1. The Classical Macro Model
The Simple Classical Model

2. The Classical Assumptions
Classical economics stressed the role of real as opposed to nominal factors in determining real output. Money was only important as a medium of exchange.
Classical economics stressed the self-adjusting nature of the economy. Government policies to insure full employment were unnecessary and generally harmful. Classical economists assumed:
Perfectly flexible wages and prices.
Perfect information.

3. A Classical Model of Output Determination
The Starting point is the Production Function
Y = F(K, N) where
Y = National output
K = Capital
N = labour
And F is a functional notation
Assume K is constant in the short run so that Y varies directly with N. So to determine output, we need to know what determines employment, N. Employment is determined from the labour market.
In the labour market, we have the demand and the supply sides.

4. Properties of the Production Function
With K given, output varies directly with the level of N
From the production function, we can compute the following:
Marginal product of labour can be derived from the production function using calculus.
FN=MPN=dF/dN=dY/dN>0
FNN=d2F/dN2<0 i.e. the economy is subject to the law of diminishing returns.
Does the following production function exhibit these properties?
Y=K0.5N0.5, K=1

5. The Labour Market
Note: Firms demand labour services and households supply labour services.
The labour market comprises
a) The Demand for labour side
b) The Supply of Labour side
: ASSUMPTIONS
1. Firms are profit maximizers
2. Households maximize their utility
3. Firms take the price level and money Wage as given; households take the money wage as constant
4. The labour market is ALWAYS in equilibrium.

6. Demand for Labour
Firms employ labour to maximise profits and the condition that must be met is:
P.MPN=W (1) where;
P= the price level of output
MPN=marginal product of labour
W= money/nominal wage.
(1) can be rewritten in a familiar form:
MPN= W/P (2).
So for the firm to maximize profit, equations (1) and (2) must hold. In fact, the two equations are the same but their use depends on the question under consideration.

7. Demand for Labour Cont’d
From equation 2, MPN= W/P, for the firm to maximize profit in hiring labour, it must employ labour at the point where the marginal product of the last worker equals the fixed money wage.
Because of diminishing returns, we consider the falling segment (the downward sloping portion) of the MPN curve.
The profit maximising level of labour demand can be graphically determined using equations 1 or 2 as shown in diagrams below.

8. The Demand for labour Curve
Producers are willing to hire up to the point where the real wage (W/P) = MPN.
Notice that in the range of diminishing returns, the demand curve for labour is downward sloping.
The demand for labour can be expressed in both real and nominal terms.
Figure1: Production Function and Marginal Product of labour Curve

9. Real vs. Nominal
The demand for labour can be expressed in real terms, i.e., Figure 2a (Top)
Firms maximize profits where W/P = MPN.
Or, alternatively, firms maximize profits where W = MPN x P. Labour demand can be expressed in nominal terms, as in Figure 2b (Bottom)
We will use both, depending on the situation.
Figure 2a labour Demand for a Firm in real Terms
Figure 2b The Demand for labour in Nominal Terms

10. Determinants of the Demand for labour by firms
We conclude from the two diagrams that labour demand is a negative function of the real wage meaning as the real wage increases, labour demand decreases and vice versa:
Nd = f (W/P) 
(-) 
That is, the demand for labour is a negative function of the real wage, i.e., the higher the real wage, the lower the demand for labour.
Can you use economic intuition to explain this?
            
or,

11. Deriving the Labour Demand Function

12. Labour Supply
Classical economists assumed that individuals maximize their utility or satisfaction.  Utility was generated by real income earned through the disutility of work that could then be used to purchase marketable goods and services as well as leisure.  There is therefore a trade-off between real income resulting from working and the pleasures or utility of leisure, doing your own thing.
U=f(Consumption, Leisure) with the following constraint:
W+L=H, H=24 hours

13. Labour Supply Ns = g (W/P) (+)
or, the supply of labour is a positive function of the real wage, i.e., the higher the real wage, the higher the supply of labour.
Classicals believed that the substitution effect of a money wage change outweighed the income effect so labour supply increases when real wage increases. The opposite is also true : labour supply decreases when real wage decreases.
So when plotted against the real wage, the labour supply curve is upward sloping.

