?

24. Growth rate is measured by the slope of the tangent line of the y or f(k) curve.
Growth rate decreases as the per-capita capital stock rises. It is true for all countries- “Convergence”
Countries that start further away from the steady state grow faster

25. 2. Actual Supply of Capital
Assume FIXED SAVINGS RATE or APS: s =S/N/Y/N = savings /income
Given an income of y
Actual savings= s · y = s f(k)

26. EXAMPLE Savings rate of 40%
s = .4 (you save a fraction of your income)
Can you draw the actual savings curve in the previous graph you have drawn?

27. 3. Required Capital for Just Keep-Up
Minimum Capital Requirement to just keep up for each work is proportional to population growth rate(n) and capital depreciation rate(d)
*if you do not replenish the economy with the minimum requirement of capital, then the level of capital and thus the level of production or income fall.

28. Example)
Y = 100; L = 20; K = 10
y = Y/L = 5
k = K/L = 10/20 = 0.5
n = 3% ; d = 5%
Then you need 8% of capital every year to keep constant each worker’s capital equipment.

29. 4. Equilibrium or Not
The Change in capital per worker is the actual supply of capital over the minimum required capital
We may call this net investment.

30. Thus: If k > 0: economy accumulates capital per worker
If k < 0: economy reduces capital per worker
If k = 0: constant capital per worker: steady state

31. Graphically
f(k)
(+n)k
k < 0
s f(k)
k > 0 k k* k0

32. Steady-state Per-capita Income or y. = Y/N is determined where s f(k
Steady-state Per-capita Income or y* = Y/N is determined where s f(k*) = (+n)k*.

33. Implications of the model
The economy converges, over time, to its steady state.
If the economy starts BELOW the steady state, it accumulates capital until it reaches the steady state.
If the economy starts ABOVE the steady state, it reduces capital until it reaches the steady state.

34. Growth rates Capital per worker grows at rate 0
Output per worker grows at rate 0
Total capital: K = k · L grows at rate n
Total output: Y = y · L grows at rate n

35. Comparative statistics
Parameters of the model: s, n, 
Predictions of the model:
In steady state:
Higher savings rate implies higher income per worker
Higher population growth implies lower income per worker

36. Savings rate and growth
(+n)k
s2f(k)
s1f(k) k
kss
kss2

37. Note that an increase in savings rate do increase the level of income, but not the rate of growth of income.

38. Population growth rate and growth
(+n2)k
(+n1)k
sf(k)
kss2 k
kss

39. Technical Innovations
How is technical innovation different for the y curve from an increase in savings rate?
-answer: In the case of technical innovation, the whole y curve goes up; the level of equilibrium y goes up and the rate of an increase in y goes up for a given level of y. So in the end, the rate of economic growth does not fall; a long-term sustainted economic growth(rates)
In the case of an increase in savings rate, y goes up but the rate of a change in y falls.
Continuous Technical Innovations
-continuous upward shift of the y curve

40. 4. Lewis Model: Dual Sector Model of Economic Growth
many LDCs had dual economies with a traditional agricultural sector and a modern industrial sector
Traditional Sector has too much labor at subsistence level
MPlabour = 0; Y = C + S + T = C + I + G
Modern Sector absorbs labor and becomes the source of economic surplus or savings

41. How does the Mechanism work?
The lack of development was due to a lack of savings and investment. The key to development was to increase savings and investment.
Lewis saw the existence of the modern industrial sector as essential if this was to happen. A growing industrial sector requiring labour provided the incomes that could be spent and saved. This would in itself generate demand and also provide funds for investment. Income generated by the industrial sector was trickling down throughout the economy.
Urban migration from the poor rural areas to the relatively richer industrial urban areas gave workers the opportunities to earn higher incomes and crucially save more providing funds for entrepreneurs to investment.

