[Last revised on Sun., Nov. 14, at 6:45 pm.]
LECTURE 25
Mon., Nov. 1, 1999
Today: A last look at the multiplier model
I. Deriving the multiplier; finding Q_{equil.}
the quick way
II. Government and taxes in the multiplier model
III. Net exports in the multiplier model
IV. Disequilibrium: recessionary, inflationary gaps
I. DERIVING THE MULTIPLIER; FINDING Q_{equil.} THE QUICK WAY
Where we left off: Three formulas for the multiplier:
(1) multiplier = (change in equilibrium GDP) / (change in autonomous spending).
(2) multiplier = 1/(1MPC)
(3) multiplier = 1/MPS
The multiplier is probably most easily calculated as 1/(1MPC). As long as you recall that in a consumption function, C = a + bQ, b is the MPC, then the computation is straightforward:
 Ex.: C = 100 + 0.75Q

MPC = 0.75
multiplier = 1/(1MPC) = 1/(10.75) = 1/0.25 = 4
Q: Why is the multiplier = 1/(1MPC)? How does this multiplier work?
A: Sticking with that same numerical example, and my chainofconsumptionspending
example from Fri., Oct. 22 (the leather jacket, the hat, the dog, the haircut,
...), let's keep track of the total, cumulative increase in spending that
results from an injection of $100 into the spending stream. We have assumed
MPC = 0.75 and that it's the same for everyone.
I spend $100 on a leather jacket. The leather jacket vendor spends
$75 (.75*$100) on a hat, and so on...
Increase in equilibrium GDP =
Increase in total spending =
$100
+ (.75)($100)
+ (.75)(.75)($100)
+ (.75)(.75)($100)
+ ...
= $100 * (1 + .75 + .75^{2} + .75^{3 }+ ...)


(GEOMETRIC SERIES converges to a finite number,
according to a simple formula)
= $100 * [1/(1.75)]


