Question

8Consider first the goods market model with constant investment that we saw in

Chapter 3. Consumption is given by:

C = Co + c1(Y-T)

And I, G and T are given.

a. Solve for equilibrium output. What is the value of the multiplier?

Now let investment depend on both sales and the interest rate:

I = b0 + b1Y -b2i

b. Solve for equilibrium output using the methods learned in chapter 3. At a

given interest rate, why is the effect of a change in autonomous spending

bigger than what it was in part (a)? Why? (Assume c1 + b1 = 1)

c.Solve for equilibrium level of investment.

d. Let’s go behind the scene in the monetary market. Use the equilibrium in the

money market M/P = d1Y – d2i to solve for the equilibrium level of the real

money supply.

How does the real money supply vary with government spending?

Answer 1

a. The equilibrium output is:

$Y = C + G + I = Co + c1(Y-T) + G + I$

The value of the multiplier is: $m = \frac{1}{1 - c1}.$

I = b0 + b1Y -b2i

b. The equilibrium output is:

$Y = C + G + I = Co + c1(Y-T) + G + b0 + b1Y - b2i$.

At a given interest rate, the effect of a change in autonomous spending is bigger than what it was in part (a) because the multiplier effect now is higher.

c. In equilibrium investment equals saving, so:

$I = S,$

$b0 + b1Y - b2i = S.$

d. In equilibrium in the money market money demand equals money supply, so:

$M/P = Ms = d1Y – d2i.$

The real money supply increases if government spending increases.