Question

Given the following information:
Consumption: 100 + 0.8 Yd
Investment: 150 – 16i
Govt. expenditure: 100
Taxes: 0.25Y
DD for money: 0.2Y – 2i
Nominal money supply: 300
Price level: 2
a) Determine equilibrium level of income and rate of interest
b) If govt expenditure increases by 50, what will be the new equilibrium of income and the
rate of interest?
c) Is there any crowding out? If yes, what is the extent of crowding out of income?

Answer 1

The Aggregate Demand is given by:

$AD = C + I + G = (100+0.8 Yd)+100+(150-16i)=(100 + 0.8x(Y-T))+100+(150-16i)=(100 + 0.8x(Y-0.25Y))+100+(150-16i)\\ AD=100+0.8x0.75Y+100+150-16i=350 + 0.6Y -16i$

Finally, we can derive the IS curve equation by setting the equilibrium condition: 

$AD = Y\\ Y = 350 + 0.6Y -16i$

So, the IS curve is given by: $Y = 875 - 40i$

 

Money demand is given by: $0.2Y - 2i$

Money supply is given by: Nominal money supply/Price $= \frac{300}{2} = 150$

Now, we can derive the LM curve, which is given by the equilibrium in money market. That is, 

$150 = 0.2Y - 2i$

So, the equation for the LM curve is:$Y = 750 + 10i$

a) Determine equilibrium level of income and rate of interest

For this, we just need to solve the system of equations given by the IS and LM curves:

$Y = 750 + 10i\\ Y = 875 - 40i\\ 750 + 10i = 875 - 40i \\ 50i = 125$

$i = 2.5.$ This is the equilibrium interest rate

$Y = 750 + 25 = 775$ . This is the equilibrium income.

b) If govt expenditure increases by 50, what will be the new equilibrium of income and the

rate of interest?

The new government expenditure is given by $100+50=150$

So now,

$AD = C + I + G = (100 + 0.8x(Y-0.25Y))+150+(150-16i) = 400 + 0.6Y -16i\\ AD = Y gives: Y = 400 + 0.6Y -16i\\ IS \space curve: Y = 1000 - 40i$

LM curve is same as before:

$Y = 750 + 10i$

Solving the two equations:

$750 + 10i = 1000 - 40i$

$50i = 250$

$i = 5.$ This is the new equilibrium interest rate

$Y = 750 + 50 = 800.$ This is the new equilibrium income.

c) Is there any crowding out? If yes, what is the extent of crowding out of income?

Since there is an increase in the interest rate, there will be a crowding out of investment. 

At the old equilibrium interest rate of 2.5: Investment $=150 – 16i = 150 - 40 = 110$

At the new equilibrium interest rate of 5: Investment $=150 – 16i = 150 - 80 = 70$

Thus there is a large crowding out and the extent of crowding out is given by: $110 - 70 = 40$