if the consumption function is C=100+0.8(Y-T), the government purchases multiper is 5. I want to ask why ?

Question

It is about economics.AGGREGATE DEMAND

Answer 1

The multiplier for government spending also depends on a range of other factors, such as how much goes into imports etc. However, I have assumed that you have a closed economy (no imprts or exports and no need for an exchange rate) and that if the government increases its spending, it doesn't need to raise taxes at some point in the future to balance its budget.

If you make these assumptions, you can get a multiplier of 5. Suppose the government spends an additional 1 unit on services so that it all goes into household incomes (ie so that Y increases by 1), the first round effect is to add 0.8 to C. If all of this goes into incomes and increases Y by a further 0.8, the second round impact is to increase C by a further 0.64, with the third and subsequent rounds' impacts each being 80% of the previous rounds impact.

The total impact will be 1+0.8+(0.8)(0.8)+(0.8)(0.8)(0.8)+(0.8)(0.8)(0.8)(0.8)+...
Using some mathematical manipulation you can prove this equals 5. Alternatively, use a spreadsheet starting with 1, and then each row underneath it multiplied by 0.8 to get the first 20 or so terms and then sum them up and you can verify this without having to do any algebra.

Answer 2

multiplier=1/1-0.8