What is the Multiplier Effect of Zakat?

Q: What is the Multiplier Effect of Zakat?
Literally the meaning of Zakat is growth or increase. To illustrate the multiplier effect in the economy we have,
Marginal Propensity to save (MPS) = Change in Savings/ Change in income
If somebody receive an extra dollar then how much perfect the extra dollar will be used for savings.
MPC= Marginal Propensity to consumption
MPS= Marginal Propensity to save
If we want to find out MPC then,
Now the question is how the concept of MPC or MPS can be aggregated to get the multiplier effect of Zakat.
Note that, Zakat money is given to certain group of people or Asnaf. The Zakat is given especially to the group of poor people. For poor people they have higher MPC.
Basically, MPC for the poor group is very high. For example, when they receive say about $100, they may spend of all hundred dollar for consumption.
Now point the case, 
                                      MPC=1 and MPS=0
The question is how then when we know that the poor people have higher MPC, how Zakat given to the poor can boost the economy.
Now once we know how to find multiplier. We know:
Δ in GDP= m* Δ in Initial Spending
Where, Δ= Change in
              GDP= Gross Domestic Product
How we count multiplier. Multiplier is given by
To understand how much the level of multiplier, we can lay out as follows:
Δ in GDP

We know the MPC for poor is very high say 0.9 and MPS is very low say 0.1 and m is 10.
Now for the rich people,
MPC=0.1 (very low)
MPS= 0.9 (very high) and
How these can effect in GDP?
Assume initial spending in the economy is $100. So, in the case of poor people we will give $100 to them from where they will spend 90% of that. So the change in GDP will be $100*10=$1000.
For the rich people, MPC is just 0.1 and m is 1.11. So the change in GDP will be $111.
Now, we want to emphasize that in the case of Zakat money. We know that, poor people have higher MPC than rich. Because of high MPC among the poor Zakat money will be given to ‘Fakir and Miskin’ that means to the petitioner and the deprived. They have high MPC. And this tends to connects huge multiplier effects in the economy. Because of that, we give Zakat money to poor people and they have higher MPC and will affect GDP as much through m.
In contrast, if money is given to the poor they will save more and the economy will face low multiplier effect. This will lead to less change in GDP.
Remember that, one of them (poor) the Zakat is grow and we can see Zakat leads to huge improvements in the economy.

                                                                                                          Composed By: Fajila Khatun.