4
= $400
(Note that in this example .75 is the MPC; also, since MPC+MPS = 1, then 1.75 = 1MPC = MPS.)
In this example, an increase in autonomous spending of $100 gives rise
to a $400 increase in equilibrium income. Thus the multiplier is
4 and we got it through the formula
multiplier = 1/(1MPC).
More generally and more realistically, investment and import spending
would also depend on the level of income, as might the government's spending,
which historically has risen as GDP has risen. In that case we would also
speak of a marginal propensity to invest, a marginal propensity
to import, and the government's marginal propensity to spend.
And the multiplier would be equal to
1 / (1  MPC  Marginal Propensity to Invest
 Government's Marginal Propensity to Spend
+ Marginal Propensity to Import)
(No, this extended multiplier will not be on the exam. But you should know the simple multiplier, 1/(1MPC), inside and out.)
The quickest way to find the multiplier and equilibrium GDP:
(1) Compute the multiplier as 1/(1MPC)
(2) Add up the total autonomous spending (= autonomous C + I + G
+ X_{net})
(3) Q_{equil.} = (total autonomous spending) * (multiplier)
[We went through several examples in class. I will include just one here.]
Ex.: Suppose you are given the following consumption and investment
functions, and that government spending, taxes, and net exports are all
zero:
C = 100 + 0.9Q
I_{p} = 100
Step (1): multiplier = 1/(1MPC) = 1/(10.9) = 1/0.1 = 10
Step (2): total autonomous spending = C_{autonomous}
+ I_{p} + G + X_{net}
= 100 + 100 + 0 + 0
= 200
Step (3): Q_{equil.} = 10 * 200 = 2000
II. GOVERNMENT AND TAXES IN THE MULTIPLIER MODEL
... complicate things only a little bit. A positive level of government spending (e.g., G = $100) gets added onto aggregate demand (AD), which one could then use to find equilibrium Q by setting AD=Q and solving for Q. Or if one is using the quickest way, shown above, to find equilibrium output, then all that changes is that we're adding a positive number, and not just zero, for G when we total up autonomous spending. When we add in government spending (i.e., go from G = $0 to some positive value for G), equilibrium GDP goes up, because aggregate demand and autonomous spending have gone up.
Taxes (T) complicate things a bit further  in particular, the consumption
function will now be different because it will no longer be true that disposable
income (DI, or aftertax income) equals GDP (Q). Instead,
DI = Q  T
and the consumption function (which is really a function of DI, because
you can't consume or save the part of your salary that gets taxed, since
you never see that money) becomes
C = a + b(DI)
= a + b(QT),
which will necessitate a couple more algebraic steps when we solve
for the multiplier and the equilibrium level of Q.
In this simplified model, we typically assume that taxes are levied
in one of two ways:
(1) a fixed, lumpsum tax (e.g., T = $100), which does not depend on
income. Everyone pays the same dollar amount and it adds up to T.
A lumpsum tax is not exactly fair (should millionaires and paupers really
pay the same dollar amount?), but it is very easy to deal with.
(2) a flatrate income tax (e.g., T = 0.2Q), in which every dollar
of income is taxed at the same rate.
In both cases, going from no taxes (T = $0) to some positive level of
taxes will lower equilibrium GDP, because it will lower consumption.
With less of their income available to spend or save, people will
consume less, thus lowering aggregate demand and lowering GDP.
III. NET EXPORTS IN THE MULTIPLIER MODEL
... complicate things hardly at all, because so far we're not assuming
a marginal propensity to import (or to export. Realistically, if
there is a marginal propensity to consume, there should be a marginal propensity
to import, because some of our consumption spending is on imports.
But we're keeping it simple for now. Exports do not really depend
on the level of U.S. GDP, but on the GDP's of other countries that would
buy our exports, so there's no marginal propensity to export). Instead,
we just assume that net exports are fixed and do not depend on the level
of income (Q), so net exports are just another form of autonomous spending.
Once again,
total autonomous spending = C_{autonomous} + I_{p}
+ G + X_{net}
IV. DISEQUILIBRIUM: RECESSIONARY, INFLATIONARY GAPS
Q: What happens when AD is not equal to Q?
A: The economy is in disequilibrium  it will either be in
a recession or it will be in an inflationary boom.
If AD < Q: The economy is in a recession or "recessionary gap" 
goods will be piling up on shelves (unintended inventory accumulation)
> What will happen? Firms will cut back on their production, try
to sell off those inventories. Eventually, equilibrium will be reached
at a lower level. Production will adjust to that lowerthanexpected
level of aggregate demand.
If AD > Q: The economy has an "inflationary gap"  since demand outstrips production, firms will sell off much of their inventories of goods that they had been planning to sell later. With a large excess demand for goods, prices of those goods will be bid up, generating inflation. Firms will expand their production to meet the higherthanexpected demand, and eventually equilibrium will be reached at a higher level.
***
Wed., Nov. 3, 1999  SECOND MIDTERM EXAM
***
PRINCIPLES OF MACROECONOMICS
WEEK 10, LECTURE 26
Fri., Nov. 5, 1999
Today: The Aggregate DemandAggregate Supply (ADAS) Model (begin)
I. Reintroducing the price level (P)
II. Aggregate demand (begin)
I. REINTRODUCING THE PRICE LEVEL (P)
The multiplier model is a fixedprice model  it never mentions prices, and implicitly assumes the price level (P) is fixed at all times.
The most widely used macro model, at the introductorycourse level,
is the aggregate demandaggregate supply (ADAS) model, in which aggregate
demand (AD) and aggregate supply (AS) curves are plotted in (Q,P) space.
That is, Q (real GDP) is on the horizontal (x) axis and P (the price
level) is on the vertical (y) axis.
 [Refer to the lefthand graph at the top of McConnell's page
233 to see a typical ADAS diagram.]
 The AD curve slopes downward, just like a micro demand curve; and
the AS curve slopes upward, just like a micro supply curve. The similarity
to micro supplyanddemand models ends there, however, because the factors
driving the shapes and shifts of these curves are different. First, note
that P represents the aggregate price level  not, as in micro
supplyanddemand diagrams, the price of a specific commodity (say, bananas)
with all other prices held constant. The AD curve (or "schedule") tell
us how the aggregate quantity demanded of all goods and services
(by households, firms, government, and foreigners) is affected by the price
level. The AS curve (or "schedule") tell us how the aggregate quantity
supplied of all goods and services (by firms) is affected by the price
level.
 The ADAS model, unlike the multiplier model, is a variableprice
model, because it realistically assumes that the price level can and
does change from time to time.
II. AGGREGATE DEMAND (AD) AND THE PRICE LEVEL
Aggregate demand (AD) has an inverse relationship with the price
level (P)
 A lower price level is good for AD (i.e., increases the sum of C,
I_{planned} , G, and X_{net})
 A higher price level is bad for AD (i.e., decreases the sum of C,
I_{planned} , G, and X_{net})
 The AD curve slopes downward.
 [See Figure 111 on McConnell's page 222 to see a typical AD
curve.]
There are three reasons why the AD curve slopes downward (or, equivalently, why a lower price level raises AD):
(1) Realwealth effect
 A lower price level raises the real value of the money in people's
pockets and bank accounts, and raises real wealth in general. (This is
the flip side of how inflation  a higher price level  lowers
people's real wealth.) Wealthier people consume more, so the increase
in aggregate real wealth raises household consumption.
* (2) Interestrate effect
 (This one has the asterisk {*} next to it because it's the most
important of the three reasons.)
 A lower price level will reduce interest rates, which will stimulate
durablegoods consumption and business investment (both of which are
types of interestsensitive spending), through the following channel:
 P falls > in the money market, less money is needed for a given
level of transactions > money demand falls > the price of money (which
is the interest rate, i) falls.
 (Alternatively and equivalently, one could say the drop in P
raises the real money supply, causing the realmoneysupply curve
to shift out while the realmoneydemand curve stays put, giving rise a
new moneymarket equilibrium at a lower interest rate. {If this last sequence
is confusing to you, don't worry  I didn't do it in class and won't test
you on it.)
(3) Foreign purchases effect (realexchangerate effect)
 A lower domestic price level, relative to the price levels
of other countries, means the home country's products become cheaper
relative to foreign products (and hence the real foreign exchange rate
rises). If the American price level falls, relative to the world price
level, then foreigners will buy more American exports and Americans will
buy fewer foreign imports, and American net exports increase.
Q: Hey, wait a minute: What about the fact that a lower price level
is bad for debtors by raising the real burden of debt? Think back to
our unit on inflation; we call this phenomenon the debtdeflation
effect, and it has severe, adverse effects on AD, because an increased
debt burden forces indebted consumers and firms to retrench (the households'
consumption falls, the firms' investment falls) and, in many cases, declare
bankruptcy or default on their debts, in which case their creditors take
a hit, too.
A: Based on the empirical evidence, it seems that the combined
positive effects  (1), (2), and (3)  of a lower price level on AD outweigh
the negative debtdeflation effect, so the net effect of lower prices
on AD is still positive. But the debtdeflation effects on debtors and
many creditors are sufficiently severe that U.S. economic policymakers
have made sure to keep the U.S. out of deflation ever since the 1940s.
A summing up
A lower price level raises aggregate demand (AD = C + I_{planned}
+ G + X_{net} ) as follows:
AD =  C +  I_{planned} +  G +  X_{net} 
increases through (1) real wealth effect and (2) interestrate effect on durablegoods consumption  increases through (2) interestrate effect  increases through (3) foreignpurchases effect 