[Joseph_E._Stiglitz,_Carl_E._Walsh]_Economics(Bookos.org) (1)

Substituting the second equation into the first equation yields
which can be solved for Y:
Y = A + bY,
Y = A/(1 − b).
This equation tells us that if A changes by $1, Y will change by 1/(1 − b). For example,
if b = .9, a $1 increase in A increases Y by $10. The factor 1/(1 − b) is called the multiplier.
It tells us how much total aggregate expenditures and output increase when
the aggregate expenditures schedule shifts by $1.
Wrap-Up
INCOME–EXPENDITURE ANALYSIS
1. Equilibrium output is the point where the aggregate expenditures schedule
equals output (income).
2. Increases in the aggregate expenditures schedule result in increases in equilibrium
output. Decreases in the aggregate expenditures schedule result in
decreases in equilibrium output.
3. The changes in equilibrium output are larger than the initial shift in the
aggregate expenditures schedule. How much larger they are depends on the
slope of the aggregate expenditures schedule. The steeper the slope, the
greater the change.
As you will learn in the next few chapters, changes in aggregate expenditures
will also influence interest rates, net exports, and inflation in ways that will act to
reduce the ultimate effect of shifts in the aggregate expenditures schedule on equilibrium
output. When we have incorporated these additional adjustments into our
analysis, the change in equilibrium output per dollar change in the AE schedule is
closer to 1.5 to 2 in the short run; it is close to 0 in the longer run as wages and prices
have time to completely adjust.
A Look Forward
We have just learned two of the central principles of macroeconomics: (1) shifts in
the aggregate expenditures schedule determine changes in the equilibrium output
of the economy, and (2) the magnitude of these changes is greater than the magnitude
of the shift up or down in the aggregate expenditures schedule. We also have
learned that the magnitude of the change in output increases with the slope of the
aggregate expenditures schedule. The remainder of this chapter explores two crit-
666 ∂ CHAPTER 30 AGGREGATE EXPENDITURES AND INCOME