The following are exogenous (not directly affected by income): G = 11 I = 4 X = M = 0 The consumption function is: C = k + cY, where k = 3, c = 0.8 Now we have to take that tax into account.  Here is a way to think about it: Look at the consumption function.  It says if you give me one more dollar of income I will spend 80 cents of it (mpc = 0.8).  BUT I can only spend what I receive.  I can only spend my after-tax or disposable income.  With a 10% tax, I don't receive Y I receive 90% of Y or Y*(1-t) where t = 10% or 0.1.   Let's define disposable income as Yd where Yd = Y*(1-t).   Therefore we restate our consumption function as C = k + cYd   Now we have, in this case, C = k + cYd or C = 3 + 0.8Yd or C = 3 + 0.8*(Y*[1-0.1]) or C = 3 + 0.72Y. Now what is the equilibrium GDP?

ENGR.ECONOMIC ANALYSIS
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The following are exogenous (not directly affected by income):

G = 11

I = 4

X = M = 0

The consumption function is:

C = k + cY, where k = 3, c = 0.8

Now we have to take that tax into account.  Here is a way to think about it:

Look at the consumption function.  It says if you give me one more dollar of income I will spend 80 cents of it (mpc = 0.8).  BUT I can only spend what I receive.  I can only spend my after-tax or disposable income. 

With a 10% tax, I don't receive Y I receive 90% of Y or Y*(1-t) where t = 10% or 0.1.  

Let's define disposable income as Yd where Yd = Y*(1-t).  

Therefore we restate our consumption function as C = k + cYd  

Now we have, in this case, C = k + cYd or C = 3 + 0.8Yd or C = 3 + 0.8*(Y*[1-0.1]) or C = 3 + 0.72Y.

Now what is the equilibrium GDP?

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