Answer to Question #215025 in Macroeconomics for Ike

Question

Given the following equations
C=50+0.8Yd
I=100
G=200
X=250
M=20+0.25Y
T=50+0.2Y
TR=100
a) calculate the equilibrium income and multiplier
b) calculate the budget stands
c) suppose the tax rate increase to 0.25. what will be new multiplier and equilibrium income.
d) calculate the change in budget stands.
e) would you expert the change in the budget stands to be more or less, if marginal propensity to consume were to be 0.9 and not 0.8.

Answer 1

$a)\\ At equilibrium,\\ Y = C + I + G + X - M\\ => Y = 50 + 0.5 ( Y - T + TR) + 100 + 200 + 250 - 20 - 0.25Y\\ => Y = 50 + 0.5 ( Y - 50 - 0.2Y + 100) + 530 - 0.25Y\\ => Y = 50 + 0.5 ( 0.8 Y + 50) + 530 - 0.25Y\\ => Y = 50 + 0.4Y + 25 + 530 - 0.25Y\\ => Y -0.4Y + 0.25Y = 605\\ => 0.85 Y = 605\\ => Y = \frac{605}{0.85}\\ => Y = 711.76\\ Equilibrium \space Income, Y = 711.76\\ Multiplier =\frac{ 1 }{ ( 1 - mpc + mpc\times t + mpi)} \\= \frac{1}{(1- 0.5 + 0.5\times 0.2 + 0.25) }\\= \frac{1}{0.85} \\= 1.18\\ b) T = 50 + 0.2\times 711.76 = 192.35\\ TR = 100\\ G = 200\\ Budget\space Deficit = TR + G - T = 300 - 192.325 \\= 107.648$$c)\\ Now,\space t = 0.25\\ So,\\ At \space equilibrium,\\ Y = C + I + G + X - M\\ => Y = 50 + 0.5 ( Y - T + TR) + 100 + 200 + 250 - 20 - 0.25Y\\ => Y = 50 + 0.5 ( Y - 50 - 0.25Y + 100) + 530 - 0.25Y\\ => Y = 50 + 0.5 ( 0.75 Y + 50) + 530 - 0.25Y\\ => Y = 50 + 0.375Y + 25 + 530 - 0.25Y\\ => Y -0.375Y + 0.25Y = 605\\ => 0.875 Y = 605\\ => Y = \frac{605}{0.875}\\ => Y = 691.43\\ Equilibrium \space Income, Y = 691.43\\ Multiplier = \frac{1 }{ ( 1 - mpc + mpc\times t + mpi)}\\ = \frac{1}{(1- 0.5 + 0.5\times 0.25 + 0.25)}\\ =\frac{ 1}{0.875}\\ = 1.14$

$d) T = 50 + 0.25\times 691.43 = 222.86\\ Budget \space Defecit = TR + G - T = 300 - 222.86 = 77.1425\\$

So, Change in Budget due to increase in tax rate$= 107.648 - 77.1425 = 30.5$

e)

Budget stand will be more if mpc increases from 0.8 to 0.9 because mpc and change in budget are positively related.