Chapter 4 Income Determination I --- Income-expenditure Model

1. Chapter 4 Income Determination I --- Income-expenditure Model

2. Contents: • Assumptions of income-expenditure Model • Two-sector economy • Three-sector economy • Four-sector economy • Different kinds of multipliers in different economies • Other points to be noticed • Paradox of thrift • Implications of private saving, public saving & national saving • Advanced Material 4.1 : Equality between investment and saving in a two-sector economy

3. Assumptions of Income-expenditure Model

4. Assumptions of income-expenditure model (or elementary Keynesian model) • The amount of resources and the state of technology remain unchanged, i.e., Yf is a constant. • There exists an unemployment of resources. The model is to find out the determinants of equilibrium GNP and the ways to eliminate unemployment. • No indirect taxes, subsidies, depreciation or net factor income from abroad, i.e., Y = GDP =GNP. • The interest rate and the price level are fixed. So nominal variables = real variables and nom. r = real r.

5. Two-sector Economy

6. Households Firms Two-sector economy • Composed of households and firms only • No government sector

7. Factor Services Income Features of households • Households provide factor services forincome.

8. Disposable Income Consumption Saving Features of households • Disposable income is either consumedor saved.

9. Marginal Propensity to Consume (MPC) Disposable Income Autonomous Consumption Consumption function C = cYd + C* • Marginal propensity to consume (MPC or c) is the change in • consumption resulting from a unit change in disposable income. c < 1. • Autonomous consumption(C*) is the consumption at zero • disposable income (the minimum amount for subsistence). C* > 0.

10. c +1 Consumption function C Graphical Illustration C = cYd + C* C* Yd 0

11. Marginal Propensity to Save (MPS) Disposable Income Autonomous Saving Saving function S = sYd + S* • Marginal propensity to save (MPS or s) is the change in saving • resulting from a unit change in disposable income. s = 1 – c. Why? • Autonomous saving is the saving at zero disposable income. • S* = -C*.Why?

12. s = (1-c) +1 Saving function Graphical Illustration S S = sYd + S* Y 0 S* = -C*

13. Factor Services Products Firms Features of firms 1.Firms employ factor services to produce goods. 2.Firms also consume final products (fixed investment & inventories) to help production.

14. Marginal Propensity to Invest (MPI) National Income Autonomous Investment Investment function I = i Y + I* • Marginal propensity to invest (MPI or i) is the change in • investment resulting from a unit change in income. • i > 0. Why? • Autonomous investment is the investment at zero income. • I* > 0. Why?

15. I = iY + I* i +1 Investment function r Graphical illustration I* Y 0

16. Equilibrium condition (2-sector economy) • Aggregate supply (AS) of final products is GNP or Y. • Without government or taxation • AS = Y = Yd = C + S

17. Equilibrium condition (2-sector economy) • Aggregate demand (AD)for final products is aggregate expenditure (E). AD = E = C + I

18. Equilibrium income(or equilibrium GNP) is reached when AS = AD • AS = AD • Y = E • C + S = C + I • S = I = Withdrawal Injection

19. Withdrawal(撤出 , W) • is the amount of income withdrawn from the circular flow, not being spent on final products. • In a 2 sector economy,saving is the withdrawal.

20. Injection(注入, J) • is the amount of expenditure on final productsinjected into the circular flow • not financedbyincome earned from production. • In a 2 sector economy,investment is the injection.

21. Consumption ABC Ltd. Saving Investment Circular flow of a 2-sector economy Injection Withdrawal Y Firms Households Yd E When I = S, an equilibrium is achieved.

22. E Y=E 45o 0 Y Meaning of a 45° line V (Y < E) Meaning of a 45o line U (Y = E) Z (Y > E)

23. Y=E E E= C+I C C* I 45o Y 0 Aggregate expenditure function • Add consumption and investment functions vertically I*

24. Adjustment mechanism 2 approaches: • Income-expenditure approach • Injection-withdrawal approach

25. E Y=E At Y1, Y > E Unplanned increase in inventories } E=C+I Y Y2 Ye Y1 0 Income-expenditure approach •  production At Y2, Y < E Unplanned decrease in inventories •  production {

26. Y2 Y1 Injection-withdrawal approach •  production E S At Y2, J > WUnintended inventory disinvestment At Y1, J < WUnintended inventory investment } I* I { •  production 0 Y Ye -C*

27. ΔEi ΔEi’ : Change in Y brought by ΔEa Multiplier effect E: E ΔEa ••• Y: Y Initial equilibrium Total change in Y = ΔE + c•ΔE + c•c• ΔE + c•c•c• ΔE + … = (1 + c + c2 + c3 + …) •ΔE = •ΔE

