I don’t understand something about the Keynes multiplier. I just came across thi

Question

I don’t understand something about the Keynes multiplier. I just came across this question:

“When the government taxes the people by $20 million, what effect does it have on GDP if MPC = 0.8?”

The answer given in the book is:

“Since MPC is 0.8, it means that $16 million was removed from the economy. We then determine the multiplier, which here is 1/0.2, or 5, and we can therefore say that the tax would cause Y to fall by $80 million."

This makes sense to me.

But then I read (in a different book) that if the government would increase its spending by $100 million, and MPC = 0.8, Y would rise by $500 million, based on the formula:

(? in G) / (1 – MPC)

Why is this true? When the gov spends money, the first step in doing so is giving it to PEOPLE, right? So why don't we say:

(? in G) * MPC = x
and then
Y rises by
x / (1 – MPC)

(In other words, why don't we say that the 100 increase in G will cause 80 to enter the multiplier, since MPC = 0.8, and therefore will cause a rise in Y of 400?)

Please help
Thank you

Explanation / Answer

Let us assume,Seth, got a military contract from the US government and earned an income of $ 100 millions. Here $100 millions is government spending, as it spends on purchase of military equiptment.

And $100 millions is the additional income you are earning. Your disposable income increases by $100 millions

This money is now sent into the economy through Seth.

Now let us assume that the MPC (Marginal Propensity to Consume) of US is 0.8. This means every dollar earned by the US citizen, 80 % is spent or consumed, or as per the definition, 80% of the income is expended and 20% is saved.

So he spends $ 80 billions, for different purposes like, car, transportation, food, movies, charity etc. Here he had spent $80 millions, and in the next level, let us assume that his cooks salary is $5million/ annum, so he gets $5 millions out of the $ 80 millions, and he too spends in the same fashion, since the spending pattern will not change in short run, and this process continues like a chain and magnifies making a shift in the GDP. This is called multiplier effect.

So Multiplier= Change in real GDP/ Initial change in spending.

Alternatively we can also find the multiplier from the MPC,

Multiplier= 1/1- MPC

Let us caliculate the multiplier and the change in GDP.

At MPC= 0.8

Multiplier=1/1-0.8

             =1/0.2   
            = 5

So, GDP change is

Change in GDP= multiplier X Initial change in spending

                     =5 x 100

                     = 500 millions.

When a tax is imposed the disposable income changes or decreases by $20 millions.

If you are earning $100, when there are no taxes.

Ur disposable income is = 100.

when taxes are imposed.

DI= 100- 20

= 80.

Initial change in income= 80-100

                                    =$-20 millions

Initial change in income is $20.

Multiplier effect is caliculated on the change in consumption, by multiplying the multiplier with initial change in income

Change in GDP= Multiplier x Initial change in income.

here initial change in income is minus 20.

Chnage in GDP= 5 x -20

                     = -100 millions.

GDP will shift left.

Your perception is not clear, MPC is marginal propencity to consume when you have an income rise or fall.

So, first income change occurs than consmuption occurs than a multiplier effect on consumption occurs.

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