Answer to Question #246456 in Macroeconomics for Manish

Question

Now we look at the role taxes play in determining equilibrium income. Suppose we have an 

economy of the type in Sections 9-4 and 9-5, described by the following functions:

C -

 50  .8YD

 −

I -

 70 

 −−G -

 200

 −−TR -

 100

 t -

 .20 

 a. Calculate the equilibrium level of income and the multiplier in this model. 

 b. Calculate also the budget surplus, BS.

c. Suppose that t increases to .25. What is the new equilibrium income? The new multiplier? 

 d. Calculate the change in the budget surplus. Would you expect the change in the surplus 

to be more or less if c -

 .9 rather than .8? 

 e. Can you explain why the multiplier is 1 when t -

 1?

Answer 1

a) Equilibrium

Y=C+I+G

Y=50+0.8(Y-T)+70+200

Y=50+0.8(Y-0.20Y)+270

Y=320+0.8Y*0.8

Y-0.64Y=320

0.36Y=320

Y=888.89

$Multiplier =\frac{1}{1-mpc+mpc*t} =\frac{1}{1-0.8+0.8*2} =\frac{1}{0.36} = 2.78$

b)

Budget Surplus = T - G - TR

=0.204Y-200-100

=0.2*888.89-300

= 177.78 - 300

= -122.22

c)

t = 0.25

Y=50+0.8(Y-0.25Y)+70+200

Y=50+0.8(0.75Y)+270

Y=320+0.6Y

0.4Y=320

Y=800

$New multiplier =\frac{1}{1-mpc+mpc\cdot t} =\frac{1}{1-0.8+0.25-0.8} =\frac{1}{0.2+0.2} =\frac{1}{0.4} = 2.5$

d)

Budget surplus

= 0.25 * 800 - 200 - 100

= -100

when t = 0.25 & mpc or c = 0.9

Y=50+0.9(Y-0.25Y)+70+200

Y=320+0.9*0.75Y

Y=320+0.675Y

0.325Y=320

Y = 984.61

Budget surplus = 0.25 * 984.61 - 200 - 100

= -53.85

Budget surplus increases when c = 0.9

e)

$Multiplier =\frac{1}{1-c+ct} =\frac{1}{1-0.8+0.8*1} =\frac{1}{1} = 1$