Answer to Question #198374 in Macroeconomics for mahi

Question

C 150+0.5Y.

1 = 300-150r.

Ms = 500,

L=0.50y+200-150r of which kPY = 0.50y and hr = 200-150r.

TAX = 50

GOVERNMENT EXPENDITURE = 500

Find (a) the equilibrium level of income and the equilibrium rate of interest, and

(b) the level of C, I, and L when the economy is in equilibrium.

(c) If the money supply increases from 500 to 600, What happen to the equilibrium level of income and the equilibrium rate of interest

What are C,I, KPY and hr at the new equilibrium?

(d) If autonomous investment falls from 300 to 150, what will happen on our entire economy?

Answer 1

(a) the equilibrium level of income and the equilibrium rate of interest

$Y=C+I+G$

$$=150+0.5Y+300-150r+500$$

$Y=0.5Y+925-150r$

$$Y=150+0.5(Y-T)+300-150r+500$$

$Y=150+0.5Y-0.5T+300-150r+500$ $Y=0.5Y+925-150r$

$0.5Y=925-150r$

$Y=1850-300r$ $...........(i)$

Finding Income Y

$kPY=Ms$

$0.50Y=500$

$Y=\frac{500}{0.5}=1000$

$Y=1000$

Finding r( interest rate)

Use equation (i)

Y=1000

Therefore the equation becomes

$1000=1850-300r$

$r= \frac{850}{300}= 2.8$

(b) the level of C, I, and L when the economy is in equilibrium

here, we replace the values of Y and r accordingly as shown below.

$C=150+0.5(1000)$

$C=650$

$I = 300-150(2.83)$

$I=-124.5$

$L=0.5(1000)+200-424.5$

$L=276$

(c) If the money supply increases from 500 to 600, What happen to the equilibrium level of income and the equilibrium rate of interest

increase in the supply of money from 500 to 600 increases the equilibrium level from 1000 to 1200.

The interest rate is lowered from 2.83 to 2.16

What are C,I, KPY and hr at the new equilibrium?

$C=150+0.5(1200)$

$C=750$

$I=300−150(2.16)$

$I=-25$

$KPY= 0.50Y$

$hr= 200-150(2.16)$

$hr= 125$

If autonomous investment decreases from 300 to 150 the national income does not change because income does not affect autonomous investment. However, there will be increase in investment expenditures. The interest rates increase hence increasing the cost of borrowing.