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

- The central bank increases the money supply by one unit.
- Calculate the change in aggregate expenditures.
- How far does the aggregate demand curve shift?
- What is the change in the interest rate and investment?
- What is the change in consumer expenditure?
- 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

------------------------------------------------------------------------------------------------------

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

--------------------------------------------------------------------------------

**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

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