1

Global Allocation of Capital

2

The Capital Market (Wall Street)

Savings and InvestmentHousehold’s Receive Income,

Consume, and Save:Buy Debt and Equity

•Firms Borrow:Issue Debt and Equity

•Governments borrow:Issue Debt

Capital Market (Wall St.):Determines rates of return

Supply of savings =Demand for savings

(investment in new capital)

Savings Investment

3

Diminishing Marginal Productivity of Capital

7.0

3.0

n

kAMPK

k

Fix A, nMPK

• MPK depends on A and k/n • For given n and A, a rise in

k leads to a fall in MPK

4

Demand for Capital

k

MPK-d • Suppose all firms can borrow at the real interest rate rw

• Suppose capital depreciates at the rate d

• Firms invest to the point where

rw = MPK(A,k*/n)-d

• The current capital stock is pre-determined

• This margin determines the desired capital stock kt+1

rw

k*

cost of capital =

A country acquires capital until the return to capital net of depreciation (MPK-d) equals the

cost of capital rw

MPK(A,k/n)-d

5

International Allocation of Capital

k

• Two countries: Alow and Ahigh

• Does Ahigh offer a higher return to capital in the long run?

• No• The country with Ahigh will

acquire more capital up until the point that rates of return are equalized.

• Both higher A and higher k lead to higher GDP

r

klow

Investors allocate capital to seek the highest return. Consequently, in equilibrium, all countries (abstracting

from risk) offer the same return to capital on the margin.

MPK(Alow,k/n)-d

MPK(Ahigh,k/n)-d

khigh

rw=MPK-d

6

Capital by Country, 2004

Source: Caselli and Feyrer, “The Marginal Product of Capital,” Quarterly Journal of

Economics, 2007

7

MPK by Country, 2004

Source: Caselli and Feyrer, “The Marginal Product of Capital,” Quarterly Journal of

Economics, 2007

MPK

8

Demand for Investment• Investment this year is capital available next year

• kt is the current (pre-determined) capital stock

• it is the level of investment, and

• kt+1 is the capital stock at the beginning of t+1

Example:

– t = 1970 – kt = $100 (the amount of capital used to produce GDP during 1970) – Depreciation rate = 5% (d = 0.05)– it = $7 (the amount of investment during 1970)– kt+1 = 100*.95+7 = $102 (the amount of capital for 1971)

kt+1=kt*(1-d)+it

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Demand for Investment

Investment demand is determined by a change in the desired capital stock

i

id

r

MPKt-d

r

it = kt+1 - kt*(1-d)

k

rw

MPKt+1-d

kt kt+1it = kt+1 - kt*(1-d)

change in capital

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The level of capital (or the capital-GDP ratio) is determined

by the level of TFP

The investment rate (the ratio of investment to GDP) is

determined by the rate of change of TFP

TFP, Capital, and Investment

11

Investment and Growth

12

Effects of Risk

• What is the effect of a rise in sovereign risk?

rw+rp = MPKi – d

• rp is the risk premium demanded for investing in country i

• As the risk premium rises, investment slows down in a country

• Thailand, Brazil, Argentina suffered massive outflows of capital

• Income and employment drop

13

Investment and Uncertainty

The rise in the risk premium following a financial crisis contributes to a collapse in

investment

14

Long-Run Labor Market(capital adjusts to a rise in labor supply)

• Suppose the supply of labor rises for exogenous reasons

• A rise in employment raises the return to capital

• In the long run capital adjusts so that the capital/labor ratio is consistent with the r = MPK - d relation

• As capital adjusts, so too does the wage rate

• In the long run, wages do not depend on the supply of labor (the labor demand curve is flat)

• In the long run, wages only depend on TFP

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Long-Run Labor Market Equilibrium

(capital adjusts to a rise in TFP)

• An increase in TFP shifts the MPN curve to MPN*.

• The new equilibrium is at point Z with higher real wage and employment.

• A shift in labor supply has no effect on the wage in the long run.

MPN*

MPN

w

n

X

Z

Is the wage rate in India low because of the abundance of labor?

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Key Message

Good Institutions:Education, Openness, Property Rights Protection

TFP growth

Investment boom, GDP growth

Greater wealth is created