Transcript Income Determination - University of Texas at Austin

Income Determination
Public Sector
Overview
 Keynesian Income Determination Models
 Private sector



Consumption demand
Investment Demand
Supply & demand for money
 Public



Sector
Government expenditure
Government taxes
Monetary policy manipulation of money supply
 International

imports, exports, net exports
Public Sector
 To the Simple model
 Consumption
& Aggregate Demand
 Savings & Investment
 We add
 Government


which could be broken down according to level (Gf, Gs&l)
or by purpose Gc, Gi
 Government

expenditures (G)
taxation
which could also be broken down in various ways
Government Expenditure - I
 Government expenditure (G)
 could
be disaggregated, but it is usually not
 it is take as given (G = G), as determined by policy
 Government expenditure
 because
it is determined by fiat, there is no distinction
between actual and planned, as with the simple version
of investment
Government Expenditure - II
 To assume G is fixed, or given, at all levels of Y
means we have an Government expenditure
fucntion like this:
G
G=G
Y
"Equilibrium Level of Y"
 Given expenditures C, I and G the equilibrium
level of Y will = C + I + G , or total aggregate
demand.
 Adding government expenditure to investment I
and savings S, the equilibrium level of Y will be
given by S = I + G
 In
the absense of taxation both investment and
government expenditures have to be financed out of
savings/surplus.
Y  C + I +G
 Equilibrium when planned expenditures = actual
expenditures, or aggregate demand (C + I + G) = aggregate
output (Y).
C+I + G = a + bY + I + G
C, I, G
C = a + bY
I+G=I+G
Y
Y
YC+I+G
 Suppose output greater than expected (A) or less than
expected (B).
C+I + G= a + bY + I + G
C, I
Unplanned
fall in
inventories
excess
inventories
B
Y
A
Y
SI+G
 Equilibrium also requires that I + G = S (planned)
S, I, G
S = -a + (1 - b)Y
I+G=I+G
Ye
SI+G
 If I + G  planned S, then the same mechanism of
firms responding to unexpected changes in
inventory will return Y to Ye
S, I, G
S = -a + (1-b)Y
I+G=I+G
Ye
Y
Algebraic Solutions
YC+I+G
 SI+G
 where S = -a + (1-b)Y
 where C = a + bY
 where I = I, or I = f + gY
 where I = I, or I = f + gY
 where G = G
 where G = G
 Solve for equilibrium Y
 Solve for equilibrium Y
Problems
 Now that we have introduced government
expenditures (G) which are determined by
government policy, we can examine the possibility
of using government expenditure for affecting the
state of the economy
 What will be the effect of an increase in
government expenditure?
Great Depression - I
 Business strike = I
C+I+G
C + I' + G
I' < I
1932
1929
Great Depression - II
 Increased G = G
C + I + G'
C+I+G
G' < G
1937
1941
Where does G come from?
 In the absence of taxation
 where
S=I+G
 G can only come from the savings liberated from I
via borrowing from the financial sector
 or from government reserves acquired in some fashion
 unless it is financed from abroad (borrowing, aid)
 so, in as much as we have not yet included international
accounts, we must assume the decline in I liberated S
and that the borrowed money means not only that the
government is running a deficit but it acquires debt
Taxation
 Taxation of all sorts are possible
 lump
sum tax = T = T, given, like a head tax
 income tax = T = To +tY (where t = tax rate)
 consumption tax = T = j + kC
 Only the first two are normally dealt with in
introductory macroeconomics
Lump Sum Tax
 Where T = T
 Then C = a + b(Y - T)
 taxes
are deducted from income and consumption
expenditures are made out of "disposable" income
 So, Y  a + b(Y - T) + I + G
 Or, S + T  I + G
 where
G can now be drawn from S via borrowing or T
via direct appropriation
Income Tax
 If T = To + tY, where t = tax rate
 then C = a + b(Y - [To +tY]
 and Y  a + b(Y - [To + tY] + I + G
 or, S + [To + tY]  I + G
Taxes & Consumption
 With either
C
= a + b(Y - T) = a + bY -bT
 or, C = a + b(Y - [To + tY]) = a + bY - bTo - btY
 we see that Consumption is less (by -bt or by -bTo - btY)
than it would have been without taxation
 So, graphically, the imposition of taxes will shift the
consumption function down
Consumption Function w/taxes
C
C = a + bY
C = a + bY - bT
Y
Contradictory effects of G & T
 So government expenditure shifts C + I up to C + I + G
 While T shifts C downward
 but these effects are not equal even if T = G
 because T shifts C downward by only -bT
 and C + I rises by G
 so if T = G, the downward shift = -bT < upward G = T
 We can study these effects in terms of the
multiplier that we have already seen with respect
to I in the private sector
Government Expenditure Multiplier
 If C = a + b(Y - T)
YC+I+G
 Ya + bY -bT + I + G
 Y = a/(1 - b) -bT/(1 - b) + I/(1 - b) + G/(1 - b)
 We can solve for dY/dG by taking the derivative,
in the process of which all values on right = 0
except for G, such that
 dY/dG = 1/(1 - b) = govt. expend. multiplier
Taxation Multiplier
 If C = a + b(Y - T)
YC+I+G
 Ya + bY -bT + I + G
 Y = a/(1 - b) -bT/(1 - b) + I/(1 - b) + G/(1 - b)
 We can solve for dY/dT by taking the derivative,
in the process of which all values on right = 0
except for T, such that
 dY/dT = -b/(1 - b) = govt. taxation multiplier
Balanced Budget Multiplier
 So if govt. expenditure multiplier = 1/(1-b)
 and, govt taxation multiplier = -b(1-b)
 then we can see just how much a balanced budget
would stimulate the economy
 Where G = T, the effects added together are:
1/(1-b) + [-b(1-b)] = (1 - b)/(1 - b) = 1
Multipliers w/income tax
 You should work through these derivations in the
case of an income tax such as T = To + tY
 Calculate the taxation multiplier
 Calculate the balanced budget multiplier
 (This is done in your book but try it yourself and
then check it against the book.)
Balanced Budget Amendment
 Some concerned with the huge deficit produced by
the Reagan Administrations and effects that deficit
was judged to have on the private sector have
called for a balanced budget amendment to the
constitution mandating a balanced budget.
 Q: What would be the effects of such an
amendment if it's mandate were implemented?
 Ans: A permanent fiscal stimulus to the economy.
Depression Countermeasures
 Now we have more Keynesian tools to use in
evaluating and designing government fiscal policy.
Back to the Depression.
 Non fiscal measures:
 legalization and
regulation of industrial unionism
 pressure to raise productivity + subsidies to R&D
 Fiscal measures
 expand
G to raise C + I + G
 cut T (or To or t) to raise C and thus C + I + G
History
 Primary "Keynesian" fiscal measure that
stimulated the economy was the vast increased in
government expenditure involved in World War II
C,I,G
C + I + G'
C+I+G
G' > G
Y
How Much?
 While we might be able to grasp much of this in
general terms, including the direction of effects,
policy makers have to know not only whether to
raise or lower taxes or government expenditure,
but by how much.
 This is the reason for econometric models based
on real numbers and guestimated parameters. They
provide guides to answering the question "how
much?"
Homework
 Work out the answers to the questions in C&F that
require you to do actual calculations.
 Check your answers against the ones in the back
of the book.
 The most important kind of question is that in
which you have to come up with recommended
policies to achieve certain designated goals-- you
will have such questions on your next test.
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