Here is a general solution to for the income-expenditure model.

`Y = C + Ip + G equilibrium condition`
`C = a + b(Y-T)
consumption function`
`Ip = Ip
investmentis fixed`

Substituting into the first equation, we get

`Y = a + b(Y-T)
+ Ip + G`

multiplying through,

`Y = a + bY
- bT + Ip
+ G`

subracting `bY`from
both sides,

`Y - bY = a
+ - bT Ip
+ G`

re-expressing the left side

`Y(1 - b)
= a + - bT Ip
+ G`

and dividing through by `(1
- b)`

` a + - bT
+ Ip + G`

gives us the final expression for equilibrium Y. What this shows is that any change in government spending or in capital investment will have a multiplied effect on national income -- multiplied by

` 1`
` -------`
` (1 - b)`

which is called, not surprisingly,
the "multiplier."