CLASS #11: INVESTMENT AND CAPITAL FLOWS IN A SMALL OPEN ECONOMY

• What determines savings and investment in an open economy?
• What determines the amount of capital flows into a country?
• What determines the Current Account in an open economy with investment?
• What are the advantages of ``Capital Account liberalization" (free capital mobility)?
• What are the consequences of capital controls?
• What are the effects of changes of the ``world" interest rates on savings, investment, and the Current Account?

Introduce ``foreigners" in the economy. For the time being there is only one good traded in the world: the introduction of the ``foreigners" in this model does not change relative prices of existing goods. The ``foreigners" in the model can be identified with a large bank, say Merril Lynch, which is willing to inelastically borrow and/or lend resources at a given interest rate r^w. Let us call D the amount of debt contracted in period 1 with Merril Lynch. For the time being there is no government in the economy (no taxes, or government spending). Also, for simplicity we assume that the household owns the firm directly (social planner solution). The household's problem is:

$$max_{\{C1,C2\}} U(C1,C2)$$

st

K2+C1=Y1+D

$$C2=F(K2)+(1-\delta)K2-(1+r^w)D$$

The last constraint can be rewritten as:

$$C2+(1+r^w)D=F(K2)+(1-\delta)K2$$

The resources of the household in the second period ( $F(K2)+(1-\delta)K2$) are used either to finance consumption (C2) or to pay Merril Lynch back ((1+r^w)D). The problem for the household is:

$$max_{\{K2,D\}} U(Y1+D-K2,F(K2)+(1-\delta)K2-(1+r^w)D)$$

FOC wrt K2:

$$\frac{U_1(C1,C2) }{U_2(C1,C2)}=(F_1(K2) + (1-\delta))$$

FOC wrt D:

$$\frac{U_1(C1,C2) }{U_2(C1,C2)}=(1+r^w)$$

Therefore we must have:

$$\frac{U_1(C1,C2) }{U_2(C1,C2)}=(F_1(K2) + (1-\delta))= (1+r^w)$$

MRS	=	MRT	=	world
				interest rate

Advantages from Capital Mobility for a country in which capital is highly productive (Autarky interest rate is higher than the world interest rate):

• invest more than in Autarky
• (possibly) consume more in the first period (depending on its preference)
• welfare is unambiguously higher

The Current Account for a country where Autarky interest rate is higher than the world interest rate is in deficit. Advantages from Capital Mobility for a country in which capital is less productive than in the rest of the world (Autarky interest rate is lower than the world interest rate):

• invest in countries where the returns to capital is higher than home, thereby getting ``more bang for the buck".
• welfare is unambiguously higher

The Current Account for a country where Autarky interest rate is higher than the world interest rate is in surplus. What determines the amount of capital invested in a country when capital can flow freely across borders?
Marginal Productivity of Capital Let us assume Cobb-Douglas production function:

$$F_1(K2)+(1-\delta)= \alpha*A*K2^{\alpha-1} +(1-\delta)$$

• Total Factor Productivity (A)
• Share of Capital in the production function ($\alpha$)
• do preferences matter?

Why is capital flying to developing countries?

• lower levels of capital, therefore higher marginal productivity of capital

In a world with free capital mobility, two countries with identical production function (A and $\alpha$) should have the same level of capital per person:

$\begin{array}{l} 1+r^w=\\ \\ =\alpha*A*K_{Mexico} ^{\alpha-1} +(1-\delta)=\\ \\ =\alpha*A*K_{US} ^{\alpha-1} +(1-\delta)\end{array}$