MGEA06H3 Study Guide - Final Guide: Keynesian Cross, Expenditure Function, Real Interest Rate
13 Dec 2018
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Ch 10 - Supplemental Notes and Exercises #1
1) The Keynesian Cross - A simple model of SR income determination. Keynes postulated
that in the SR an economy’s aggregate (real) income was determined largely by the desire
to spend by households, firms, and the government.
Thus, the problem during recessions and depressions, according to Keynes, was inadequate
spending. The Keynesian cross is an attempt to model this insight. Put another way, Keynesians
believe that AD Shocks (that cause AD to be too low or high) are the primary drivers of the
business cycle. This implies that there may be an important role for the government to attempt to
mitigate the business cycle (i.e. when AD is too low the government could try to buy the way out
of a recession by increasing G, cutting T, or increasing M
s
either of which would stimulate AD).
Lastly, the IS Curve plots the relationship between the real interest rate (r) and the level of real
income (Y) that arises when the market for goods and services is in equilibrium.
The Keynesian Cross can prove useful in deriving the IS Curve. Lets look at a simple example,
imagine that the following equations describe our economy:
Planned Expenditure, E = C + I + G (i.e. Closed economy S.T. NX = 0)
C = C
0
+ C
1
(Y - T) I = I
0
- I
1
r
G = G
0
and T = T
0
E = [ C
0
+ I
0
+ G
0
- C
1
T
0
] + C
1
Y - I
1
r Planned Expenditure Function
(given an r)
Equilibrium: Actual Expenditure = Income = Y = Planned Expenditure = E
Y = E
Y = [ C
0
+ I
0
+ G
0
- C
1
T
0
] + C
1
Y - I
1
r
(1 - C
1
)Y = [ C
0
+ I
0
+ G
0
- C
1
T
0
] - I
1
r
Y = (1/[1 - C
1
])
[ C
0
+ I
0
+ G
0
- C
1
T
0
] - (I
1
/[1 - C
1
])
r IS Curve
Given a value for r, the above expression yields the Keynesian Cross (SR) equilibrium level of
real aggregate output (for example, if r = 5 percent then equilibrium Y is determined). If r
changes then the curve shifts as does the resulting equilibrium level of aggregate real output Y*.
δY = (1/[1 - C
1
])[ δG - C
1
δT ] where 0 < C
1
= MPC < 1
δY/δG = 1/[1 - C
1
] The Government Expenditure Multiplier
(i.e. δT = 0 )
δY/δT = - C
1
/[1 - C
1
] The Tax Multiplier (i.e. δG = 0 )
If δG = δT, then δY/δG = 1 The Balanced Budget Multiplier
(i.e. δG = δT )
Exercises:
a) Suppose C
0
= 100, C
1
= 0.6, I
0
= 500, I
1
= 50, and T
0
= G
0
= 500. What is the planned expenditure function?
If r = 4 (percent) what is the resulting equilibrium output? If r = 6 (percent) what is the resulting equilibrium
output (in the goods and services market)?
b) Suppose r = 4 percent solve for the equilibrium level of aggregate real output when T = tY, where 0 < t <1 is
the income tax rate. What is the slope of the IS curve and the multipliers?
c) If C = C
0
+ C
1
(Y - T) - C
2
r, what is the IS Curve, its slope and the multipliers?
d) If NX = NX
0
- NX
1
Y, what is the IS Curve, its slope and the multipliers? (Later you can let NX
1
= 0.25).
2
MGEA06H3 Full Course Notes
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Document Summary
Ch 10 - supplemental notes and exercises #1. The keynesian cross - a simple model of sr income determination. Keynes postulated that in the sr an economy"s aggregate (real) income was determined largely by the desire to spend by households, firms, and the government. Thus, the problem during recessions and depressions, according to keynes, was inadequate spending. The keynesian cross is an attempt to model this insight. Put another way, keynesians believe that ad shocks (that cause ad to be too low or high) are the primary drivers of the business cycle. Lastly, the is curve plots the relationship between the real interest rate (r) and the level of real income (y) that arises when the market for goods and services is in equilibrium. The keynesian cross can prove useful in deriving the is curve. Lets look at a simple example, imagine that the following equations describe our economy: Planned expenditure, e = c + i + g.
