Ranjit Dighe
WEEK 12 (LECTURES 31 & 32)
April 17 & 21, 2000

[These lectures go with Case & Fair's Chapter 10, as well as some of Chapter 9. There was no class on Wed., April 19, because of Quest Day.]

Mon., April 17, 2000


* Today:
I. Disequilibrium: inflationary, recessionary gaps
II. Fiscal policy: an introduction

* [I spoke for about 35-40 minutes about Friday's stock-market crash (which I said does not necessarily mean that a recession is just around the corner) and the weekend's protests outside the joint meeting of the World Bank and the International Monetary Fund in Washington, DC. You kind of had to be there...]


Q: What happens when AD is not equal to Y?
A: Economy is in disequilibrium -- it will either be in a recession or it will be in an inflationary boom.

If AD < Y:
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 lower-than-expected level of aggregate demand.

If AD > Y:
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 higher-than-expected demand, and eventually equilibrium will be reached at a higher level.


Defn. FISCAL POLICY-- the spending and taxing policies used by the government to influence the economy.
-- Fiscal policy can be complex (since there are many different taxes and many different spending programs, and they have different multipliers associated with them), but for now we will focus on changes in the absolute levels of government purchases (G) and tax revenues (T).

G = purchases of goods & services by the government (federal, state, & local).
-- Note: does not include transfer payments (Social Security, welfare), interest payments on the national debt (to government bond holders), or subsidies.

T = total tax receipts (to be precise, T stands for net taxes, which are tax revenues minus transfer payments and subsidies).

--> G - T is the government's budget deficit. If G - T > 0, deficit; if G - T < 0, surplus.
      T - G is the government's budget surplus.

-- LUMP-SUM TAX: A tax that is collected as a "lump-sum" dollar amount, regardless of income.
---- Ex.: Everyone pays $10, so if there are 200 people, T = $2000
---- This obviously isn't the way most taxes work, but it makes the math in these models way, way easier.

-- INCOME TAX: Taxes are proportional to income. If everyone is taxed at the same rate t (we call this a flat tax), then T = tY.
---- Ex.: If the tax rate is 15%, then T = .15Y (and t = .15).

Fiscal policy can be either EXPANSIONARY (intended to increase real GDP) or CONTRACTIONARY (intended to reduce inflation or reduce the budget deficit).


Fri., April 21, 2000


* Today:
I. Fiscal policy (continued)
II. Fiscal policy and the multiplier


I. FISCAL POLICY (continued)

(1) EXPANSIONARY FISCAL POLICY occurs when the government deliberately increases its deficit in order to stimulate the economy.
-- In expansionary fiscal policy, the government increases its spending (G) or cuts taxes (T) or both.
---- Expansionary fiscal policy stimulates the economy because it increases aggregate demand (AD).
------ When the government increases G, it adds directly to AD, since G is part of AD (= C+Ip+G+EX-IM).
------ When the government cuts T, it increases people's disposable income (total income minus taxes), and people will spend much of that extra income, so consumption (C) increases.
------ In both cases, AD will also increase indirectly through the multiplier effect, as the initial increase in G or C touches off a whole chain of consumption.
------ In both cases, real GDP will increase and so will the price level. Expansionary fiscal policy (or a fiscal expansion) means the economy is moving northwest along the Phillips Curve, to a point of lower unemployment and higher inflation. (This is an example of demand-pull inflation.) This will cause equilibrium real GDP (Y) to increase and the equilibrium price level (P) to increase.

(2) CONTRACTIONARY FISCAL POLICY occurs when the government deliberately reduces its deficit in order to slow down the economy (usually with the goal of reducing inflation or of reducing the deficit for its own sake).
-- In contractionary fiscal policy, the government cuts its spending (G) or raises taxes (T) or both.
---- Contractionary fiscal policy contracts the economy because it decreases AD.
---- The net effect of contractionary fiscal policy, all other things equal, is to induce a recession or at least slow down the rate of growth of the economy. A fiscal contraction would cause the economy to move southeast along the Phillips Curve, to a point of higher unemployment and lower inflation. As a result, equilibrium Y decreases and equilibrium P decreases.

