IAI May 2010 Q32

[dextar]

An economy is characterized by following equations:
C = 100 + cYd =100 + 0.75Yd,
I = 45,
G = 80,
T = 20 + 0.20Y,
R = 40,
X = 40,
M = 30 + 0.10Y,
where C is consumption function, c is marginal propensity to consume, Yd is
Disposable income (Y – T + R), I is autonomous investment, G is autonomous
government purchases, T is tax function, Y is level of income, R is autonomous
transfer payments by the government, X is autonomous exports, M is import function.
Find equilibrium income.

I approached it as
Y=Cd+W=Cd+S+T+M
but solution is saying
Y= C+ c(Y – T –tY + R) + I + G +X – M – mY

Can anyone pls explain this expression.

 

[Margaret Wood]

This is a really difficult question and one that should no longer be asked. The aggregate demand function used in the textbook is much simpler as consumption is now a function of national income rather than disposable income.

There are two ways of finding the equilibrium income:

(1) aggregate demand = aggregate supply
(2) planned injections = planned withdrawals.

I think you were trying to do the second method (though I think you wrote W where you should have had J, ie Y=Cd +J=Cd+W, which comes down to finding Y such that J=W).

Using (1) as the examiners have done:

Agg demand = Agg supply (output=GDP=Y)
C+I+G+X-M = Y
100+0.75Yd +45+80+40 -30-0.1Y = Y
235 +0.75Yd-0.1Y = Y
235+0.75(Y-T+R)-0.1Y = Y
235+0.75(Y-20-0.2Y+40)-0.1Y = Y
235+0.75(20+0.8Y)-0.1Y = Y
235+15+0.6Y-0.1Y = Y
250+0.5Y = Y
So Ye = 500.

Using (2) J=W, which is probably harder in this case:

J = I+G+X = 45+80+30 = 165

W = S+T*+M where T* = T-R
S = Y-C=Y-(100+0.75Yd) = -100+0.25Yd
= -100+0.25(Y-T+R) = -100+0.25(20+0.8Y)
= -100+5+0.2Y = -95+0.2Y
T*= 20+0.2Y-40 = -20+0.2Y
M = 30+0.1Y
So W =-95+0.2Y-20+0.2Y+30+0.1Y = -85+0.5Y

So setting J=W
165 = -85+0.5Y
250 = 0.5Y
Ye = 250

This is really nasty and I hope the examiners won't ask anything as difficult as this one!

 

[dextar]

waho nice work!!
Thanks a lot for detailed explanation.
In general, if the equilibrium is not there and Planned injections is not equal to planned withdrawls
Y=Cd+W
E=Cd+J
Am I correct? That is the reason I tried writing Y=Cd+W

 

[Margaret Wood]

I'm not sure what you mean by equilibrium not being there.

You usually have to find equilibrium by either of the two methods:

1. aggregate demand (E) = aggregate supply (Y)
2. planned injections (J) = planned withdrawals (W)

These two are equivalent since:

aggregate demand (E) = C+I+G+X-M = Cd +J
income (Y) = Cd +S+T+M = Cd + W

So setting E = Y is the same as setting Cd +J = Cd + W, ie J =W.

So what you have said, ( ie Y = Cd + W and E = Cd +J ) is correct but you won't find equilibrium by using one of these equations; you have to put the two equations together.