1. Income Determination Public Sector

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

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

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

5. Government Expenditure - II nTo assume G is fixed, or given, at all levels of Y means we have an Government expenditure fucntion like this: G = G G Y

6. "Equilibrium Level of Y" nGiven expenditures C, I and G the equilibrium level of Y will = C + I + G, or total aggregate demand. nAdding 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.

7. Y  C + I +G nEquilibrium 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 YeYe

8. Y  C + I + G nSuppose output greater than expected (A) or less than expected (B). C+I + G= a + bY + I + G Y C, I AB excess inventories Unplanned fall in inventories YeYe

9. S  I + G nEquilibrium also requires that I + G = S (planned) I + G = I + G S = -a + (1 - b)Y YeYe S, I, G

10. S  I + G nIf I + G  planned S, then the same mechanism of firms responding to unexpected changes in inventory will return Y to Y e I + G = I + G S = -a + (1-b)Y YeYe S, I, G Y

11. Algebraic Solutions Y  C + I + G u where C = a + bY u where I = I, or I = f + gY u where G = G u Solve for equilibrium Y S  I + G u where S = -a + (1-b)Y u where I = I, or I = f + gY u where G = G u Solve for equilibrium Y

12. Problems nNow 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 nWhat will be the effect of an increase in government expenditure?

13. Great Depression - I Business strike =  I C + I + G C + I' + G I' < I 19291932

14. Great Depression - II Increased G =  G C + I + G' C + I + G G' < G 19411937

15. Where does  G come from? nIn the absence of taxation u where S = I + G   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

16. Taxation nTaxation of all sorts are possible u lump sum tax = T = T, given, like a head tax u income tax = T = T o +tY (where t = tax rate) u consumption tax = T = j + kC nOnly the first two are normally dealt with in introductory macroeconomics

17. Lump Sum Tax nWhere T = T nThen C = a + b(Y - T) u 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 u where G can now be drawn from S via borrowing or T via direct appropriation

18. Income Tax nIf T = T o + tY, where t = tax rate nthen C = a + b(Y - [T o +tY] and Y  a + b(Y - [T o + tY] + I + G or, S + [T o + tY]  I + G

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

20. Consumption Function w/taxes C = a + bY C = a + bY - bT Y C

21. Contradictory effects of G & T nSo government expenditure shifts C + I up to C + I + G nWhile T shifts C downward nbut these effects are not equal even if T = G u because T shifts C downward by only -bT u and C + I rises by G u so if T = G, the downward shift = -bT < upward G = T nWe can study these effects in terms of the multiplier that we have already seen with respect to I in the private sector

22. Government Expenditure Multiplier nIf C = a + b(Y - T) Y  C + I + G Y  a + bY -bT + I + G nY = a/(1 - b) -bT/(1 - b) + I/(1 - b) + G/(1 - b) nWe can solve for dY/dG by taking the derivative, in the process of which all values on right = 0 except for G, such that ndY/dG = 1/(1 - b) = govt. expend. multiplier

23. Taxation Multiplier nIf C = a + b(Y - T) Y  C + I + G Y  a + bY -bT + I + G nY = a/(1 - b) -bT/(1 - b) + I/(1 - b) + G/(1 - b) nWe can solve for dY/dT by taking the derivative, in the process of which all values on right = 0 except for T, such that ndY/dT = -b/(1 - b) = govt. taxation multiplier

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

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

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

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

28. History nPrimary "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

29. How Much? nWhile 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. nThis is the reason for econometric models based on real numbers and guestimated parameters. They provide guides to answering the question "how much?"

30. Homework nWork out the answers to the questions in C&F that require you to do actual calculations. nCheck your answers against the ones in the back of the book. nThe 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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