14. Plotted against the real wage, an Individual Labour Supply Curve is upward sloping on

15. Equilibrium Output and Employment
To determine what the equilibrium levels of employment and output will be in an economy, according to the classical model, we first of all get the employment level from the labour market (N*). With N determined, we put it into the production function and obtain equilibrium output (Y*). The following 4 equations are needed:
   1. Nd = f (W/P)
2. Ns = g (W/P)
3. Ns = Nd   
4. Y = F (K*, N)  

16. Determinants of the Position of the Labour Supply Curve
A change in population growth rate
A change in preference for leisure as against working for more hours
A change in the training content of institutions responsible for training potential labour supply.

17. Equilibrium in the labour Market
Equilibrium in the labour market yields the market real wage (W/P)0 and the level of employment (N0).
Given the (N0) level of employment, the level of income is determined at (Y0).
The economy automatically adjusts to full employment at (N0).
Figure 3 Classical Output and Employment Theory

18. Numerical Illustration
A classical economy is described by the following functions:
Y=200KN-1/4N2
Ns=300+8W/P
a) Derive the labour demand function and determine its slope. Assume K=1
b) Determine N*, (W/P)* and Y*.
c) Provide a rough sketch of your answers.

19. Effect of a Change in Price
Price level change has no effect on real variables.
As P , W  in the same proportion, so that (W/P) and N are unchanged.
Effect can be shown to be the same: no matter whether we use real wage (W/P) as in part a, or nominal wage (W) as in part b, price level changes have no real effect in the classical system.
Figure 4 labour Market Equilibrium and the Money Wage

20. The Aggregate Supply Curve
If we plot various levels of prices (the absolute price level) and their respective level of Y, we plot out a vertical aggregate supply curve.
The level of real output is not affected by nominal variables.
Real output is affected only by real variables.
Figure 5 Classical Determination of Aggregate Supply

21. Shifts in the Aggregate Supply Curve
A change in the level of capital stock is a change in a real factor.
As K, the production function shifts up, which shifts the labour demand curve, i.e., the MPN or Nd .
The real wage (W/P) and the real level of employment (N).
The level of real output is only affected by real variables.
Real output is not affected by nominal variables.
Figure 6 The Effect on Output, the Real Wage, and Employment of an Increase in the Capital Stock in the Classical System

22. The Classical Macro Model
Money in the Classical System

23. Classical Aggregate Demand
Classical economics is supply-side economics.
Real output on the supply side is determined by the real factors of production—land, labour, capital, and entrepreneurial ability. Y=F(K,N) is real!
All variables that are supply side determined are real variables—Y, N, MPN, W/P, S, I, C, r.
Autonomous variables, such as G and T are real.
The demand side is important only in determining the nominal variables—W, P, MPNxP.
The money supply, M, is a nominal variable.
The classical aggregate demand curve is an implicit aggregate demand.
What is the role of money in determining aggregate demand?

24. Determination of Price in the classical model
To classical economists, the quantity of money determines the price level. That is, P=f(Ms). To determine the direction and the extent to which price depends on money supply, we need a theory: The Quantity Theory of Money of which two versions will be discussed –
the Fisherien and;
the Cambridge Versions.
The building blocks for the 2 approaches is the equation of exchange: MV=PY

25. The Equation of Exchange
MV=PY where;
M= Quantity of money supply
V= Velocity of money
P= general or average price level
Y= real output (quantity of goods & services an economy produces in a year)
MV= Total value of money used to purchase goods in a year
PY=total value of goods produced in a year
MV=PY is a truism!

26. The Equation of Exchange & the Quantity Theory of Money
To move from the EE to the QTM, we need to know how the variables in the EE are determined.
ASSUMPTIONS
M= money supply is exogenously determined by the central bank
V= Velocity of money is fixed by institutional factors
y= real output is determined by supply factors. To classical economists, y is fixed at the full employment level of output.
With these assumptions, we can make P the subject of the expression:
P=(MV)/Y

27. The Equation of Exchange & the Quantity Theory of Money
With V and Y fixed, their ratio is also fixed so P becomes a function of the quantity of money in a country.
INTERPRETATION:
P is directly proportional to M which means that:
1. P increases whenever M increases and vice versa;
2. P increases by the same proportion to M
If M increases by 10%, P increases by the same 10%, for example
If M increases by 40%, P increases by the same 40%
In short, P is solely determined by money supply. This the quantity theory of money as expounded by Fisher.
BUT HIS VERSION IS TOO MECHANICAL! WHAT IS THE ECONOMICS BEHIND IT?

