Question

Assume that the consumption function is given by

C_t = 150 + 0.75(Y_t – T)

I = 250; G = 500; T = 500

(2 point) Write down the planned expenditure as a function of current output/income (Y_t):

PE (Y_t+1) = ____________________________________.

(4 points) What is the equilibrium level of income? Show your work.

(4 points) If G increases to 550, what is the new equilibrium level of income? Show your work.

Given

Yt+1=Ct+I+G

Ct=50+0.8(Yt-T)

I = 200 – 5r

MD = Y – 25r

G = 300, T = 350, M = 2500.

(5 points) Derive the goods market equilibrium (IS curve) function. Show your work clearly.

(5 points) Derive the money market equilibrium (LM curve) function. Show your work clearly.

(5 points) What are the equilibrium level of output/income and interest rate? Show your work clearly.

(5 points) Graph the IS and LM curves derived in a and b respectively. Note: you need to clearly label two points of each curve.

Answer 1

Question 1

(a)

Calculate the Planned expenditure as a function of current output/income (Yt) -

PE(Yt+1) = Ct + I + G

PE = 150 + 0.75(Yt - T) + 250 + 500

PE = 150 + 0.75(Yt - 500) + 250 + 500

PE = 150 + 0.75Yt - 375 + 250 + 500

PE = 0.75Yt + 525

(b)

At equilibrium,

Yt = PE

Yt = 0.75Yt + 525

Yt - 0.75Yt = 525

0.25Yt = 525

Yt = 525/0.25 = 2,100

The equilibrium level of income is 2,100.

(c)

Now, G increases to 550

PE(Yt+1) = Ct + I + G

PE = 150 + 0.75(Yt - T) + 250 + 550

PE = 150 + 0.75(Yt - 500) + 250 + 550

PE = 150 + 0.75Yt - 375 + 250 + 550

PE = 0.75Yt + 575

At equilibrium,

Yt = PE

Yt = 0.75Yt + 575

Yt - 0.75Yt = 575

0.25Yt = 575

Yt = 575/0.25 = 2,300

The new equilibrium level of income is 2,300.