# Problem Set 3

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Economics
School
California Coast University
Type
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Problem 1. Suppose the economy is given by the following:
Consumption function: C= 26 + 0.6(Yd)
Investment function: I= 23-50r
Government spending: G = 10
Tax collections: T = 10
Exports schedule: X= 6- ϵ
Imports schedule: (IM) = 2 + 3ϵ
Money supply: M = 492
Nominal Money demand L(Y)= 5Y-50r
Price level=1
Labor supply=50
Production function=2N
QUESTIONS
a) Find the equation of the IS curve
Y = C + I + G + X - IM
Y = 26 + 0.6*(Y - 10) + 23 - 50r + 10 + 6 - ϵ - (2 + 3ϵ)
Y = 26 + 0.6*Y 6 + 23 - 50r + 10 + 6 2 - ϵ - 3ϵ
Y = 57 + 0.6Y - 50r - 4ϵ
Y = 142.5 125r 10 ϵ
Rearranging to obtain the IS curve equation:
r = 1.14 0.008Y 0.08 ϵ
b) Find the equation of the LM curve
M/P = L(Y)
492/1 = 5Y 50r
5Y = 492 = 50r
Y = 98.4 + 10r
Rearranging to obtain the equation of the LM curve:
r = 0.1Y-9.84
c) Find the equation for the AD
Y = 142.5 125r - 10 ϵ
R = 0.1Y 9.84
Y = 142.5 125*(0.1Y - 9.84) - 10 ϵ
Y = 142.5 12.5Y + 1230 - 10 ϵ
13.5Y = 1372.5 - 10 ϵ
Y= 101.67 0.74 ϵ
d) Plot the IS and LM equations in terms of r and Y

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e) Plot the IS and the LM equations in terms of ϵ
f) Find the equilibrium output and interest rate for this economy assuming a free
floating exchange rate regime and a world interest rate r* of 0.16.
R = 1.14 0.008Y 0.008 ϵ
R = 0.1Y 9.84
1.14 0.008Y 0.008 ϵ = 0.1Y 9.84
1.14 0.08 ϵ + 9.84 = (0.1 + 0.008)Y
Y = (10.98 0.08 ϵ) / 0.108
Y = 101.67 0.74 ϵ
As demonstrated by the graphs shown in part e, ϵ-=2
Y= 101.67 0.74*2 = 100.19
R = 0.1Y 9.84 = 0.1*100.19 9.84 = 0.179
R’ = r – r* = 0.179 0.16 = 0.019

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Problem 1. Suppose the economy is given by the following: Consumption function: C= 26 + 0.6(Yd) Investment function: I= 23-50r Government spending: G = 10 Tax collections: T = 10 Exports schedule: X= 6- ϵ Imports schedule: (IM) = 2 + 3ϵ Money supply: M = 492 Nominal Money demand L(Y)= 5Y-50r Price level=1 Labor supply=50 Production function=2N QUESTIONS a) Find the equation of the IS curve Y = C + I + G + X - IM Y = 26 + 0.6*(Y - 10) + 23 - 50r + 10 + 6 - ϵ - (2 + 3ϵ) Y = 26 + 0.6*Y – 6 + 23 - 50r + 10 + 6 – 2 - ϵ - 3ϵ Y = 57 + 0.6Y - 50r - 4ϵ Y = 142.5 – 125r – 10 ϵ Rearranging to obtain the IS curve equation: r = 1.14 – 0.008Y – 0.08 ϵ b) Find the equation of the LM curve M/P = L(Y) 492/1 = 5Y – 50r 5Y = 492 = 50r Y = 98.4 + 10r Rearranging to obtain the equation of the LM curve: r = 0.1Y-9.84 c) Find the equation for the AD Y = 142.5 – 125r - 10 ϵ R = 0.1Y – 9.84 Y = 142.5 – 125*(0.1Y - 9.84) - 10 ϵ Y = 142.5 – 12.5Y + 1230 - 10 ϵ 13.5Y = 1372.5 - 10 ϵ Y= 101.67 – 0.74 ϵ d) Plot the IS and LM equations in terms of r and Y e) Plot the IS and the LM equations in terms of ϵ f) Find the equilibrium output and interest rate for this economy assuming a free floating exchange rate regime and a world interest rate r* of 0.16. R = 1.14 – 0.008Y – 0.008 ϵ R = 0.1Y – 9.84 1.14 – 0.008Y – 0.008 ϵ = 0.1Y – 9.84 1.14 – 0.08 ϵ + 9.84 = (0.1 + 0.008)Y Y = (10.98 – 0.08 ϵ) / 0.108 Y = 101.67 – 0.74 ϵ As demonstrated by the gr ...
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