Find the value of the income Y and the consumption C given that Y = C + I + G income C = 18 + 0.8Y Consumption expenditures I = 12 Investment G = 10 Gov expenditures find the value of...
Find the value of the income Y and the consumption C given that
Y = C + I + G income
C = 18 + 0.8Y Consumption expenditures
I = 12 Investment
G = 10 Gov expenditures
find the value of the income Y and the consumption C
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We have
1) ` Y = C + I + G`
2) `C = 18 + 0.8Y`
And are given
`I = 12` and
`G =10`
Substituting the values for `I` and `G` into 1) we get
1) `Y = C + 12 + 10 = C + 22`
Substituting 2) into 1) we get
1) `Y = 18 + 0.8Y + 22`
`implies` `0.2Y = 40` `implies` `Y = 200`
Substituting this value for `Y` into 1) we get
1) `200 = C + 22` `implies` `C = 178`
Check
1) `Y = C + I + G = 178 + 12 + 10 = 200`
2) `C = 18 + 0.8Y = 18 + 160 = 178`
Therefore Y = 200 and C = 178
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