k refers to multiplier.
The multiplier is a process whereby an increase or a decrease in the economic variables affecting the circular flow of income, that is injections such as consumption, government expenditure and exports and withdrawals such as savings, taxation and imports, can have amplified effects on national income.
For example, if the govt increases its expenditure (which it will do during a reccession) national income will rise by much more times the amount of the money spent by the government. Likewise, during a reccession, firms will cut down their production and lay off workers - this will lead to a fall in national income but this also induces national income to fall by much more times.
The multiplier process can also be explained through the spillover effects which it has in the economy. If a government increases its expenditure by employing more workers, then the workers will have a greater disposable income. They will demand more goods and services and this increased demand will lead to a greater rise in national income.
The formula for multiplier as you know, is 1/MPS or 1/(1-MPC)
This shows that for each round of expenditure generated in the economy, a small proportion of it is saved and the rest consumed. The bottomline her is "one man's expenditure is another man's income"... The round of expenditures will keep going on in the economy: each time a proportion is saved and the income left is used to buy goods and services.
Thus, the multiplier would stop when consumption would equal zero and the amount calculated as per the multiplier has been reached.
I hope that made some sense... lol.
Revise accelerator effect as well if you are taking exams on Thursday!