Question

1. Assume the money sector can be described by the following two equations:

           md = (1/4)Y - 10i   and ms = 400.

     In the expenditure sector only investment spending (I) is affected by the interest rate (i), and the equation of the IS-curve is: Y = 2,000 - 40i.

1. Assume the size of the expenditure multiplier is a = 2. What is the effect of an increase in government purchases by DG = 200 on income and the interest rate?   

2. Can you determine how much investment is crowded out as a result of this increase in government purchases?

3. If the money demand equation were changed to md = (1/4)Y, how would your answers in a. and b. change?

Answer 1

Solution:

Equilibrium in money market occurs where md = ms

(1/4)Y - 10i = 400

So, we have Y = 4*(400 + 10i)

Y = 1600 + 40i

Now, with increase in government expenditure of 200, with multiplier of 2, this increases aggregate demand by 2*200 = $400

So, new IS curve: Y = (2000 + 400) - 40i = 2400 - 40i

Initial equilibrium i can be found as: 1600 + 40i = 2000 - 40i

So, i = 400/80 = 5

Then, Y = 1600 + 40*5 = $1,800

Now, an increase in government spending will result in new equilibrium as:

1600 + 40i = 2400 - 40i

i = 800/80 = 10

Y = 1600 + 40*10 = $2,000

Notice that with increase in spending, Y should have increased by $400 (as shown through multiplier), but due to crowding out effect of decrease in investment as a result of increase in interest rate (since interest affects only investment, so entire effect through interest rate can be accrued to investment spending), Y has actually increased by (2000 - 1800 =) $200 and not $400.

So, investment worth $200 has been crowded out.

If md is changed to the function indicated as given, it means that money demand is not affected by interest rate. In other words, LM curve will be a vertical straight line at (1/4)Y = 400

Y = 400*4 = $1,600

So, the increase in government spending, shifting the IS curve outward, so the entire government spending increase effect will be crowded out by decreased investment, giving the result as unchanged equilibrium Y and only increased interest rate level.

Mathematically, LM and IS intersection occurs at:

1600 = 2000 - 40i

i = 400/40 = 10

After shift in IS: 1600 = 2400 - 40i

i = 800/40 = 20

So, new Y = 2400 - 40*20 = $1,600 which is unchanged!