Answer to Question #122851 in Macroeconomics for deep

Question

Suppose that the following equations describe an economy.

Y = Cd + Id + G
Cd = 180 + 0.8(Y – T)
Id = 140 – 8r + 0.1Y
T = 400
G = 400
(Md/P) = 6Y – 120i MS = 6000 i = πe + r

Assume expected inflation πe = 0 and price level P = 1.

.If government purchases (G) increases to $440, everything else held constant, find new equilibrium for output and interest rate.
What are effects of fiscal expansion above on consumption and investment? find the new levels of consumption and investment.
Instead of increasing the government purchases G, find new equilibrium values for output and the interest rate if the central bank increases the money supply to 6600. What are the effects of monetary expansion above on consumption and investment,find the new levels of consumption and investment)?
Judging from your answers to the previous questions, what are the differences in the effects of expansionary fiscal and monetary policies above on Y, i, C and I?

Answer 1

a) If government purchases (G) increases to $440, everything else held constant, find new equilibrium for output and interest rate.

Lets calculate the equilibrium income.

$$Y = C + I + G\\[0.3cm] Y = 180 + 0.8(Y - 400) + 140 - 8r + 0.1Y + 400\\[0.3cm] 0.1Y = 400 - 8r\\[0.3cm] Y = 4,000 - 80r.......................(i)$$

In the money market, money demand is equal to the money supply. Thus:

$$6Y - 120r = 6000\\[0.3cm] 6Y = 6000 + 120r\\[0.3cm] Y = 1000 + 20r...........................(ii)$$

Equating equations (i) and (ii):

$$4,000 - 80r = 1000 + 20r\\[0.3cm] 100r = 3,000\\[0.3cm] r^* = 30\%$$

Therefore:

$$Y^* = 1000 + 20(30)\\[0.3cm] Y^* = 1600$$

Recall that the multiplier is calculated as:

$$m = \dfrac{\Delta Y}{\Delta G} = \dfrac{1}{MPC}$$

From the consumption function, MPC = 0.8. Therefore:

$$\dfrac{\Delta Y}{\Delta G} = \dfrac{1}{1 - 0.8} = 5$$

If government purchases increases to $440, this means that:

$$\Delta G = 440 - 400 = 40$$

Therefore:

$$\dfrac{\Delta Y}{40} = 5\\[0.3cm] \Delta Y = 40\times 5 = 200$$

Thus, the new income is:

$$Y^{**} = Y^* + \Delta Y\\[0.3cm] Y^{**} = 1600+ 200 = \color{red}{1,800}$$

The new interest rate will be:

$$Y = 4,000 - 80r\\[0.3cm] 1,800= 4000 - 80r\\[0.3cm] -2,200= -80r\\[0.3cm] \color{red}{r^{**} = 27.5\%}$$

b) What are effects of fiscal expansion above on consumption and investment? find the new levels of consumption and investment.

The levels of consumption and investment will increase. The new levels are:

$$C = 180 + 0.8(1,800- 400)\\[0.3cm] \color{red}{C = 1300}$$

$$I = 140 – 8(27.5) + 0.1(1,800)\\[0.3cm] \color{red}{I = 100}$$

c) Instead of increasing the government purchases G, find new equilibrium values for output and the interest rate if the central bank increases the money supply to 6600. What are the effects of monetary expansion above on consumption and investment,find the new levels of consumption and investment)?

If the central bank increases the money supply to 6,600, then in the money market:

$$6Y - 120r = 6600\\[0.3cm] 6Y = 6600 + 120r\\[0.3cm] Y = 1100 + 20r$$

Therefore:

$$4,000 - 80r = 1100 + 20r\\[0.3cm] 100r = 2900\\[0.3cm] r^{**} = 29\%$$

The new income is:

$$Y = 1100 + 20(29)\\[0.3cm] Y^{**} = 1,680$$

The new consumption is:

$$C = 180 + 0.8(1,680- 400)\\[0.3cm] \color{red}{C = 1204}$$

The new investment is:

$$I = 140 – 8(29) + 0.1(1,680)\\[0.3cm] \color{red}{I = 76}$$

d) Judging from your answers to the previous questions, what are the differences in the effects of expansionary fiscal and monetary policies above on Y, i, C and I?

The decrease in interest rate under the expansionary fiscal policy is more than the change in the interest rate under the monetary policy. This means that the fiscal policy leads to a larger increase in investment as well as consumption compared to the monetary policy.