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Production, Investment, and the Current AccountPowerPoint Presentation

Production, Investment, and the Current Account

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Presentation Transcript

Announcements

- Problem Set 3 available now in my web page
- Due: Next week (April 11th)

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

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 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

- 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.

- 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

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

Capital K

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.

- 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) + 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

- Note that K(t) will fall if r(t) increases. profits equal to:

- K(t) will increase if MPK(t) increases profits equal to:

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 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*

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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