open economy equilibrium solve

Taking into account the following:

C= Ca = 0.75 (Y-T)
Ca = 1000- 20r
Ip = 600 – 20r
T = 400 + 0.15Y
M = 500 + 100 e + 0.0375Y
G = 1,000
X = 400 – 100e + 0.01Yf
(M/P)d = 0.4Y – 40r
Ms/P = 2,000

E = 2
Yf = 100,000
X = exports
M = imports

Please show all your work and answer the following:

a) What are the equations for IS and LM curves? What is the equilibrium income and interest rate?

b) Suppose foreign income rise to 108,000 and the interest rate is allowed to temporarily diverge from the world economy’s interest rate. Whatr are the equations for IS and LM curves? What is the new equilibrium income and interest rate?

c) Suppose that the exchange rate is flexible. Assuming no change in fiscal or monetary policy, how much would you expect the exchange rate to change in response to the increase in foreign incomes? Please show numberical calculations for this answer.

d) Suppose the exchange rate is flexible. If economic policy makers would like to avoid a change in the real exchange rate due to the increase in foreign income, what policy option should they pursue? Please explain using an IS-LM diagram.

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