Question

In: Economics

The economy is represented by the following equations: Financial Sector: L=(Md/P)=4Y-120i (Ms/P)=$5,300 Real Sector: C=$120+0.8YD YD=Y-TA+TR...

The economy is represented by the following equations:

Financial Sector:

L=(Md/P)=4Y-120i

(Ms/P)=$5,300

Real Sector:

C=$120+0.8YD

YD=Y-TA+TR

TA=0.25Y

TR=100

I=$200-18i

G=$400

Y=AD=C+I+G

a). Solve for the equilibrium level of Y and i

b). If G increases from 400 to 430, find the new equilibrium Y and I

c). Using the equilibrium values from a). and b). calculate the Crowding Out effect from expansionary fiscal policy

d). Convert both the IS and LM curves from a). into slope-intercept form    

Solutions

Expert Solution

a)

IS curve is given by

Y = C + I + G

Y = 120 + 0.8YD + 200 - 18i + 400

Y = 720 + 0.8(Y - TA + TR) - 18i  

Y = 720 + 0.8(Y - 0.25Y + 100) - 18i

Y = 720 + 0.8Y(0.75Y + 100) - 18i  

Y = 720 + 0.6Y + 80 - 18i  

Y - 0.6Y = 800 - 18i  

0.4Y = 800 - 18i  

Y = 2000 - 45i  

Equation of IS curve is

Y = 2000 - 45i

LM curve is given by

Md/P = Ms/P  

4Y - 120i = 5300  

4Y = 5300 + 120i  

Y = 1325 + 30i

LM curve equation is

Y = 1325 + 30i

In Equilibrium YIS = YLM  

2000 - 45i = 1325 + 30i  

2000 - 1325 = 30i + 45i  

675 = 75i

i = 9

Y = 1325 + 30(9)  

Y = 1595

Equilibrium level of income is Y = 1595 and  

Equilibrium level of interest rate is i = 9

b)

Now G increases from 400 to 430

New equation of IS curve would be

Y = 120 + 0.8YD + 200 - 18i + 430

Y = 750 + 0.8(Y - TA + TR) - 18i  

Y = 750 + 0.8(Y - 0.25Y + 100) - 18i

Y = 750 + 0.8Y(0.75Y + 100) - 18i  

Y = 750 + 0.6Y + 80 - 18i  

Y - 0.6Y = 830 - 18i  

0.4Y = 830 - 18i  

Y = 2075 - 45i  

New equation of IS curve is

Y = 2075 - 45i

LM curve equation is

Y = 1325 + 30i

In Equilibrium YIS = YLM  

2075 - 45i = 1325 + 30i

2075 - 1325 = 30i + 45i

750 = 75i  

i = 10  

Y = 1325 + 30(10)

Y = 1625

The new equilibrium level of Y and i are 1625 and 10 respectively.

In fact Y = 1625 is the new equilibrium value of income when there is an interest rate effect. So we call this as

Y2 = 1625

when there is no interest rate effect then equilibrium value of income is given by  

Y/G = 1/(1 - c + ct)

c = 0.8  

t = 0.25

Y/G = 1/(1 - 0.8 + 0.80.25)  

Since G increases from 400 to 430 therefore G = 430 - 400 = 30  

Y/30 = 1/0.4

Y = 30/0.4

Y = 75  

New equilibrium level of income when there is no interest rate effect is Y1 = Y + Y = 1595 + 75 = 1670

c)  

Crowding out effect = Y1 - Y2 = 1670 - 1625 = 45

d)

We have

IS :  Y = 2000 - 45i

Y = 2000 - 45i  

45i = 2000 - Y  

i = 44.44 - 0.022Y

Slope intercept form of IS curve is

i = 44.44 - 0.022Y

Likewise

LM curve is

Y = 1325 + 30i

Y - 1325 = 30i  

0.033Y - 44.16 = i

Slope intercept form of LM curve is

i = 0.033Y - 44.16

Rahul Sunny answered 1 year ago
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