Question

1.

Suppose an economy is represented by the following equations:

C=500+.75(Y-T)

I=1000 -50r

(M/P)d=Y-200r

G=1000

T=1000

M=6000

P=2

Use these equations to derive both the IS and LM curves.  

Suppose that a newly elected president cuts taxes by 20%. Assuming that the money supply is held constant, what is the equilibrium interest rate in this economy? Round your answer to the nearest tenth. Do not use a percent sign when entering your answer. Your answer should not be given as a proportion (if you think the answer is that r=23% then you would input 23 rather than .23, for example).

2.

Suppose an economy is represented by the following set of equations:

C=500+.75(Y-T)

I=1000 -50r

(M/P)d=Y-200r

G=1000

T=1000

M=6000

P=2

Use these equations to derive both the IS and LM curves.  

Suppose that a newly elected president cuts taxes by 20%. Assuming that the money supply is held constant, what is the equilibrium output in this economy?

Please do not use a comma in your answer.

Answer 1

IS curve is given by

Y = C + I + G

= 500 + 0.75(Y - T) + 1000 - 50r + 1000

= 2500 + 0.75(Y - 1000) - 50r

= 2500 + 0.75Y - 750 - 50r  

= 1750 + 0.75Y - 50r

Y - 0.75Y = 1750 - 50r

0.25Y = 1750 - 50r

Y/4 = 1750 - 50r

Y = 7000 - 200r  

LM curve is given by

(M/P)^d = (M/P)^s  

Y - 200r = 6000/2

Y - 200r = 3000

Y = 3000 + 200r  

In equilibrium Y_IS = Y_LM

7000 - 200r = 3000 + 200r

7000 - 3000 = 200r + 200r

4000 = 400r

r = 4000/400

= 10

Y = 3000 + 200(10)

= 3000 + 2000

= 5000

So equilibrium output and interest rate are 5000 and 10 respectively.

Now Taxes are cut by 20% by newly elected president  

So new taxes T = 1000 - 200 = 800 where 200 = 20%of 1000

NEW IS Curve will be

Y = C + I + G

=   500 + 0.75(Y - T) + 1000 - 50r + 1000  

= 2500 + 0.75(Y -T) - 50r

= 2500 + 0.75(Y - 800) - 50r

= 2500 + 0.75Y - 600 - 50r  

= 1900 + 0.75Y - 50r  

Y - 0.75Y = 1900 - 50r

0.25Y = 1900 - 50r

Y/4 = 1900 - 50r  

Y = 7600 - 200r

In equilibrium Y_IS = Y_LM  

7600 - 200r = 3000 + 200r

7600 - 3000 = 200r + 200r

4600 = 400r

r = 4600/400

= 11.5

Y = 3000 + 200(11.5)

= 3000 + 2300

= 5300

So new equilibrium output and interest rate are 5300 and 11.5 respectively.

Finally we can say that this tax cut causes to increase in equilibrium output from 5000 to 5300 as well as equilibrium interest rate from 10 t0 11.5