Income Determination Public Sector Overview n Keynesian Income

Income Determination Public Sector

Overview n Keynesian Income Determination Models u Private sector Consumption demand n Investment Demand n Supply & demand for money n u Public Sector Government expenditure n Government taxes n Monetary policy manipulation of money supply n u International n imports, exports, net exports

Public Sector n To the Simple model u Consumption & Aggregate Demand u Savings & Investment n We add u Government expenditures (G) which could be broken down according to level (Gf, Gs&l) n or by purpose Gc, Gi n u Government n taxation which could also be broken down in various ways

Government Expenditure - I n Government expenditure (G) u could be disaggregated, but it is usually not u it is take as given (G = G), as determined by policy n Government expenditure u because it is determined by fiat, there is no distinction between actual and planned, as with the simple version of investment

Government Expenditure - II n 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" n Given expenditures C, I and G the equilibrium level of Y will = C + I + G , or total aggregate demand. n Adding government expenditure to investment I and savings S, the equilibrium level of Y will be given by S = I + G u In the absense of taxation both investment and government expenditures have to be financed out of savings/surplus.

Y C + I +G n Equilibrium when planned expenditures = actual expenditures, or aggregate demand (C + I + G) = aggregate output (Y). C+I + G = a + b. Y + I + G C, I, G C = a + b. Y I+G=I+G Y Y

Y C+I+G n Suppose output greater than expected (A) or less than expected (B). C+I + G= a + b. Y + I + G C, I Unplanned fall in inventories excess inventories B Y A Y

S I+G n Equilibrium also requires that I + G = S (planned) S, I, G S = -a + (1 - b)Y I+G=I+G Ye

S I+G n 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 n. Y C+I+G n S I+G u where S = -a + (1 -b)Y u where C = a + b. Y u where I = I, or I = f + g. Y u where G = G u Solve for equilibrium Y

Problems n 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 n What will be the effect of an increase in government expenditure?

Great Depression - I C+I+G n Business strike = I C + I' + G I' < I 1932 1929

Great Depression - II C + I + G' n Increased G = G C+I+G G' < G 1937 1941

Where does G come from? n In the absence of taxation u where S=I+G u G can only come from the savings liberated from I via borrowing from the financial sector u or from government reserves acquired in some fashion u unless it is financed from abroad (borrowing, aid) u 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 n Taxation of all sorts are possible u lump sum tax = T, given, like a head tax u income tax = To +t. Y (where t = tax rate) u consumption tax = T = j + k. C n Only the first two are normally dealt with in introductory macroeconomics

Lump Sum Tax n Where T = T n Then C = a + b(Y - T) u taxes are deducted from income and consumption expenditures are made out of "disposable" income n So, Y a + b(Y - T) + I + G n Or, S + T I + G u where G can now be drawn from S via borrowing or T via direct appropriation

Income Tax n If T = To + t. Y, where t = tax rate n then C = a + b(Y - [To +t. Y] n and Y a + b(Y - [To + t. Y] + I + G n or, S + [To + t. Y] I + G

Taxes & Consumption n With either u. C = a + b(Y - T) = a + b. Y -b. T u or, C = a + b(Y - [To + t. Y]) = a + b. Y - b. To - bt. Y u we see that Consumption is less (by -bt or by -b. To - bt. Y) than it would have been without taxation u So, graphically, the imposition of taxes will shift the consumption function down

Consumption Function w/taxes C C = a + b. Y - b. T Y

Contradictory effects of G & T n So government expenditure shifts C + I up to C + I + G n While T shifts C downward n but these effects are not equal even if T = G u because T shifts C downward by only -b. T u and C + I rises by G u so if T = G, the downward shift = -b. T < upward G = T n 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 n If C = a + b(Y - T) n. Y C+I+G n Y a + b. Y -b. T + I + G n Y = a/(1 - b) -b. T/(1 - b) + I/(1 - b) + G/(1 - b) n We can solve for d. Y/d. G by taking the derivative, in the process of which all values on right = 0 except for G, such that n d. Y/d. G = 1/(1 - b) = govt. expend. multiplier

Taxation Multiplier n If C = a + b(Y - T) n. Y C+I+G n Y a + b. Y -b. T + I + G n Y = a/(1 - b) -b. T/(1 - b) + I/(1 - b) + G/(1 - b) n We can solve for d. Y/d. T by taking the derivative, in the process of which all values on right = 0 except for T, such that n d. Y/d. T = -b/(1 - b) = govt. taxation multiplier

Balanced Budget Multiplier n So if govt. expenditure multiplier = 1/(1 -b) n and, govt taxation multiplier = -b(1 -b) n then we can see just how much a balanced budget would stimulate the economy n Where G = T, the effects added together are: 1/(1 -b) + [-b(1 -b)] = (1 - b)/(1 - b) = 1

Multipliers w/income tax n You should work through these derivations in the case of an income tax such as T = To + t. Y n Calculate the taxation multiplier n Calculate the balanced budget multiplier n (This is done in your book but try it yourself and then check it against the book. )

Balanced Budget Amendment n 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. n Q: What would be the effects of such an amendment if it's mandate were implemented? n Ans: A permanent fiscal stimulus to the economy.

Depression Countermeasures n Now we have more Keynesian tools to use in evaluating and designing government fiscal policy. Back to the Depression. n Non fiscal measures: u legalization and regulation of industrial unionism u pressure to raise productivity + subsidies to R&D n Fiscal measures u expand G to raise C + I + G u cut T (or To or t) to raise C and thus C + I + G

History n 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? n 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. n This is the reason for econometric models based on real numbers and guestimated parameters. They provide guides to answering the question "how much? "

Homework n Work out the answers to the questions in C&F that require you to do actual calculations. n Check your answers against the ones in the back of the book. n 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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