1. MACROECONOMICS AND THE GLOBAL BUSINESS ENVIRONMENT
4/7/2019
MACROECONOMICS AND THE GLOBAL BUSINESS ENVIRONMENT
Capital Accumulation and Economic Growth
PowerPoint by Beth Ingram
University of Iowa
Copyright © 2005 John Wiley & Sons, Inc. All rights reserved.

2. Key Concepts Definition of Capital and Investment
Decreasing Marginal Return
Convergence in Rates of Growth
The Steady State
The Golden Rule

3. Growth Transitions Labor Growth Capital Growth TFP Growth 4/7/2019
I use this slide to talk about the transition from growth based on labor growth to capital growth to TFP growth
TFP Growth

4. Decreasing marginal product
4/7/2019
Decreasing marginal product
An increase in the quantity of labor increases Real GDP
But growth rate decreases as labor increases
(billions of 1996 $)
Real GDP 15 12 6
500
1000
1500
Labor Hours

5. Decreasing marginal product
4/7/2019
Decreasing marginal product
An increase in the quantity of capital increases Real GDP
But growth rate decreases as capital increases
(billions of 1996 $)
Real GDP 15 12 6
500
1000
1500
Quantity of Capital

6. Capital (K)
Total value of the machines and buildings used to produce output
Capital depreciates (wears out)
Assume constant rate of depreciation, d
Assume depreciation is fraction of capital stock, d*K

7. Diminishing Marginal Return
Growth will be fast when level of capital is low
Growth slows down as capital accumulates
Eventually, firms won’t add new capital – firms only replace depreciated capital
Economy reaches a Steady State

8. Optimal Investment Value of new capital is
(Marginal Product) x (Price of Output)
Suppose 6 x $2 = $12
Cost of new capital
Denoted by “r”
Suppose r = $12
Purchase new capital if
MP x Price of output= r

9. Decreasing Marginal Product of Capital
Marginal Product = r/p
Marginal product of capital
Cost of Capital, r/p
Marginal Product
Capital Stock

10. Firms will cease to add capital when marginal
4/7/2019
Firms will cease to add capital when marginal
return is less than the marginal cost…
Stop here if r > 3.75%
$15
(billions of 1996 $)
Real GDP
$12 $6
$80
$160
$240
Capital
(billions of 1996 $)

11. Comments on interest rates (R)
What determines the interest rate?
Interaction of savings and investment
Effect of changes in the interest rate
High interest rate economy is a low capital economy
Low interest rate economy is a high capital economy

12. Determination of R
Savings
Interest Rate R0
Investment I0
Output

13. Effect of TFP growth Capital (billions of 1996 $) (billions of 1996 $)
4/7/2019
Effect of TFP growth
$20
(billions of 1996 $)
Real GDP
$12 $6
$80
$160
$240
Capital
(billions of 1996 $)

14. Determination of R
Savings R1
Interest Rate R0
Investment I0 I1
Output

15. Steady State Output Real GDP C + G + X - M Investment
Investment (20% of GDP)
Capital Stock

16. Steady State Output Investment = Depreciation Depreciation
= d x Capital Stock
Real GDP
Investment
Capital Stock

17. Investment exceeds depreciation; capital stock must decline
Output
Depreciation
Real GDP
Investment
KLow
Kss
KHigh
Capital Stock

18. Depreciation exceeds investment; capital stock must increase
Output
Depreciation
Real GDP
Investment
KLow
Kss
KHigh
Capital Stock

19. Increase in Investment Rate
Output
Depreciation
Real GDP
Investment (30% of GDP)
Investment (20% of GDP)
K20%
K30%
Capital Stock

20. Investment Rate
The higher the investment rate of a country, the greater the steady state capital stock and its output level

21. The Golden Rule Level of Capital
Depreciation = d x Capital Stock
“d” is a technological parameter
NIPA
3% for structures
8% for equipment
New Capital = Investment – d x K
Steady State
Because of diminishing returns, will reach point where increases in capital stock don’t pay off
Investment = d*K

22. The Golden Rule Real GDP C I Capital Stock
4/7/2019
The Golden Rule
Make consumption as high as possible
(ignore G and X-M for the moment)
Steady State Investment = d x K
Output
Real GDP C
Recall that Output = C + I (forget G and X-Im for now). At crossing point, C = 0!!.
Countries pick a level of capital per worker, but that capital level must be maintained. There is a tradeoff…
If capital it too low, lack of capital keeps output low and, hence, consumption and investment low. If capital is too high, must dedicate high fraction of output to maintaining the capital stock and consumption will be too low. Golden rule finds level of capital per worker that maximizes consumption. I Ks
Capital Stock

