Question

In a open economy.

C = 25+0.92(Y-T)

Y=6755

G=164

T=104

I=1406-13r

NX=100-10e

r*=19

If r* change from 19 to 10

What will happen to Y, C, I, S?

Answer 1

In an open economy,

C = 25 + 0.92 (Y – T)

Y = 6755

G = 164

T = 104

I = 1406 – 13 r

NX = 100 – 10 e

r^* = 19

We know that, at equilibrium,

Y = C + I + G +NX

Or, 6755 = 25 + 0.92 (6755 – 104) + 1406 – (13 * 19) + 164 + 100 – 10 e

Or, 6755 = 25 + 6118.92 + 1406 – 247 + 264 – 10 e

Or, 10 e = 811.92

Or, e = 81.192 ...........................................(1)

So, when r^* = 19,

Y^* = 6755

C^* = 25 + 0.92 (Y – T) = 25 + 0.92 (6755 – 104) = 6143.92

I^* = 1406 – 13 r^* = 1406 – (13 * 19) = 1406 – 247 = 1159

And, we know that, at equilibrium,

I^* = S^*

So, S^* = 1159

Now, r_New^* = 10

At equilibrium,

Y = C + I + G +NX

Or, Y = 25 + 0.92 (Y – 104) + 1406 – (13 * 10) + 164 + 100 – (10 * 81.192)[because, e = 81.192, from equation (1)]

Or, 0.08 Y = 25 – 95.68 + 1406 – 130 + 264 – 811.92

Or, 0.08 Y = 657.4

Or, Y_New^* = 8217.5

C_New^* = 25 + 0.92 (Y – T) = 25 + 0.92 (8217.5 – 104) = 7489.42

I_New^* = 1406 – 13 r_New^* = 1406 – (13 * 10) = 1406 – 130 = 1276

And, we know that, at equilibrium,

I_New^* = S_New^*

So, S_New^* = 1276

Hope, all the mathematical derivations are clear to you. Thank You.