28. Multiplier effect • Multiplier(k) • isthe ratio of the total change in equilibrium income to the initial change in autonomous expenditure (or autonomous withdrawal) that brought it about. • Mathematical expression:

29. Mathematical derivation of equil. income & multiplier In a 2-sector economy • E = C + I, where C = cYd + C* and I = I* In equilibrium, Y = E = C + I = cYd + C* + I* = cY + C* + I* • Y – cY = C* + I* • (1 – c)Y= C* + I* • Equilibrium Y = .(C* + I*)

30. Mathematical derivation of equil. income & multiplier When C* or I* changes by ΔEa • ΔY = . ΔEa 

31. Q4.1: • Calculate the value of multiplier and explain its meaning in each of the following cases. • MPC = 1 • MPS = 1

32. Q4.2: If the autonomous expenditure decreases by ΔE, what will be the change in equilibrium income?

33. Three-sector Economy

34. Three-sector economy Firms Households Government

35. Government Expenditure • Government’s expenditure is mainly financed by taxation

36. Government expenditure function (G) • is fixed by the budget at the beginning of a fiscal year. • G is a constant (G*) independent of any variables. G = G*, where G > 0

37. Tax function • No indirect taxes is assumed. • Only direct taxes are concerned. There exist three kinds of direct tax systems.

38. Equilibrium condition (3-sector economy) • Aggregate supply (AS) of final products is GNP or Y. • Yd = Y – T = C + S • Y = Yd + T = C + S + T

39. Equilibrium condition (3-sector economy) • Aggregate demand (AD) for final products is E. • E = C + I + G

40. Equilibrium income(or equilibrium GNP) is reached when AS = AD • AS = AD • Y = E • C + S + T = C + I + G • S + T = I + G Withdrawal Injection =

41. Consumption ABC Ltd. Saving Tax Investment Government expenditure Circular flow of a 3-sector economy Injection Withdrawal Y Firms Households E When I + G = S + T, equilibrium is achieved.

42. Mathematical derivation of equil. income & multiplier In a 3-sector economy with a lump-sum tax system • E=C+I+G, where C = cYd + C*; Yd = Y – T’ and • I = I* and G = G* In equilibrium, Y = E = C + I + G = cYd + C* + I* + G* Y = c(Y-T’) + C* + I* + G* = cY- cT’+ C* + I* + G* • (1–c)Y = C* + I*+ G*- cT’ • Equilibrium Y = .(C*+I*+G*- cT’)

43. Mathematical derivation of equil. income & multiplier When C* or I* or G* changes by ΔEa • ΔY = . ΔEa • Multiplier =

44. Mathematical derivation of equil. income & multiplier Under a lump-sum tax system Equil. income:   Multiplier:

45. Mathematical derivation of equil. income & multiplier In a 3-sector economy with a proportional tax system • E=C+I+G, where C = cYd + C*; Yd = Y - tY - T*; • I = I* and G = G* In equilibrium, Y = E = C + I + G = cYd + C* + I* + G* Y = c(Y - tY - T*) + C* + I* + G* = cY - ctY - cT* + C* + I* + G* (1 - c + ct)Y = C* + I* + G* - cT*  Equilibrium Y = • (C*+I*+G*-cT*)

46. Mathematical derivation of equil. income & multiplier When C* or I* or G* changes by ΔEa • ΔY = •ΔEa • Multiplier =

47. Under a proportional tax system  Equil. income: Multiplier:  As t > 0, (1-c) < (1-c+ct)   • The multiplier of proportional tax system is smaller than the multiplier of lump-sum tax system.

48. Mathematical derivation of equil. income & multiplier With the addition of a proportional transfer payment, where Yd = Y - tY - T* + qY + Q* In equilibrium, Y = E = C + I + G = cYd + C* + I* + G* • Y = c(Y-tY-T*+qY+Q*) + C* + I* + G* • (1–c+ct-cq) •Y = C* + I* + G* -cT* + cQ* Equilibrium Y = • (C*+I*+G*-cT*-cQ*)

49. Mathematical derivation of equil. income & multiplier When C* or I* or G* changes by ΔEa • ΔY = • ΔEa • Multiplier =

50. Under a proportional tax & transfer payment system Equil. income: Multiplier: As q<0, (1-c+ct)<(1-c+ct-cq)  > • The multiplier with a proportional transfer payment is smaller than the multiplier without it.