Question

c = 100 + 0.8 (y - t)

i = 500 - 50r

g = 400

t = 400

M^d = P(0.2y + 500 – 25r)

Price level is fixed at 1.

The money supply is 520

1. The central bank increases the money supply by one unit.
2. Calculate the change in aggregate expenditures.
3. How far does the aggregate demand curve shift?   
4. What is the change in the interest rate and investment?
5. What is the change in consumer expenditure?
6. What is the change in the government budget balance, and why?

Answer 1

IS equation:

y = c+ i + g

y = 100 + 0.8(y-t) + 500 -50r +400

y = 100 + 0.8(y-400) + 500 -50r +400

y = 100 + 0.8y - 320 + 500 - 50r +400

y = 680 + 0.8y -50r

0.2y = 680 - 50r

y = 3400 - 250r

LM equation:

Ms/P = Md

520/1 = (0.2y + 500 – 25r)

520 = 0.2y + 500 - 25r

0.2y = 20 + 25r

y = 100 + 125r

At equilibrium : IS = LM

3400 - 250r = 100 + 125r

375r = 3300

r = 8.8

y = 100 + 125*8.8 = 1200

c = 100 + 0.8 (y - t) = 100 + 0.8(1200-400) = 740

i = 500 - 50r = 500 - 50*8.8 = 60

g = 400

t =400

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Now consider money supply increase by one unit such that Ms=521

New LM equation:

Ms/P = Md

521/1 = (0.2y + 500 – 25r)

521 = 0.2y + 500 - 25r

0.2y = 21 + 25r

y = 105 + 125r

Given, IS equation , new equilibrium is: IS = LM

3400 - 250r = 105 + 125r

375r = 3295

r = 8.78667

y = 100 + 125*8.78667 = 1198.333

c = 100 + 0.8 (y - t) = 100 + 0.8(1198.333-400) = 738.6667

i = 500 - 50r = 500 - 50*8.78667 = 60.66667

g = 400

t =400

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Calculate the change in aggregate expenditures:

1198.333 - 1200 = -1.66667

How far does the aggregate demand curve shift:  

The aggregate expenditure shift to an extent of change in aggregate expenditure as P=1, that is -1.66667

What is the change in the interest rate and investment:

Change in interest rate: 8.78667 - 8.8 = - 0.01333

Change in investment = 60.66667 - 60 = 0.66667

What is the change in consumer expenditure:

738.6667 - 740 = -1.333

What is the change in the government budget balance: There is no change in government budget balance , that is remains zero,as both g and t are independent of y