28. The Cambridge Approach to the Quantity Theory
In this version, we move away from the mechanical nature of the version of the QTM by Fisher. As championed by A. Marshall & A.C. Pigou , the QTM is put in the context of demand for money where the average money holdings is a constant fraction of nominal income:
Md=k(Py), k>0 and 0<k<1

29. The Cambridge Approach to the Quantity Theory Cont’d
We can move from the equation of exchange to money demand:
k= 1/v
From the money market equilibrium, an increase in Ms results in excess supply of money and excess spending and given the fixed output supply, prices will go up. This is the economics behind this version of this QTM: So the price level is determined by MS.

30. Classical Aggregate Demand
The Classical aggregate demand curve plots combinations of price level (P) and real output (Y) consistent with the equation of exchange, MV = PY, for a given money supply (M) and a fixed velocity (V).
Assume M = 300 and V = 4.
Figure 4-1 The Classical Aggregate Demand Curve
Points such as P = 12.0 and Y = 100 or P = 6.0 and Y = 200 (PY = 1200 = MV in each case) lie along the aggregate demand curve.
An increase in the money supply to M = 400 shifts the aggregate demand curve to the right.

31. Deriving the AD Equation:
We use the equation of exchange MV=PY to derive the classical AD equation. Since P and Y are variables and M and V are fixed constants, we can make P the subject of the equation above:
Given M=300 and V=4, the ADC equation is :
300*4=PY
1200=PY (1)
P=1200/Y (2)
Thus, both (1) and (2) can be taken as ADC equation.

32. Effects of a Change in the Money Supply in the Classical System
Successive increases in the money supply, from M1 to M2 and then to M3, shift the aggregate demand curve to the right, from Yd(M1) to Yd(M2) to Yd(M3).
Figure 4.2 Aggregate Supply and Aggregate Demand in the Classical System
The price level rises from P1 to P2 to P3.
Output, which is supply-determined, is unchanged (Y1 = Y2 = Y3).

33. The Classical Theory of the Interest Rate
In the classical system, the equilibrium interest rate was the rate at which the amount of funds individuals & firms desired to lend was just equal to the amount of funds others desired to borrow.
The market in which the interest rate is determined is the Loanable Funds market or the Bonds market.
In this market, entities borrow by selling (issuing) bonds. By buying these bonds entities give out their savings or idle funds.
Like any market there ARE TWO SIDES: THE DEMAND & the SUPPLY SIDES
Household, firms and government constitute the demand side of the loanable funds market.
Household, firms and government also constitute the supply side of the loanable funds market.

34. The Classical Theory of the Interest Rate Cont’d
The SSLF may also be called the saving function or the demand for bonds
Similarly, the DDLF may also be called the Investment function or the supply of bonds
ASSUMPTIONS
1. Classical economists assume that the LF market is always in equilibrium, i.e. SSLF=DDLF
2. The interest rate is perfectly flexible. With excess demand for funds, the interest rate increases to clear the market and with excess supply the interest rate decreases.
This flexibility in the interest rate guarantees that exogenous changes in a particular component of AD do not affect the level of AD .

35. The SSLF and DDLF Schedules
At higher interest rate, people are enticed to save more so this gives an upward sloping SSLF schedule.
For the demand for Loanable funds curve, at higher interest rate, the cost of borrowing increases so demand for loanable funds will reduce so we postulate a downward sloping DDLF curve.

36. Supply and Demand for loanable funds curves

37. Demand and Supply of Loanable Funds Schedules
Putting the two together give the loanable funds market shown in Figure This market determines the amount borrowed and lent at the market equilibrium interest rate .

38. The Loanable Funds Theory of Interest Rates
The equilibrium interest rate (ro) is the rate that equates:
The supply of loanable funds consists of new saving (S),
The demand for loanable funds, which consists of investment (I) plus the bond-financed government deficit (G -T).
Figure 4: Interest Rate Determination in the Classical System
NOTE: The Loanable Funds Theory is a real theory of interest rates.

39. Changes in Autonomous Spending
An autonomous decline in investment shifts the investment schedule to the left from I0 to I1—the distance I.
The equilibrium interest rate declines from r0 to r1.
As the interest rate falls, there is an interest-rate-induced increase in investment—distance B.
Figure 4.4 Autonomous Decline in Investment Demand

40. Changes in Autonomous Spending
There is also an interest-rated-induced decline in saving, which is an equal increase in consumption—distance A.
The interest-rate-induced increases in consumption and investment just balance the autonomous decline in investment.
There is no change in real output.
Figure 4.4 Autonomous Decline in Investment Demand
NOTE: A change in autonomous spending changes only the composition of output!

