Question

QUESTION 1 (2,000 pts)

Suppose the Jewett-Stahanczyk-Gonzalez economy can be described by the following values:

"C" ̅" = 200",

(" I " ) ̅"= 240"      "G" ̅" = 145" "T" ̅" = 160"   ("NX" ) ̅" = 100"

mpc = 0.75,    c = 5 ,    d = 30 ,    x = 15

a)     Solve for the equation for the IS curve (call it IS₁). Show at least three lines of derivation.

b)     Consider the situation where the goods and services market is in equilibrium. Calculate the real GDP if the real interest rate is 5% (that is, r = 0.05). (Consider this as point A)

c)    Consider the situation where the goods and services market is in equilibrium. Calculate the real GDP if the real interest rate is 10% (that is, r = 0.1). (Consider this as point B)

Suppose the government now decides to run a budget deficit of $30 without changing taxes.

d) Solve for the new equation for the IS curve (call it IS₂).

e)     Consider the situation where the goods and services market is in equilibrium after the policy change. Calculate the real GDP if the real interest rate is 5% (that is, r = 0.05). (Consider this as point C)

f)     Calculate the government spending multiplier.

g) Neatly sketch the IS curves from parts a and e, labeling them IS₁ and IS₂, respectively. Make sure to show points A, B, and C in the diagram

Answer 1

a). equation for IS₁ is given as follows:

Y = + mpc(Y - T) - c.r + - d.r + G + - x.Y

Y = 200 + 0.75(Y - 160) - 5r+ 240 - 30r + 145 + 100 - 15Y

Y+ 15Y -0.75Y = 200 - 120 - 5r + 240 - 30r + 245

15.25Y = 565 - 35r

Y= 37.04 - 2.29r

b). if r=0.05, then

Y = 37.04 -2.29(0.05) = 36.93 point A

c). if r=0.1,then Y= 36.81 point B

d). Budget deficit of $30 means G - T = 30

G - 160 = 30

G= 190

new IS₂ equation is given as below:

Y = + mpc(Y - T) - c.r + - d.r + G + - x.Y

Y = 200 + 0.75(Y - 160) - 5r+ 240 - 30r + 190 + 100 - 15Y

Y = 40 - 2.29r

e). when r=0.05

Y = 40 - 2.29(0.05) = 39.89 point C

f). government spending multiplier is given as:

Y = G 1/(1- mpc) = 45 1/(1- 0.75) = $180

g).