42. Policy Implications of Lewis model
Induced Displacement of Population from Rural to Urban Sector
Government may use push and pull factors using Institutions or System
-‘Vanity Effect’ as a magnet: Glamorous/modernized Urban Sector versus Backward/‘Suppressed’ Rural Area
-Income Inequality is as a ‘magnet’

43. Lewis Model is Unbalanced Economic Growth Strategy (不均衡的经济发展战略）
This is a practical strategy.
Let’s reflect on side-effect/problems
-Sustainability in the long-run: Ravaging impacts of labor saving technology; How much and how long is the modern sector absorb the surplus labor? What will happen to no-longer-needed surplus labor?
-Inequality between agricultural – industrial sectors
Income Inequality; Urbanization issues
Urban/Modern Sector may not Save but Spend: Urban ‘Consumerism’
Rural-Urban Migration is larger than what the urban sector can absorb: Rural Poverty simply becomes Urban Poverty

44. Case Studies: Casual Analysis
England in 18th Century
Enclosure Movement
U.S. in 19th century
Slave-Emancipation
Japan
Korea in the 1970s and the 1980s
*New Village Movement (Sae-Ma-Eul-Un-Dong)
Taiwan (part of China)
China

45. *Quantitative Analysis: Income (Distribution) Inequality and Economic Growth
Income Inequality is measured by Gini-Coefficient
Some international comparisons argue as economy grows, Gini Coefficient generally rises first and then fall
It is in line with Lewis’ theory: Income inequality is not only inevitable, but also necessary for economic growth
- Case studies of Korea, Japan, and China (presentation)

46. 5. Rostow's Model- the Stages of Economic Development .
In 1960, the American Economic Historian, WW Rostow suggested that countries passed through five stages of economic development

47. Stage 1 Traditional Society -dominated by subsistence (defined as no economic surplus, meaning output being consumed by producers rather than traded);
-trade being carried out by barter, meaning goods being exchanged directly for other goods;
-Agriculture being the most important industry;Production being labor intensive using only limited quantities of capital.
Stage 2 Transitional Stage (the preconditions for takeoff) -Increased specialization starting to generate surpluses for trading.
-an emergence of a transport infrastructure to support trade; External trade also occurs concentrating on primary products; Entrepreneurs emerge
-savings and investment grow.
Stage 3 Take Off -Rapid Industrialization or Industrial Revolution
- Growth concentrated in a few regions of the country and in one or two manufacturing industries.
- The level of investment reaches over 10% of GNP.
- The economic transitions are accompanied by the evolution of new political and social institutions that support the industrialization.
- The growth is self-sustaining: investment leads to increasing incomes in turn generating more savings to finance further investment.
Stage 4 Drive to Maturity -Industrial Diversification; producing a wide range of goods and services; reliance on exports and imports may start decreasing
Stage 5 High Mass Consumption - Mass Consumption（大众消费）; Domestic Aggregate Demand is the major determinant of Business (Cycles)
- Consumer durable industries; Service sector

48. Limitations
Deterministic Path for All?
Rostow predict that every economy is going through the same stage.
However, some economies are stuck in the first stage forever while other economies “take off”.
-leaving a room for ‘cultural explanation’
It does not set down the detailed nature of the pre-conditions for growth; What sparks the take-off?
-Exogenous Shocks as a Catalyst for Great Transformation?
It is not very helpful as a policy prescription. Perhaps its main use is to highlight the need for investment.
* Explaining the fast is always easier than Predicting
the future

49. Major Contribution of Rostow’ Model
Emphasis of ‘Take-Off’
-Economic Development is
not a continuous process;
-There should be
some Event for Great Transformation.

50. *Case Studies: Catalyst for Take off
Catalysis for Take Off= Exogenous Shocks
Japan
Meiji Revolution; Korean War
Korea
President Park, Jeong Hee; Vietnam War
China
Deng Xiao Ping’s Reform
Jiang Ze Min’s “Southern Journey(Nan Xun)”
Iraq War?

51. 6. Endogenous Growth Theory
-Excellent Summary
All seem to converge on the importance of Human capital-> education -> knowledge
-Implications:
“Institutions Matter” : only institution guarantees repetitive human behaviours.
-Criticism:
Not so specific about the fundamental institutions that make differences across countries
Analytical focus is still mainly on human capital(individual) rather than on institution(collective and social).
How can we attempt to explain a deeper factor –institutional difference across countries?

52. *Value System as a ‘Foundation’ Institution for Economic Growth:
Max Weber arguned that
“Protestant Work Ethic” sanctioned hard work, frugality and wise investment.
Rodney Stark is one of the most highly regarded sociology of religion scholars alive today. He recently published The Victory of Reason: How Christianity Led to Freedom, Capitalism, and Western Success.
Professor Tu Wei-Ming at Harvard University said that Neo-Confucianism of the Far East is similar to protestant ethic.
- refer to the essence of his idea