when C=97.5+0.75Y; I=20; G=20; T=0, the equilibrium level of income is
represented by the expression:
 Y(E)=(1/(1-MPC))*E(0) where MPC=marginal propensity to consume, E(0)=
the sum of all autonomous expenditures.

 Is this statement right? why?

Hi mike5, 

Yes, that is correct.  The equilibrium level of Y (output) is equal to
the MPC multiplied by autonomous expenditures E.  Taxes are 0, which
is why this expression is valid in this instance.

Consumption depends on the current level of income, which is given by
a + bY, where a is some initial value, and b is the MPC.  However, if
there were taxes then the tax rate T is subtracted from the MPC when
computing the multiplier, so C = a + b(1-T)Y, since people consume
less if their money is going to taxes.

With taxes in the equation, Y(E) = (1/(1-MPC(1-T)))*E(0).  

Since T is given as 0 already, 
Y(E) = (1/(1-MPC(1-0)))*E(0) or just 
Y(E) = (1/(1-MPC))*E(0).  

E is going to be the sum of autonomous expenditures, or a of (a + bY)
plus I plus G.

You can find a good outline of the basic Keynesian model here:
http://www.ucd.ie/~economic/staff/mkelly/commerce/macro1.pdf and it
continues here:
http://www.ucd.ie/~economic/staff/mkelly/commerce/macro2.pdf

I hope this answers your question.  Please ask for clarification if
you need more information.

hibiscus

Search Strategy: macro income multiplier +"y(e)", macro government
expenditure +"1-mpc"

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Request for Answer Clarification by mike5-ga on 07 Dec 2002 21:06 PST

hi, 
I thought the equation is C=a+b(Y-T), where a is autonomous
consumption expenditures determined by factors other than income, b is
marginal propensity to consume.
Does a equal to E(0)? what is E(0)?

thanks for your help

---

Clarification of Answer by hibiscus-ga on 07 Dec 2002 21:44 PST

Sorry, yes, you are correct, and I see that I haven't been nearly
clear enough.  Many appologies.

E(0) is initial autonomous expenditure (the 0 means it's from the
starting time 0).  E(0) = C(0) + I(0) + G(0), so in fact income Y is
Y=C(0) + b(Y-T) + I(0) + G(0), or just
Y=b(Y-T) + E(0)
Y=b(1-T)Y + E(0)

So, from this you can figure out the equilibrium value of Y.

Y - b(1-T)Y = E(0)
Y(1 - b(1-T)) = E(0)
Y = E(0) / (1 - b(1-T))
or 
Y = (1/(1-b(1-T))*E(0)
which is 
Y = (1/(1-MPC))*E(0)

You can read more about this (but in their examples E(0) is called
A(0) at http://www.digitaleconomist.com/ae_4020.html

Let me know if this doesn't clear things up.

hibiscus