# 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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Expert Answers

mathsworkmusic | Certified Educator

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**