A few examples of real-life fiscal policy decisions:

--> Common thread: The government often uses its spending and taxing decisions (fiscal policy) in order to influence the state of the economy.

Of the government's two main tools for managing the economy, fiscal policy and monetary policy, Keynes and early Keynesians (economists who generally agreed with Keynes's ideas) emphasized fiscal policy.


When the government increases G, the people whom it pays for those extra goods and services now have higher incomes, and they will spend some of that extra income (consumption increases), touching off a whole chain of consumption (C). The ultimate, cumulative increase in AD and Y will be a multiple of the original increase in G, because C will increase, too.

When the government cuts taxes, people spend their extra after-tax income, and that initial increase in consumption leads to more consumption, by the people who sell the goods or services in each round of consumption. Again, because of the multiplier effect, the ultimate increase in AD and Y (which is entirely an increase in C in this case) will be a multiple of the original tax cut.

The government spending multiplier is the same as the regular multiplier:

{spending multiplier} = 1 / (1-MPC),

because G is a component of autonomous spending.

-- Ex.:  If MPC = 0.9, then the government spending multiplier is 10 (= 1/(1-0.9) = 1/0.1).

The multiplier associated with a given change in taxes, the tax multiplier, is negative, because higher taxes reduce people's disposable income, thereby reducing their consumption. The tax multiplier is smaller (in absolute value) than the spending multiplier because not all of a tax increase represents income that otherwise would have been consumed -- the marginal propensity to consume is less than 1, so some fraction of every dollar gets saved, which does not add to aggregate demand or GDP. The initial change in consumption associated with a $1 tax increase is

- MPC * ($1) = -MPC.
That amount is the change in autonomous spending that results from a $1 tax increase, and we multiply it by the regular multiplier to get:
{tax multiplier} = - MPC / (1-MPC)

-- If MPC = 0.9, then the tax multiplier is -9 (= -0.9/(1-0.9) = -0.9/0.1 = -9/1).

Q: What would happen if the government increased spending and taxes by equal amounts, applying these multipliers?

-- (The result may surprise you. For most of us, our automatic response is to think that would somehow be a bad thing for the level of GDP, since higher taxes plainly lower our disposable incomes and leave less for our consumption. Or we might think that it would have zero effect on GDP, because the higher spending and the higher taxes would seem to offset each other. But, in the context of the multiplier model, both of those guesses would be wrong. Instead....)
A: An equal increase in G and T would actually raise GDP, in the context of the multiplier model.

-- Why: Recall that the government-spending multiplier is

{spending multiplier} = 1 / (1-MPC),
     and the tax multiplier is
{tax multiplier} = - MPC / (1-MPC).
-- Add the two together and you get the multiplier for an equal increase in government spending and taxes. Equivalently, it is the increase in equilibrium GDP that results from a $1 increase in G and a $1 increase in T. We call it the BALANCED-BUDGET MULTIPLIER (BBM; or perhaps more accurately the tax-and-spend multiplier), and it is equal to the sum of those other two:

{BBM} = 1/(1-MPC) - MPC/(1-MPC)
              = (1-MPC) / (1-MPC) (combining the two terms, which have a common denominator)
              = 1

So the balanced-budget multiplier is 1, meaning that a given increase in G (say, $1 million) coupled with an equal increase in T ($1 million) would raise equilibrium GDP by that same amount ($1 million).

-- We call it the balanced-budget multiplier because an equal increase in G and T would not change, let alone increase, the government's budget deficit. If the budget were balanced to begin with (a deficit of $0), it would still be balanced after an equal increase in G and T.
-- (The term balanced-budget multiplier does not necessarily mean that the overall budget is in balance, just that we're increasing G and T by equal amounts.)
-- This is a startling result. Having grown up in a conservative era in which politicians of both parties say they're against "big government" and talk about how they want to cut government spending ("Put an end to tax and spend!"), it's easy to forget that government spending, even when it's wasteful, is counted in GDP and provides incomes for the people from whom the government is purchasing goods and services. This, by the way, is why many political conservatives hate Keynes, since Keynes originated the concept of the multiplier, including the balanced-budget multiplier.
-- Why the balanced-budget multiplier is positive: The spending multiplier is larger than the tax multiplier, because some fraction of any dollar of income that is taxed would have been saved instead of consumed, and savings do not contribute to GDP. (That fraction, by the way, is the marginal propensity to save, and is estimated as .05 for the United States today.)

