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May 4th, 2018, 07:21 AM  #1 
Member Joined: Mar 2017 From: Israel Posts: 70 Thanks: 2  Macroeconomics
Hello Can you help me please about the next exercise: In a certain economy, the following behavioral functions are presented (in millions dollars): Disposable Income: Yd Private Consumption: C = 160 + 0.6Yd Investment: I = 50 + 0.15Y Public consumption: G = 100 The government doesn't invest, and assume that in the state of origin (outside of the country) the government finances all its expenses by taxes. Find the private consumption as a function of national product. Thanks! Last edited by IlanSherer; May 4th, 2018 at 07:58 AM. 
May 4th, 2018, 08:26 AM  #2 
Member Joined: Mar 2017 From: Israel Posts: 70 Thanks: 2 
Oh, I forgot to add something: Product: Y All firm profits are divided. The tax is constant/fixed. 
May 4th, 2018, 11:23 AM  #3  
Senior Member Joined: May 2016 From: USA Posts: 1,084 Thanks: 446  Quote:
Are you assuming a closed or an open economy. I am guessing closed, in which case I assume $Y = C + I + G.$ You gave no definition for $Y_d.$ I am guessing that $Y_d = Y  T \text { and } G = T \text { by assumption.}$ I am further guessing that you meant the tax rate is fixed rather than the taxes themselves. If my guesses are correct, we have $Y = C + I + G.$ $Y_d = Y  T.$ $C = 160 + 0.6Y_d.$ $I = 50 + 0.15Y.$ $G = T.$ We have six variables (Y, Y_d, C, I, G, and T) and five equations. $C = 160 + 0.6Y_d \implies Y_d = \dfrac{C  160}{0.6}$. $\text {But } Y_d = Y  T \implies T = Y  Y_d = Y  \dfrac{C  160}{0.6}.$ $T = G \text { and } Y = C + I + G \implies Y = C + I + T.$ $T = Y  \dfrac{C  160}{0.6} \text { and } Y = C + I + T \implies$ $Y = C + I + Y  \dfrac{C  160}{0.6} \implies I = \dfrac{C  160}{0.6}  C = \dfrac{0.4C  160 }{0.6}.$ $I = 50 + 0.15Y \text { and } I = \dfrac{0.4C  160 }{0.6} \implies$ $50 + 0.15Y =\dfrac{0.4C  160 }{0.6} \implies 30 + 0.09Y = 0.4C  160 \implies 0.4C = 190 + 0.09Y \implies$ $C = 475 + 0.225Y.$ Does that make any sense? Let's see. $C + I \le Y \implies 475 + 0.225Y + 50 + 0.15Y \le Y \implies$ $525 \le 0.625Y \implies \le Y.$ $Y = 840 \implies C = 475 + 0.225Y = 664 \text {and }$ $I =50 + 0.15Y = 176 \implies 664 + 176 = 840.$ Y = 840 means that government expenditures and therefore taxes are zero. $Y_d = Y  T = 840  0 = 840 \text { and } 160 + 0.6 * 840 = 664.$ So let's try another. $Y = 1200 \implies I = 50 + 180 = 230.$ $Y = 1200 \implies C = 475 + 270 = 745.$ $\text {But } T = G = Y  C  I = 1200  230  745 = 225.$ $\therefore Y_d = 1200  225 = 975 \implies 745 = 160 + 0.6 * 975 = 745.$ Our algebra was correct. Now notice the implication. It is G that determines Y. It actually makes more sense to solve for Y in terms of G. $I = 50 + 0.15Y \text { and } Y = C + I + G \implies 0.85Y = 50 +C + G.$ $C = 160 + 0.6Y_d \text { and } Y_d = Y  T \implies C = 160 + 0.6Y  0.6T.$ $G = T \text { and } C = 160 + 0.6Y  0.6T \implies C = 160 + 0.6Y  0.6G.$ $C = 160 + 0.6Y  0.6G \text { and } 0.85Y = 50 +C + G \implies$ $0.85Y = 50 + 160 + 0.6Y  0.6G + G \implies 0.25Y = 210 + 0.4G \implies Y = 4(210 + .4G).$ We can check that with the values we already found. $G = 0 \implies Y = 4(210 + 0.4 * 0) = 4 * 210 = 840.$ $G = 225 \implies Y = 4(210 + 0.4 * 225) = 4(210 + 90) = 1200.$  
May 5th, 2018, 05:12 AM  #4  
Senior Member Joined: May 2016 From: USA Posts: 1,084 Thanks: 446 
I see that part of my answer got garbled. Quote:
 
May 5th, 2018, 05:14 AM  #5  
Senior Member Joined: May 2016 From: USA Posts: 1,084 Thanks: 446 
I see that part of my answer got garbled. Quote:
 
May 5th, 2018, 08:03 AM  #6 
Member Joined: Mar 2017 From: Israel Posts: 70 Thanks: 2  It's ok, I already understood you And sorry for bad english, I tried to find the right words, in my language it's one word when in English it's a few words (one meaning against several meanings). But you understood and guessed correctly, thanks! 

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