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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
slide5

The Savings Function

Interest

Rate

S

r*

S

S*

Savings

slide6

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.
slide10

Output F(K)

F(K)

Capital K

slide11
The marginal product of capital (MPK) is given by the derivative of the production function F.
  • Since F is strictly concave, the MPK is a decreasing function of K (i.e. F’(K) falls with K)
  • In our example, if F(K) = A Kα, the MPK is

MPK = F’(K) = αA Kα-1

profit maximization
Profit Maximization
  • 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.
slide14
In period t, a firm that operates with capital K(t) makes profits equal to:

Π(t) = F(K(t)) – [r(t)+ δ] K(t)

  • Profit maximization requires:

F’(K(t)) = r(t) + δ

f k t r t
F’(K(t)) = r(t) + 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).
slide17

MPK = F’(K)

r(t) + δ

Capital K(t)

slide18

MPK = F’(K)

r(t) + δ

K(t)

Capital

slide20

MPK = F’(K)

r(t) + δ

K(t)

Capital

slide21

MPK = F’(K)

A Fall in r:

r’(t) < r(t)

r(t) + δ

r’(t) + δ

K(t)

K’(t)

Capital

slide23

MPK = F’(K)

r(t) + δ

K(t)

Capital

slide24

MPK = F’(K)

An increase in MPK

r(t) + δ

K(t)

K’(t)

Capital

investment
Investment
  • 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)

slide26
Now recall
  • 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
  • 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*

slide28

The Investment Function

Interest

Rate

I

r*

I

I*

Investment

slide29

An increase in investment,

May be due to an increase in the future MPK

Interest

Rate

I’

I

r*

I’

I

I*

I**

Investment

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