41. Effect of Increase in Government Spending in the Classical Model
At point E, the equilibrium interest rate r0 equates the supply of loanable funds, S, with the demand for loanable funds, I.
Figure 4.5 Effect of Increase in Government Spending in Classical Model
Adding government deficit spending, (G - T)1 shifts the demand for loanable funds to the right to point F. The interest rate rises from r0 to r1.

42. Effect of Increase in Government Spending in the Classical Model
The increase in the interest rate causes a decline in the quantity of investment from I0 to I1, a distance B, and an increase in saving, which is an equal decline in consumption, from S0 to Sl, a distance A.
Figure 4.5 Effect of Increase in Government Spending in Classical Model
The decline in investment and consumption just balances the increase in government deficit spending, (G - T)1.

43. Crowding Out
We have a name for what happens when the government increases its deficit.
It is called crowding out—100% crowding out or complete or total crowding out in the Classical case.
Govt spending crowds out private spending, partly from investors (less I) and partly from consumers (less C, that is to say, more S)
The level of output (Y) does not change.
The only change is in the composition of output.
Is that change real or nominal?
So we have seen that a bond-financed increase in G has no effect on output and employment!

44. Numerical Illustration
You are given the following functions:
(1) I = r
(2) S = 8 + 3r
(3) I = S
a) Find r* and I*
b) If the there is GHȼ30 million-bond financed increase in government expenditure, find:
i) the new r* and I*. How will AD and Y be affected? Explain.
ii) how much of investment is crowded out? How much of consumption is affected? Explain.
iii) redo ii) using loanable funds diagrams.

45. Policy Implication of the classical Equilibrium Model
Monetary policy Effects:
Will monetary policy have real effects? That is, will it cause employment and output to change? The answer is no because the resultant change in price will not affect the real wage because the money wage will increase in proportion to the price level. So N, Y are not affected.

46. Expansionary Monetary Policy Effects in the classical equilibrium model
Increases in the money supply from M1 to M2 and then to M3, shift the aggregate demand curve to the right, from Yd(M1) to Yd(M2) to Yd(M3).
Figure 4.2 Aggregate Supply and Aggregate Demand in the Classical System
The price level rises from P1 to P2 to P3.
Output, which is supply-determined, is unchanged (Y1 = Y2 = Y3).

47. Fiscal Policy in the classical system
Assume G goes up. We have to know how it is financed. There are 3 ways of raising the money:
1. Borrowing (increase in demand for loanable funds) – a bond-financed increase in G
2. Increase in Taxes (A Tax-financed increase in G)
3. Increase in money supply (Money-financed increase in G)
For option 3, we already know the effect. Only prices will change but N, Y, Real wage, Interest rate will all not change. The AD curve will shift to the right on the vertical AS curve.

48. A bond-financed increase in G
For a bond-financed increase in G, DDLF curve will shift to the right and at initial interest rate, there will be excess demand for funds so the interest rate increases.
The increase in the interest rate has two effects on AD.
1. There is an interest rate induced fall in investment
2. With the interest rate increasing, saving will increase which is mirrored by an equal reduction in consumption (a component of AD)

49. A bond-financed increase in G Cont’d
Because classical economists believed that the loanable funds market is always in equilibrium, the rise in the interest rate will cause reductions in consumption and investment whose magnitude will be equal to the initial increase in G. So on net there will be no change in AD; only that its components will change, consumption and Investment have reduced but G has increased.
A bond-financed increase in G has no real effect!

50. A bond-financed Increase in Government Spending in the Classical Model
The increase in the interest rate causes a decline in the quantity of investment from I0 to I1, a distance B, and an increase in saving, which is an equal decline in consumption, from S0 to Sl, a distance A.
Figure 4.5 Effect of Increase in Government Spending in Classical Model
The decline in investment and consumption just balances the increase in government deficit spending, (G - T)1.

51. Tax Policy
There are two types of tax policies: A lump-sum tax Change (To) & a Change in the marginal tax rate (t) Demand -Side Effects 1. T=To+ tY, 0<t<1. Assume To (Lump-sum taxes) are reduced – this is expansionary fiscal policy. The resultant budget deficit (the revenue lost by the tax cut) can again be bond-financed or money financed and the effects have already been analysed – it has no real effects.

