Question

Assume the money sector can be described as

money demand=(1/4)Y-10i

money supply=400

IS equation:Y=2000-40i

(a) if multiplier is 2 what is the effect of increase in government purchases by 200 on income and interest rate?

(b) can you determine how much investment is crowded out as a result of this increase in government purchases

(c) if money demand equation were changed to [money demand=(1/4)Y, how would your answer in (a) and (b) change?

Answer 1

$Given \rightarrow\space LM-curve$

$md=\frac{1}{4}Y-10i$ $\space ms=400$

The LM curve can be written as:

$\frac{1}{4}-10i=400\implies Y=1600+40i..............................(1)$

IS curve

$Y=2000-40i............................................................(2)$

To find equilibrium level of Y and i we have to equate (1)=(2)

$1600+40i=2000-40i\\40i+40i=400\\80i=400\\i=\frac{400}{80}=5\%\\Y=2000-40(5)=1800$

a.

multiplier=2 government purchases increases by 200

therefore, the change in Y when there is a change in government spending can be written as

$\Delta Y = multiplier \times \Delta G\\\implies \Delta Y=2\times 200 \implies \Delta Y=400$

Therefore, the IS curve shifts to the right for every interest rate, Y increases by 400 units than before hitting new values in (2)

Now IS con be constructed using the values in the above table above

$Y-200=\frac{2400-2000}{0-10}(i-10)\\\implies4-2000=\frac{400}{-10}(i-10)\\\implies Y-200=-40i+400\\\implies Y=2400-40i...............................(3)$

(3) represents the new equation

solving (1) and (3)

$1600+40i=2400-40i\\\implies 40i+40i=2400-1600\\\implies 80i=800\\\implies i=\frac{800}{80}\implies i'=10\%\\\implies Y=2400-(40\times10)\implies Y'=2000$

Therefore, the interest rate increase from 5% to 10% and income increase from 1800 to 2000.

b.

As the government purchases increases, the interest rate increases, leading to a fall in private investment (as investment falls with rise in interest rate.) The private firms will continue to borrow on the original IS curve (2).

Hence it can be obtained by plugging the value of new interest rate in (2).

$\therefore\space private \space investment=2000-40\times10=1600$

The fall in private investment $=1800-1600=200$

Hence investment crowded out 200

c.

If $md=\frac{1}{Y},$

Then LM curve $\implies 0.25Y=400\implies Y=1600...................4$

Equating (4) with (3)

Therefore, when Y doesn't depend on i, then interest rate changes to 20% and Y changes to 1600

Putting the new interest rate on the old is eqn(2),

we get:

$Y''=2000-40\times20=1200$