find equilibrium level of income

Question

C = 100 + .9yd

T = 100

I = 150

G = 200

Yd = Y- Y

Answer 1

Hi Daniel - this is an algebra problem once you set it up.  The key is that aggregate expenditure, AE, equals Y in equilibrium.  AE = C + I + G + NX.  In this problem you have autarky, or NX = 0, so AE = C + I + G.  Here are the steps:

In equilibrium, Y = AE, or

Y = C + I + G

First put in the formula for C:

Y = 100 + 0.9(Y - T) + I + G

Next, plug in the knowns and solve for Y:

Y = (100 + 0.9Y - 0.9*100) + 150 + 200

Y = 450 - 90 + 0.9Y

Y = 360 + 0.9Y

0.1Y = 360, therefore:

Y = 3,600 in equilibrium.