A three-part example

Let us compare the different equilibrium levels of GDP for the same economy (1) with no government spending or taxes, (2) with government spending but no taxes, and (3) with equal amounts of government spending and taxes. Consumption, planned investment, and net exports in this economy are:

C = 500 + 0.95*DI (DI = disposable income = Y - T)
Ip = 500
EX = IM = EX-IM= 0
If G=T=0, then the economy is:
C = 500 + 0.95*DI = 500 + 0.95*(Y-0) = 500 + 0.95Y
Ip = 500
G = 0
EX-IM = 0
Solving with our favorite shortcut ([i] find total autonomous spending, Cautonomous + Ip + G + EX - IM, [ii] find the multiplier, 1/(1-MPC), and then [iii] multiply them together to get equilibrium GDP (Yequil.):
(i) {autonomous spending} = Cautonomous + Ip + G + EX - IM = 500 + 500 + 0 + 0 = 1000
(ii) {multiplier} = 1/(1-MPC) = 1/(1-.95) = 1/.05 = 20
(iii) Yequil. = {autonomous spending} * {multiplier} = 1000 * 20 = 20,000
Now assume that the government spends $100 but collects no taxes. With a multiplier of 20, we can already conclude that equilibrium GDP will be $2000 [=20*$100] higher than before and hence will be $22,000, but let's do it the long way. The economy is now:
C = 500 + 0.95*DI = 500 + 0.95*(Y-0) = 500 + 0.95Y
Ip = 500
G = 100
EX - IM = 0
Solving for Yequil.:
(i) {autonomous spending} = Cautonomous + Ip + G + EX - IM = 500 + 500 + 100 + 0 = 1100
(ii) {multiplier} = 1/(1-MPC) = 1/(1-.95) = 1/.05 = 20
(iii) Yequil. = {autonomous spending} * {multiplier} = 1100 * 20 = 22,000
Note that the increased government spending (G increased from $0 to $100) has caused GDP to increase by 20 times that amount. The government-spending multiplier here is 20.

Now assume the government spends $100 and collects $100 in lump-sum taxes. (Note: its deficit, G-T, is $0.) The economy is now:

C = 500 + 0.95*DI = 500 + 0.95*(Y-100) = 500 + 0.95Y - 95 = 405 + 0.95Y
Ip = 500
G = 100
EX - IM = 0
Solving for Yequil.:
(i) {autonomous spending} = Cautonomous + Ip + G + EX - IM = 405 + 500 + 100 + 0 = 1005
(ii) {multiplier} = 1/(1-MPC) = 1/(1-.95) = 1/.05 = 20
(iii) Yequil. = {autonomous spending} * {multiplier} = 1100 * 20 = 20,100
Comparing the results of (1) and (3), we see that equilibrium GDP is $100 higher ($20,100) when the government taxes and spends $100 than when government spending and taxes were both zero (equilibrium GDP was $20,000).
-- Another notable result is that despite the higher taxes in (3) as compared to (1), private consumption is the same in both cases. To verify, equilibrium consumption is:
---- in case (1): Cequil. = 500 + 0.95*Yequil. = 500 + 0.95*20000 = 500 + 19000 = 19,500
---- in case (2): Cequil. = 405 + 0.95*Yequil. = 405 + 0.95*20100 = 405 + 19095 = 19,500
---- While the tax increase on its own would have hurt consumption and GDP, the equal spending increase, through its larger multiplier effect, raises GDP and leaves consumption unchanged. Society is better off in the sense that consumption has not fallen and now there is $100 in extra government services.

Parting question: In the U.S. today, the MPC is about .95, which would imply that the multiplier is 20 (as in the above example). Yet empirical estimates of the multiplier in the U.S. economy put it at about 1.4. The question is, What makes the real-life multiplier so much smaller than 20? (Or, how do we "beat the multiplier down" from 20 to 1.4?)