52. Tax Policy Cont’d
Assume the government reduces the tax rate. This policy will have real effects as the after tax real wage will increase so labour supply will increase and employment will increase so through the production function, output will increase at a given price level. Thus, the AS curve shifts to the right on a constant AD curve so output increases and prices decline.

53. Supply-Side Effect
In part a, a reduction in the marginal tax rate (from 0.40 to 0.20) increases the after-tax real wage for a given pretax real wage.
The labor supply curve shifts to the right, moving from A to B.
Employment and output increase, as shown in part b of the graph, moving from A to B on the production function.
Figure 4.6 The Supply-Side Effects of an Income Tax Cut

54. Figure 4.6c The Supply-Side Effects of an Income Tax Cut
This increase in output is represented by the shift to the right in the vertical aggregate supply curve in part c, from A to B. Income  from Y0 to Y1, while price  from P0 to P1.

55. An Alternate Version of Figure 4-6

56. The Keynesian Revolution
Intermediate Macroeconomics

57. The Keynesian Revolution
The Keynesian revolution was a reaction against both classical and neoclassical economics.
Keynes aimed his big guns at AC Pigou’s “revised and updated” version of classical economics.
He all but destroyed the Quantity Theory of Money.
He turned Say’s Law on its head. He emphasized the demand side to the exclusion of the supply side.
Keynes lumped all previous writers together—called them Classicals.
This makes some sense in that he did not argue with the “micro” portion—in fact, he largely ignored it.

58. The Keynesian Revolution
Keynes directed his attack against AC Pigou’s more modern version of the Macroeconomic model, not Adam Smith’s version.
The Keynesian Revolution all but destroyed “classical” economics
i.e., it destroyed the macro part of neoclassical economics
It left intact the micro portion
Keynesian revolution was so overwhelming that at one point Richard Nixon said, “We are all Keynesians now!”

59. The Problem with Classical Economics
The Classicals believed the economy would automatically adjust to full employment.
They believed that if wages and prices were perfectly flexible, and if there existed perfect information, then the equilibrium level of output would be the full employment level.
They believed in Say’s Law.
Any change in G or T would only affect the composition of output, not the level of output.
They believed that money served only as a medium of exchange, and that it had no real effect.

60. The Simple Math of the Simple Keynesian System
At equilibrium: Y = E
Therefore Y = C + I + G is the ex ante equilibrium condition.
But Y is also identical to C + S + T.
Therefore C + I + G  C + S + T
Or: I + G = S + T (the ex ante equilibrium condition.)
leakages = injections is also an expression of the ex ante equilibrium condition.

61. The Components of “Aggregate Demand”
Consumption is an endogenous variable.
Consumption varies with income.
C = f(Y), ceteris paribus
Specifically C = a + bYD
Where “a” is the vertical axis intercept and “b” is the slope.
YD is disposable income.
As income changes, so does consumption.
i.e., C = bYD
Therefore b = C/YD (marginal propensity to consume)

62. The Components of “Aggregate Demand”
Saving is also an endogenous variable.
Saving means “not consuming.”
If C = a + bYD, and if Y  C + S + T, then
Y – T = YD = C + S
Or: S = YD – C
S = YD – a – bYD
S = – a + YD – bYD, or S = – a + (1 – b) YD
As income changes, so does saving.
i.e., S = (1 – b)YD
Therefore (1 – b) = S/YD (marginal propensity to save)

63. The Components of “Aggregate Demand”
Investment (I) and Government spending (G) are assumed to be autonomous (or exogenous) variables.
I = I0
Initially we assume r = r0, which means I = I0 and is exogenous.
Later, r becomes an endogenous variable, which means I is then endogenous.
G = G0
G will be treated as exogenous throughout the course.
Taxes can be exogenous or endogenous.
T = T0
T = T0 + tY

64. Three Sector Model with Lump Sum Tax
Y  AS, Ex Post, By Definition
E = AD, Ex Ante
E = C + I + G, Ex Ante
At Equilibrium: AS = AD, or Y = E
Therefore: Y = C + I + G
Where: C = a + bYD
YD = Y - T
T = T0
I = I0
G = G0
Starting with Equilibrium Condition: Y = C + I + G
Substituting: Y = a + b(Y - T0) + I0 + G0

