Macroeconomics

1 4-1

Elements of the Model

Before examining the components of the dynamic AD –AS model, we need to

introduce one piece of notation: Throughout this chapter, the subscript t on a

variable represents time. For example, Y is used to represent total output and

national income, as it has been throughout this book. But now it takes the form

Y

t

, which represents national income in time period t. Similarly, Y

t

−1

represents

national income in period t

− 1, and Y

t

+1

represents national income in period

t

+ 1. This new notation will allow us to keep track of variables as they change

over time.

Let’s now look at the five equations that make up the dynamic AD–AS model.

Output: The Demand for Goods and Services

The demand for goods and services is given by the equation

Y

t

= Y−

t

–

a

(r

t

–

r) + 

e

t

,

where Y

t

is the total output of goods and services, Y

−

t

is the economy’s natural

level of output, r

t

is the real interest rate, 

e

t

is a random demand shock, and 

a

and

r are parameters greater than zero. This equation is similar in spirit to the

demand for goods and services equation in Chapter 3 and the IS equation in

Chapter 10. Because this equation is so central to the dynamic AD –AS model,

let’s examine each of the terms with some care.

The key feature of this equation is the negative relationship between the real

interest rate r

t

and the demand for goods and services Y

t

. When the real inter-

est rate increases, borrowing becomes more expensive, and saving yields a

greater reward. As a result, firms engage in fewer investment projects, and con-

sumers save more and spend less. Both of these effects reduce the demand for

goods and services. (In addition, the dollar might appreciate in foreign-

exchange markets, causing net exports to fall, but for our purposes in this chap-

ter these open-economy effects need not play a central role and can largely be

ignored.) The parameter 

a

tells us how sensitive demand is to changes in the

real interest rate. The larger the value of 

a

, the more the demand for goods and

services responds to a given change in the real interest rate.

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The first term on the right-hand side of the equation, Y

−

t

, implies that the

demand for goods and services rises with the economy’s natural level of output.

In most cases, we can simplify matters by taking this variable to be constant; that

is, Y

−

t

will be assumed to be the same for every time period t. We will, however,

examine how this model can incorporate long-run growth, represented by

exogenous increases in Y

−

t

over time. A key piece of that analysis is apparent in

this demand equation: as long-run growth makes the economy richer, the

demand for goods and services grows proportionately.

The last term in the demand equation, 

e