MGEA06H3 Final: Ch10&11-AD1-Solutions
13 Dec 2018
School
Department
Course
Professor
1
Ch 10 - SOLUTIONS to Supplemental Notes and Exercises #1
1) Keynesian Cross & the Construction of the IS Curve
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)?
E = [ C
0
+ I
0
+ G
0
- C
1
T
0
] + C
1
Y - I
1
r Planned Expenditure Function (given r)
E = 800 + 0.6Y - 50r
When r = 4 (percent), E = 600 + 0.6Y
Equilibrium, Y = E, implies Y = 600 + 0.6Y
Y* = (600/0.4) = 1,500
When r = 6 (percent), E = 500 + 0.6Y
Equilibrium, Y = E, implies Y = 500 + 0.6Y
Y* = (500/0.4) = 1,250
If C
1
is decreased to C
1
= 0.5, then
E = 850 - 50r + 0.5Y
When r = 4 (percent), E = 650 + 0.5Y
Equilibrium, Y = E, implies Y = 650 + 0.5Y
Y* = (650/0.5) = 1,300
Note, here the IS Multipliers are: δY/δG = 1/[1 - C
1
] = 2.5 = δY/δC
0
= δY/δI
0
δY/δT = - C
1
/[1 - C
1
] = - 1.5
δY/δG = 1 (when δT = δG, balanced budget change)
These expressions are for the case when C
1
= 0.6. Note, when C
1
= 0.5 the last three
expressions above become 2, -1 and 1 respectively.
2
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? i.e., T is endogenous now (determined by/dependent on Y) and all of
the other inputs are the SAME as in part (a)
E = [ C
0
+ I
0
+ G
0
] - C
1
tY + C
1
Y - I
1
r Planned Exp Function (when r is given)
Equilibrium, Y = E, Y = [ C
0
+ I
0
+ G
0
] + C
1
(1-t)Y - I
1
r
Y( 1 - C
1
(1-t) ) = [ C
0
+ I
0
+ G
0
] - I
1
r
So, Y* = (1/[ 1 - C
1
(1-t) ])
[ C
0
+ I
0
+ G
0
] - (I
1
/[ 1 - C
1
(1-t) ])
r
IS Curve
Suppose that t = 0.4 and as before r = 4 (percent), C
0
= 100, C
1
= 0.6, I
0
= 500, I
1
= 50, and G
0
= 500.
Now the IS Curve slope = - [ 1 - C
1
(1-t) ]/(I
1
) = - 0.0128 (in part (a) it was - 0.008)
i.e. the IS Curve has become steeper
r = 4 (percent)
E = 900 + 0.36Y Planned Exp Function
Equilibrium, Y = E, Y = 900 + 0.36Y
Y* = (900/0.64) = 1,406.25
i.e. the equilibrium level of Y has fallen
IS Multipliers: δY/δG = (1/[ 1 - C
1
(1-t) ]) = 1.5625 = δY/δI
0
= δY/δC
0
δY/δt = (- C
1
/[ ( 1 - C
1
(1-t) )
2
])[ C
0
+ I
0
+ G
0
] - (- C
1
I
1
/[ ( 1 - C
1
(1-t) )
2
])r
= (-0.6/(0.64
2
))( 900) + 120/(0.64
2
) = - 1,025.39
(i.e. effect of 100% tax increase)
c) If C = C
0
+ C
1
(Y - T) - C
2
r, what is the IS Curve, its slope and the multipliers? Again all
other inputs are the SAME as in part (a).
E = [ C
0
+ I
0
+ G
0
- C
1
T
0
] + C
1
Y - C
2
r - I
1
r Planned Exp Function (when given r)
Equilibrium, Y = E,
Y = (1/[1 - C
1
])
[ C
0
+ I
0
+ G
0
- C
1
T
0
] - ({I
1
+ C
2
}/[1 - C
1
])
r
IS’ Curve
3
Note: (1) New slope = - ( [1 - C
1
]/{I
1
+ C
2
}) i.e. flatter IS Curve (as C
2
> 0)
(2) Same Multipliers as in part (a)
Flatter IS curve
Implies a lower Y in part (c) vs. part (a) (i.e.
for any given r and the same values of the
other parameters)
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). Again all other inputs are the same as in part (a), for example same
parameter values and NX
0
= 0 and NX
1
= 0.25.
E = [ C
0
+ I
0
+ G
0
+ NX
0
- C
1
T
0
] + C
1
Y - NX
1
Y - I
1
r Planned Exp Function
Y = (1/[1 + NX
1
- C
1
])
[ C
0
+ I
0
+ G
0
+ NX
0
- C
1
T
0
] - ( I
1
/[1 + NX
1
- C
1
])
r
IS’ Curve
New IS curve slope = - ( {1 + NX
1
- C
1
}/I
1
) = - 0.013 IS steeper than in part (a)
Government Spending Multiplier = δY/δG = (1/[1 + NX
1
- C
1
]) = 1.5385 lower than
part (a)
You will note that this is the SAME result that is referred to in Chapter 11 of the textbook
(i.e. smaller multipliers in the open economy). In the text, the point is that the full
multiplier in equilibrium is smaller now than in the past due to increased globalization
(i.e. more openness and greater economic integration internationally).
2
MGEA06H3 Full Course Notes
Verified Note
2 documents
Document Summary
Ch 10 - solutions to supplemental notes and exercises #1. Keynesian cross & the construction of the is curve. Suppose c0 = 100, c1 = 0. 6, i0 = 500, i1 = 50, and t0 = g0 = 500. E = [ c0 + i0 + g0 - c1t0 ] + c1y - i1(cid:1)r. When r = 4 (percent), e = 600 + 0. 6y. Equilibrium, y = e, implies y = 600 + 0. 6y. When r = 6 (percent), e = 500 + 0. 6y. Equilibrium, y = e, implies y = 500 + 0. 6y. If c1 is decreased to c1 = 0. 5, then. When r = 4 (percent), e = 650 + 0. 5y. Equilibrium, y = e, implies y = 650 + 0. 5y. Note, here the is multipliers are: y/ g = 1/[1 - c1] = 2. 5 = y/ c0 = y/ i0. Y/ t = - c1/[1 - c1] = - 1. 5.
