Question

A is an open economic in a long run.

C = 25+0.92(Y-T)

Y=6755

G=164

T=104

I=1406-13r

NX=100-10e

r*=19

If r* change to 10, and NX change to 200-10e

Find impact on ouptut and real exchange rate and all other aggregate variables.

Provide the status quo and the change brought in. numerical, diagrams and interpretation are required

Is this a good thing or not?

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

NX = 100 - 10 e = 100 - 811.92 = -711.92

Now, r_New^* = 10 , NX_New = 200 - 10 e

At equilibrium,

Y = C + I + G +NX

Or, Y = 25 + 0.92 (Y – 104) + 1406 – (13 * 10) + 164 + 200 – (10 * 81.192)[because, e = 81.192, from equation (1)]

Or, 0.08 Y = 25 – 95.68 + 1406 – 130 + 364 – 811.92

Or, 0.08 Y = 757.4

Or, Y_New^* = 9467.5

C_New^* = 25 + 0.92 (Y – T) = 25 + 0.92 (9467.5 – 104) = 8639.42

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

NX_New = 200 - 10 e = 200 - 811.92 = - 611.92

∆ = Final Impact – Initial Impact

∆NX = NX_New – NX = (- 611.92) – (- 711.92) = 100

∆Y = Y_New^* - Y^* = 9467.5 – 6755 = 2712.5

∆r = r_New^* - r^* = 19 – 10 = 9

∆I = I_New^* - I^* = 1276 – 1159 = 117

∆S = S_New^* - S^* = 1276 – 1159 = 117

∆C= C_New^* - C^* = 8639.42 – 6143.92 = 2495.5

Y has inceased, also C, S, I and NX has increased. It is obviously a good thing. The economy is expanding.

IS_OLD : Y = 25 + 0.92(Y – 104) + 1406 – 13 r + 164 + 100 – 10 e

So, 0.08 Y = 25 - (0.92 * 104) + 1406 – 13 r + 264 – 10 e

dY/dr = - 13/0.08

So, slope of IS_OLD = dr/dY = - 0.08/13 = - 0.0062 (approx)

IS_NEW : Y_NEW = 25 + 0.92(Y – 104) + 1406 – 13 r_NEW + 164 + 200 – 10 e

So, 0.08 Y_NEW = 25 - (0.92 * 104) + 1406 – 13 r_NEW + 364 – 10 e

dY_NEW/dr_NEW = - 13/0.08

So, slope of IS_NEW = dr_NEW/dY_NEW = - 0.08/13 = - 0.0062(approx)

So, both the slope of the IS curves are the same.

So, IS_NEW is a rightward shift of IS_OLD whose slope is - 0.0062.