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Production, Investment, and the Current Account. Roberto Chang Rutgers University April 2013. Announcements. Problem Set 3 available now in my web page Due: Next week ( April 11 th ). Motivation. Recall that the current account is equal to savings minus investment.

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Production investment and the current account

Production, Investment, and the Current Account

Roberto Chang

Rutgers University

April 2013


Announcements
Announcements

  • Problem Set 3 available now in my web page

  • Due: Next week (April 11th)


Motivation
Motivation

  • Recall that the current account is equal to savings minus investment.

  • Empirically, investment is much more volatile than savings.

  • Reference: chapter 6, section 3 of FT


Recall the savings function
Recall: The Savings Function

  • Recall that we had derived a national savings function from a basic model of consumer choice


The Savings Function

Interest

Rate

S

r*

S

S*

Savings


Interest

Rate

An increase in savings.

This may be due to

higher Y(1).

S

S’

S

S’

Savings


The setup
The Setup

  • Again, we assume two dates t = 1,2

  • Small open economy populated by households and firms.

  • One final good in each period.

  • The final good can be consumed or used to increase the stock of capital.

  • Households own all capital.


Firms and production
Firms and Production

  • Firms produce output with capital that they borrow from households.

  • The amount of output produced at t is given by a production function:

    Q(t) = F(K(t))


Production function
Production Function

  • The production function Q(t) = F(K(t)) is increasing and strictly concave, with F(0) = 0. We also assume that F is differentiable.

  • Key example: F(K) = A Kα, with 0 < α < 1.


Output F(K)

F(K)

Capital K



MPK = F’(K) derivative of the production function F.

Capital K


Profit maximization
Profit Maximization derivative of the production function F.

  • In each period t = 1, 2, the firm must rent (borrow) capital from households to produce.

  • Let r(t) denote the rental cost in period t.

  • In addition, we assume a fraction δ of capital is lost in the production process.

  • Hence the total cost of capital (per unit) is r(t) + δ.



F k t r t
F’(K(t)) = r(t) + profits equal to: δ

  • This says that the firm will employ more capital until the marginal product of capital equals the marginal cost.

  • Note that, because marginal cost is decreasing in capital, K(t) will fall with the rental cost r(t).


MPK = F’(K) profits equal to:

Capital K


MPK = F’(K) profits equal to:

r(t) + δ

Capital K(t)


MPK = F’(K) profits equal to:

r(t) + δ

K(t)

Capital



MPK = F’(K) profits equal to:

r(t) + δ

K(t)

Capital


MPK = F’(K) profits equal to:

A Fall in r:

r’(t) < r(t)

r(t) + δ

r’(t) + δ

K(t)

K’(t)

Capital



MPK = F’(K) profits equal to:

r(t) + δ

K(t)

Capital


MPK = F’(K) profits equal to:

An increase in MPK

r(t) + δ

K(t)

K’(t)

Capital


Investment
Investment profits equal to:

  • The amount of capital in the economy at the beginning of period 2 is given by:

    K(2) = (1-δ)K(1) + I(1)

  • Hence investment in period one is

    I(1) = K(2) - (1-δ)K(1)


Now recall profits equal to:

  • K(1) is given as an initial condition

  • K(2) is a decreasing function of r(2)

  • Hence the equation

    I(1) = K(2) - (1-δ)K(1)

    implies that I(1) is a decreasing function of r(2)


The investment function
The Investment Function profits equal to:

  • But in an open economy, r(t) must be equal to the world interest rate r*

     Investment in period 1 is a decreasing function of the world interest rate r*


The profits equal to: Investment Function

Interest

Rate

I

r*

I

I*

Investment


An increase in investment, profits equal to:

May be due to an increase in the future MPK

Interest

Rate

I’

I

r*

I’

I

I*

I**

Investment


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