Prof. Gustavo Indart
Department of Economics
University of Toronto
ECO 100Y
INTRODUCTION TO ECONOMICS
Solution to Problem Set 13
Problem 1
a)
AE
AE
380
A
200
b
B
45
E
200
400
Y
b)
Consider the triangle A in the above diagram. The hight of this triangle is 380 –
200 = 180 and its base is 400 – 200 = 200. Therefore the slope of the
hypothenus is 180/200 = 0.9.
c)
If equilibriuim GDP is 200 and the potential GDP is 400, we have a recessionary
gap of 200.
d)
If the slope of the AE curve is 0.9, the simpleKeynesian) expenditure multiplier is
β
= 1 / (1 – 0.9) = 10. Therefore,
∆
Y =
β∆
G or 200 = 10
∆
G, and
∆
G = 20.
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2
Problem 2
a)
The savings function is S = –10 + sYD, where s = 1 – c is unknown. But when YD
= 400, S = 70. Therefore, 70 = –10 + s(400) or s = 80/400 = 0.2. Accordingly, c =
1 – 0.2 = 0.8.
b)
YD = Y – TA, and therefore
∆
YD
∆
Y –
∆
TA. If
∆
TA = –10, then
∆
YD = –(–10) =
10. Therefore,
∆
C = c
∆
YD = 0.8(10) = 8.
c)
If prices increase, real wealth will decrease. Since individuals accumulate wealth
to be able to maintain a certain level of consumption after they retire, the
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 Fall '09
 INHEART
 Economics, Harshad number, AE curve, Prof. Gustavo Indart, Department of Economics University of Toronto

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