23. The Golden Rule Real GDP C I Capital Stock
4/7/2019
The Golden Rule
Make consumption as high as possible
(ignore G and X-M for the moment)
Steady State Investment = d x K
Output
Maximize this
Real GDP C
Recall that Output = C + I (forget G and X-Im for now). At crossing point, C = 0!!.
Countries pick a level of capital per worker, but that capital level must be maintained. There is a tradeoff…
If capital it too low, lack of capital keeps output low and, hence, consumption and investment low. If capital is too high, must dedicate high fraction of output to maintaining the capital stock and consumption will be too low. Golden rule finds level of capital per worker that maximizes consumption. I Ks
Capital Stock

24. The Golden Rule Real GDP C I K0 K1 Capital Stock
4/7/2019
The Golden Rule
Note: C is getting smaller as K increases to K1
Steady State Investment = d x K
Output
Real GDP C
Recall that Output = C + I (forget G and X-Im for now). At crossing point, C = 0!!.
Countries pick a level of capital per worker, but that capital level must be maintained. There is a tradeoff…
If capital it too low, lack of capital keeps output low and, hence, consumption and investment low. If capital is too high, must dedicate high fraction of output to maintaining the capital stock and consumption will be too low. Golden rule finds level of capital per worker that maximizes consumption. I K0 K1
Capital Stock

25. The Golden Rule Real GDP C I K2 K0 Capital Stock
4/7/2019
The Golden Rule
Note: C is getting smaller as K decreases to K2
Steady State Investment = d x K
Output
Real GDP C
Recall that Output = C + I (forget G and X-Im for now). At crossing point, C = 0!!.
Countries pick a level of capital per worker, but that capital level must be maintained. There is a tradeoff…
If capital it too low, lack of capital keeps output low and, hence, consumption and investment low. If capital is too high, must dedicate high fraction of output to maintaining the capital stock and consumption will be too low. Golden rule finds level of capital per worker that maximizes consumption. I K2 K0
Capital Stock

26. Golden Rule Capital stock is too high Capital stock is too low
Output is used to maintain an overly-large capital stock
Consumption is low
Capital stock is too low
Output is used to support consumption
Capital is too low to produce sufficient output

27. Golden Rule Marginal Product of Capital = Rate of Depreciation
4/7/2019
Golden Rule
Marginal Product of Capital = Rate of Depreciation
This is in Cobb-Douglas case.
Cobb – Douglas parameter (a) = Savings Rate

28. The Golden Rule Real GDP C I Ks Capital Stock
4/7/2019
The Golden Rule
d = MPK
Steady State Investment = d x K
Output
Real GDP C
Recall that Output = C + I (forget G and X-Im for now). At crossing point, C = 0!!.
Countries pick a level of capital per worker, but that capital level must be maintained. There is a tradeoff…
If capital it too low, lack of capital keeps output low and, hence, consumption and investment low. If capital is too high, must dedicate high fraction of output to maintaining the capital stock and consumption will be too low. Golden rule finds level of capital per worker that maximizes consumption. I Ks
Capital Stock

29. The Golden Rule What level of capital might a free market choose?
Are there forces that keep a country away from the Golden Rule?

30. The Asian Miracle Why did Asian economies grow so fast after 1950?
Can this experience be repeated elsewhere?

31. Growth Accounting Asian Tigers, 1966 - 1990
4/7/2019
Growth Accounting Asian Tigers,
Note that this slide is repeated from Chapter 3.

32. Growth accounting in emerging markets, 1960–1994.

33. Savings in Singapore % of Wages Employees Employers
4/7/2019
Savings in Singapore
Employees
Employers
Central Provident Fund Contributions
% of Wages

34. Does source of growth matter?
Growth means high standard of living
Growth through capital accumulation
Eventually dissipates
Comes at a cost (low consumption in previous generations)
Transition to TFP-induced growth?

35. Summary Marginal Product of Capital Steady State Investment
Implications of decreasing MPK
Role in determining Steady State
Steady State Investment
Investment = Depreciation
Growth can no longer be achieved through investment
Dependence on investment rate and savings rate
Golden Rule
The Asian Tigers
Copyright © 2005 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in Section 117 of the 1976 United States Copyright Act without the express written permission of the copyright owner is unlawful. Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information contained therein.