Access over 20 million homework & study documents

Problem Set 3

Content type
User Generated
Subject
Economics
School
California Coast University
Type
Homework
Rating
Showing Page:
1/9
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

Sign up to view the full document!

lock_open Sign Up
Showing Page:
2/9
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

Sign up to view the full document!

lock_open Sign Up
Showing Page:
3/9

Sign up to view the full document!

lock_open Sign Up
End of Preview - Want to read all 9 pages?
Access Now
Unformatted Attachment Preview
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 ...
Purchase document to see full attachment
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Anonymous
I was having a hard time with this subject, and this was a great help.

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4