I am having trouble with c d & e. Answer c says \"derive the equation\" I think

Question

I am having trouble with c d & e. Answer c says "derive the equation" I think I am looking at NXa incorrectly.

Consider the following economy

Ca =   1800 ;  c = 0.8 ; T = 1200 + 0.20 Y; IP = 1800 ; G = 2000; NX = 600 – 0.08 Y.

a) What is the value of the autonomous Tax Ta ( Hint: see the formula and compare)

my answer - Ta = 1,200

b) Compute the value of the multiplier

my answer - mps = 1-c    1-.8 = .2 multiplier = 1/.2 multiplier = 5

c) Derive the equation of the autonomous spending

my answer - Ap = Ca - C*Ta+I+G+NXa

                    Ap = 1800 - .8(1200) + 1800 + 2000 + 600 = 5240

d) Find the equation of the IS curve

e) Compute the new IS curve when government spending increases by 100.What is the difference between the two IS curves?

Explanation / Answer

Consumption function:

C = Ca + c x (Y - T)

C = 1800 + 0.8 x (Y - 1200 - 0.2Y) = 1800 + 0.8 x (0.8Y - 1200)

Or,

C = 1800 - (0.8 x 1200) + 0.64Y = 840 + 0.64Y

(a) Correct. Autonomous tax = 1,200

(b) Correct. Multiplier = 1 / (1 - MPC) = 1/ 0.2 = 5

(c) Correct. An equation does not always involve variables (Y here), it can simply be a number on the right side.

(d) IS Curve:

Y = C + I + G + NX

= 840 + 0.64Y + 1800 + 2000 + 600 - 0.08Y

(1 - 0.64 + 0.08) Y = 840 + 1800 + 2000 + 600

0.44Y = 5,240

You can leave the equation in this form itself, or solve for it as follows:

Y = 5,240 / 0.44 = 11,909.09

(e) Now, G = 2000 + 100 = 2100

New IS curve is:

(1 - 0.64 + 0.08) Y = 840 + 1800 + (2000 + 100) + 600

0.44Y = 5,340

Y = 12,136.36

Difference between the IS curves = 12,136.36 - 11,909.09

= 227.27

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