65. Three Sector Model with Lump Sum Tax (Continued)
Simplifying Terms: Y = a + bY - bT0 + I0 + G0
Collecting Y’s on Left Side: Y - bY = a - bT0 + I0 + G0
Factor out Y: Y(1-b) = a - bT0 + I0 + G0
Divide both sides by (1-b): Y = (1/1-b) (a - bT0 + I0 + G0)
Solving for Delta ( ) Equations:
 Y = (1/1-b)  a
 Y = (1/1-b)  I
 Y = (1/1-b)  G
 Y = (-b/1-b)  T

66. The Simple Graphics of the Simple Keynesian Model
The Keynesian Model
The Simple Graphics of the Simple Keynesian Model

67. Keynesian Consumption Function
The consumption function shows the level of consumption (C) corresponding to each level of disposable income (YD).
The slope of the consumption function (C/ YD) is the marginal propensity to consume (b), the increase in consumption per unit increase in disposable income.
The intercept for the consumption function (a) is the (positive) level of consumption at a zero level of disposable income.
Figure 5.3 Keynesian Consumption Function

68. Figure 5.4 Keynesian Saving Function
The saving function shows the level of saving (S) at each level of disposable income (YD).
The slope of the saving function is the marginal propensity to save (1 – b), the increase in saving per unit increase in disposable income.
The intercept for the saving function (– a) is the (negative) level of saving at a zero level of disposable income.

69. Translating from YD to Y
Starting with C where a is the intercept and b is the slope:
Let:
YD = Y – T
Substituting:
C = a + b(Y – T)
Rearranging:
C = a + bY – bT
Or:
C = a – bT + bY
Here, the term (a – bT) is the intercept and b is the slope of the consumption function when plotted with Y on the horizontal axis, rather than YD.

70. Figure 5.5 Determination of Equilibrium Income

71. Determination of Equilibrium Income
At point A in part a, the equilibrium level of income is Y, where C + I + G intersects the 45° line.
At that point, output (Y) equals aggregate expenditures (AD), i.e., Y = C + I + G.
At point A in part b, the equilibrium level of output, Y, is determined at the point where the I + G and S + T schedules intersect so that I + G = S + T.
At the level of income YL, which is less than equilibrium output Y, aggregate demand > output, ( C + I + G) > Y.
At points greater than equilibrium output Y, output exceeds aggregate demand.

72. Figure 5.6 Effect of an Increase in Autonomous Investment on Equilibrium Income

73. Figure 5.7 Effect of an Increase in Taxes on Equilibrium Income

74. Effect of an Autonomous Increase in Taxes on Equilibrium Income
An increase in taxes from T0 to T1 shifts the aggregate expenditure schedule (AD) downward in part a, from (C + I + G) 0 to (C + I + G) 1 to equilibrium point B, since taxes are in the intercept.
Equilibrium income falls from Y0 to Y1.
The change in income per dollar change in taxes depends on the tax multiplier; Y = (– b/1 – b) T.
In part b, starting at point A, the saving plus taxes schedule shifts up, from S + T0 to S + T1.
Equilibrium changes from A to B. Income decreases from Y0 to Y1.

75. Figure 5.8 An Example of Fiscal Stabilization Policy

76. An Example of Fiscal Stabilization Policy
Beginning at point A in part a, a decline in autonomous investment from I0 to I1 shifts the AD schedule downward from EP = (C G0) to EL = (C + I1 + G0), moving to equilibrium point B.
A compensating increase in discretionary government spending from G0 to G1 shifts the AD schedule back to equilibrium point A where (C + I1 + G1) = EP = (C G0).
Equilibrium income is again at YP .
In part b, starting at point A, the decline in autonomous investment expenditure shifts the I + G schedule downward, from I0 + G0 to I1 + G0 moving to equilibrium point B, decreasing income from YP to YL .
A compensating increase in discretionary government spending from G0 to G1 shifts the I + G schedule upward, to I1 + G1, moving back to equilibrium point A, and increasing income back to YP.

77. The Keynesian System II
Money in the Keynesian System

78. Interest Rate as a Variable
In the simple Keynesian model, interest rates are assumed to be constant.
What happens if interest rates are allowed to vary?
What is the relationship between interest rates and the level of investment?
What affects interest rates in the Keynesian System?
The Supply of Money
The Demand for Money
Keynes introduced a monetary theory of interest rates, as opposed to the real theory of interest rates in the Classical system.

