How a Change in Taxes Affects GDP
If an increase in government spending leads to an increase in total spending and GDP, then an increase in taxes must lead to a decrease in total spending and GDP, and vice versa. When the government raises taxes, private spending decreases. Keynes noted, however, that the decrease in overall spending from a tax increase is not as large as the increase in overall spending from the same amount of a government spending increase. The reason for this is that people save a portion of their additional income (tax refund) whereas the government spends all of its money. The example in the next paragraph illustrates this.
The Tax Multiplier
Let’s say that taxes increase by $1,000. Therefore, people’s aftertax income (income available for consumption or savings) decreases by $1,000. If the MPC is 80%, then people would have only consumed $800 of this $1,000. Thus, total spending throughout the economy decreases by 5 (the multiplier) times $800 = $4,000. This $4,000 is 4 times the change in taxes.
Mathematically, we can prove that the tax multiplier is the negative of the spending multiplier minus 1. In the above example, the regular spending multiplier from the previous section is 5 and, therefore, the tax multiplier is 4. Thus,
The tax multiplier = – (the regular multiplier – 1) In the above example: 
The following applications provide further explanations of this concept.
Examples of How a Change in Taxes Affects GDP
Example 1
Problem: Let’s say that we are experiencing a recession and the government decreases taxes by $25 billion. Let’s also assume that the MPC equals .75. By how much will GDP increase?
Solution: Because the MPC equals .75, the regular (spending) multiplier equals 4, and the tax multiplier equals 3.
The spending multiplier = 1 / (1 minus .75) = 1 / .25 = 4. The tax multiplier equals 4 minus 1 with a negative sign: (4 – 1) = 3.
To get the increase in GDP, we multiply the multiplier by the decrease in taxes:
Change in GDP = 3 * $25 billion = +$75 billion.
This means that if GDP was $800 billion before the change, it will be $875 billion after the change.
Recessionary Gap
Example 2
Problem: Let’s say that we are experiencing a recessionary gap of $360 billion. A recessionary gap is how much GDP needs to increase from the current GDP in order to achieve full employment. Also assume that the MPC equals .90. How much will the government have to decrease taxes in order to close the recessionary gap?
Solution: We know that the decrease in taxes times the tax multiplier equals the increase in GDP. The MPC is .9, so the regular multiplier is 1 / (1 – .9) = 10.
That means that the tax multiplier is (10 – 1) = 9.
So: (the change in taxes) * (the tax multiplier) = the change in GDP.
So: (the change in taxes) * (9) = $360 billion.
So: (the change in taxes) = $360 / (9) = $40 billion.
In other words, if the government decreases taxes by $40 billion, and the tax multiplier is 9, then GDP will increase by $360 billion. Since we need to add $360 billion to GDP to achieve full employment, we will have closed the recessionary gap.
Inflationary Gap
Example 3
Problem: Let’s say that we are experiencing an inflationary gap of $200 billion. An inflationary gap is how much GDP needs to decrease from the current GDP in order to achieve full employment without causing inflation. Also assume that the MPC equals .80.
Solution: The change in taxes * the tax multiplier = the change in GDP.
The regular multiplier is 5 (calculation: 1 / (1 – .8), so the tax multiplier is 4.
So: (the change in taxes) * (4) = $200 billion.
So: (the change in taxes) = ($200) / (4)= +$50 billion.
In other words, if the government increases taxes by $50 billion, and the tax multiplier is 4, then GDP will decrease by $200 billion. Since we need to lower GDP by $200 billion to achieve full employment without inflation, we will have closed the inflationary gap.
The Balanced Budget Multiplier
When the government increases spending by a certain amount and it increases taxes by the same amount, then GDP will increase by that amount. The following example illustrates this.
Example 4
Problem: Let’s say the government increases spending by $1,000 and also increases taxes by $1,000, and the MPC equals .8. By how much will GDP change?
Solution: The multiplier equals 5 and so the tax multiplier equals 4. Therefore, GDP will increase by $5,000 from the $1,000 additional government spending (5 times $1,000). And GDP will decrease by $4,000 from the additional $1,000 in taxes (4 times $1,000). Thus, on balance, equilibrium income (GDP) will increase by $1,000 ($5,000 minus $4,000).
Therefore, when the government spends $1,000 and imposes taxes of $1,000, it balances its budget, while increasing equilibrium GDP by $1,000.
Thus, when the government changes spending and taxes by the same amount, then equilibrium income (GDP) changes by 1 times this amount. We say that
The balanced budget multiplier = 1.

The balanced budget multiplier implies that if the government increases spending and taxation by the same amount, then equilibrium national income (GDP) rises by this amount.
This balanced budget stimulation is possible, according to Keynes, because when the government receives $1,000, it spends it all. On the other hand, when private citizens receive $1,000, they spend only a fraction of it (in the above example, they spend 80%). They save the other fraction. Because savings, according to Keynes, is a “leakage” from the economy, the economy “loses” 20% in stimulation if private citizens spend it, compared to no loss (no savings) if the government spends it.
Do you agree with Keynes that it is possible to stimulate the economy by, for example, $1 trillion, simply by raising government spending and taxes by $1 trillion?
For a video explanation of additional examples involving the Keynesian multiplier, please watch:
Hi
Could you help with the following question. The answer is B, but why?
Nikhil, the balanced budget multiplier of 1 refers to dollar amounts of taxes and government spending that are the same (which is why the budget is balanced). So if the government increases spending by a certain amount (for example, $100) and taxes go up by that same amount ($100), then according to Keynes, total spending in the economy goes up by $100. If you have tax in the form of a function, the multiplier can only be 1 if the spending function is the same (G = Ga + GY).
Peter, which question are you referring to? If you can copy it in your message, I will respond.
Dear Dr. Bouman with a recessionary gap of $60b and an MPC of .8
Whats the combination of government spending and taxes will eliminate this gap?
I work on this problem and can’t seem to get your suggested answers of Spending of $10b and Decrease in Taxes of $2.5b.
Respectfully,
Mannie
Mannie, thanks for your question.
We have a recessionary gap of $60 billion, so we have to increase total spending in the economy (GDP) by $60b. If you increase government spending by $10b and decrease taxes by $2.5b, then you will achieve this. Explanation: you have to use the two Keynesian equations that involve the multipliers:
change in government spending * multiplier = change in the economy’s spending, and
change in taxes * tax multiplier = change in the economy’s spending.
The multiplier is 1 / (1.8) = 5. The tax multiplier is 1 – 5 = 4. So:
$10b * 5 = $50 b, and
$2.5 * 4 = $10 b
$50b + $10b = $60b, which is the desired increase in the economy’s total spending.
Hope this helps.
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this is awesome. thanks so much!
I must say a very big thank you to all who contributed to this project and having access to it all for free… Thanks, I gained a lot…..
It’s very good . You explain exactly in the
same manner that I wanted.
Gracias, Robert. Even though Keynes supported it, the budget balanced multiplier does not really work in the long run. The balanced budget multiplier is based on the idea that people’s savings is a loss to economic stimulation. However, savings goes into banks and other financial markets and eventually get borrowed and spent. So savings eventually (in the long run) leads to spending and this means that in the long run $1,000 in government spending has the same effect as $1,000 in the hands of people who spend $800 of it and save $200 of it. So a government that spends #1,000 and taxes the people #1,000 has a zero effect on economic stimulation. It then becomes an issue of: do you want your government to spend money, or do you want private citizens to spend money? Who spends the money more wisely and more efficiently? What is better for the economy?