SOLUTION: this is from (barron's)algebra book...the level of national income (y) in a country can be found from the two-equation system...Y=C+I+G

Algebra ->  Equations -> SOLUTION: this is from (barron's)algebra book...the level of national income (y) in a country can be found from the two-equation system...Y=C+I+G       Log On


   

Question 300927: this is from (barron's)algebra book...the level of national income (y) in a country can be found from the two-equation system...Y=C+I+G
C=a+bY solve for Y and C assuming that I(investment spending),G (government spending),a, and b are known.
i have no clue how to do this one.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Y=C%2BI%2BG
C=a%2BbY
Let's substitute to simplify the knowns.
d=I%2BG
So then,
1.Y=C%2Bd
2.C=bY%2Ba
You're solving for C and Y.
You can do a direct substitution using eq. 1 in eq. 2 and solving for C.
C=bY%2Ba
C=b%28C%2Bd%29%2Ba
C=bC%2Bbd%2Ba
C-bC=bd%2Ba
C%281-b%29=bd%2Ba
C=%28bd%2Ba%29%2F%281-b%29
Then go back and solve for Y using eq. 1,
Y=C%2Bd
Y=%28bd%2Ba%29%2F%281-b%29%2Bd
Y=%28bd%2Ba%29%2F%281-b%29%2Bd%281-b%29%2F%281-b%29
Y=%28bd%2Ba%2Bd%281-b%29%29%2F%281-b%29
Y=%28bd%2Ba%2Bd-bd%29%2F%281-b%29
Y=%28a%2Bd%29%2F%281-b%29
Now we can go back and re-substitute,
highlight_green%28C=%28b%28I%2BG%29%2Ba%29%2F%281-b%29%29
highlight_green%28Y=%28a%2BI%2BG%29%2F%281-b%29%29