Income DeterminationPublic 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 expenditures (G)

which could be broken down according to level (Gf, Gs&l) or by purpose Gc, Gi

Government 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).

I + G = I + G

C = a + bY

C+I + G = a + bY + I + G

Y

C, I, G

Ye

Y C + I + G

Suppose output greater than expected (A) or less than expected (B).

C+I + G= a + bY + I + G

Y

C, I

AB

excessinventories

Unplannedfall in

inventories

Ye

S I + G

Equilibrium also requires that I + G = S (planned)

I + G = I + G

S = -a + (1 - b)Y

Ye

S, I, G

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

I + G = I + G

S = -a + (1-b)Y

Ye

S, I, G

Y

Algebraic Solutions

Y C + I + G where C = a + bY where I = I, or I = f + gY where G = G Solve for equilibrium Y

S I + G where S = -a + (1-b)Y where I = I, or I = f + gY where G = G 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

19291932

Great Depression - II

Increased G = G C + I + G'

C + I + G

G' < G

19411937

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 = a + bY

C = a + bY - bT

Y

C

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 Ya + 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 Ya + 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'

G' > G

Y

C,I,G

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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