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.
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!
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
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.