79. Figure 6.1 Effect of a Decrease in the Interest Rate on Investment, Aggregate Expenditures, and Equilibrium Income

80. The Effect of Variable Interest Rates in the Keynesian System
In part a, as the interest rate decreases from r0 to r1, investment increases from I0 to I1.
In part b, this increase in investment, I, shifts the aggregate expenditure schedule (AD) up since the intercept is larger, from
E0 = C + I0 + G0
to E1 = C + I1 + G0.
Output increases from Y0 to Y1.
Think in terms of the circular flow mechanism where C + I1 + G0 > Y. (excess demand for output)

81. Keynes’s Monetary Theory of Interest Rates
In the Keynesian System, interest rates are determined by the demand for and supply of money.
The money supply is a policy variable determined by the Central Bank.
It is an exogenously determined variable.
The demand for money is an endogenous relationship.
This is one of Keynes’ major innovations.
Figure 6.3 Determination of Equilibrium Interest Rates

82. Keynesian Theory of Money Demand
Keynes offered three reasons for why people hold money.
The transactions demand
The precautionary demand
The speculative demand
Classical economists considered money only as a medium of exchange (the transactions demand).
Keynes introduced the idea that money can be held as an asset—as a store of value.
This is his speculative demand.

83. Keynesian Theory of Money Demand
The transactions demand depends of the level of income.
Md = f(Y)
We assume prices are constant, so that the nominal money demand (Md) and the real money demand (Md/P) are the same. (Ms and Ms/P are also the same.)
The precautionary demand also depends on Y.
The speculative demand depends not on interest rates, per se, but on our expectations of what interest rates will be in the future.

84. The Relationship between Interest Rates and the Value of Assets
Define terms:
P = Annual interest payment
r = rate of interest
V = value of the asset.

85. The Relationship between Interest Rates and the Value of Assets
P = r x V.
Let V = $100 and r = 10%, then P = $10.
If r = 10% when a $100 bond (face value) is issued, then the predetermined P is $10.
P and the face value never change, but r can fluctuate on a daily basis for a variety of reasons.
What if r  to 11%?
Then V = P/r = $10/.11 = $90.90.
As r , V  and vice versa!
What happens if you try to sell your $100 bonds that pays a coupon rate of $10?

86. The Relationship between Interest Rates and the Value of Assets
You suffer a large capital loss?
Now consider what if r  to 9%?
Then V = P/r = $10/.09 = $
As r , V  and vice versa!
What happens if you try to sell your $100 bonds that pays a coupon rate of $10?
You earn a huge capital gain!
Why do people hold money for speculative purposes?
To take advantage of the changes in capital values when the interest rate fluctuates.

87. The Speculative Demand for Money
Keynes assumed that assets were held in two forms, bonds and money.
While this may be unrealistic, it is the only two options we have for holding assets in this particular version of the Keynesian model.
We hold money when interest rates are low and we fear that they might go up and cause us to suffer a capital loss.
We hold bonds when interest rates are high and we expect that they are more likely to go down than go up.
In essence we buy bonds when interest rates are high and bond prices are low.
We hold money when interest rates are low and bond prices are high.

88. The Speculative Demand
The individual's speculative demand for money is shown in part a. At any interest rate above the critical rate (rci), the speculative demand for money is zero.
Below the critical interest rate, the individual shifts into money.
Part b shows the aggregate speculative demand for money schedule (M2).
As the interest rate becomes lower, it falls below the critical rate for more individuals, and the speculative demand for money rises.
Figure 6.4 Individual and Aggregate Speculative Demand Curves for Money

89. The Total Demand for Money
Keynes Liquidity Preference function is:
Md = L(Y, r)
The equation takes the form of:
Md = c0 + c1Y – c2r
Where c0 is the intercept, + c1 is the slope with regard to Y, and – c2 is the slope with regard to r.
Both c1 and c2 are > 0.
At equilibrium, Ms = Md, where Ms is an exogenous policy variable. Therefore:
Ms = Md = c0 + c1Y – c2r is the equilibrium condition in the money market.

90. How Changes in Ms Affect Interest Rates
An increase in the money stock from Ms0 to Ms1 causes an initial excess supply of money.
How do people get rid of excess, unwanted cash?
They buy bonds, no matter what their expectations are.
What happens to the PBonds?
PBonds
r 
PBonds and r always move in opposite directions.
The interest rate falls from r0 to r1 to restore equilibrium in the money market.

91. Figure 6.5 Equilibrium in the Money Market