Tax increase in the aggregate supply and demand model

This post considers the effects of a tax increase, given the aggregate supply and demand model.

George W. Bush passed two tax cuts, the Economic Growth and Tax Relief Reconciliation Act of 2001 and the Jobs and Growth Tax Relief Reconciliation Act of 2003. Allowing all the tax cuts to expire would raise taxes by $200 billion according to estimation of Tax Foundation.

a. U.S. marginal propensity to consume is assumed to be 2/3. What is likely to happen to the followings: do they rise or fall, and by how much if Bush Tax cuts expire? (Assuming all else equal.)
i. Private Saving
ii. Public Saving
iii. National Saving
iv. Investment

b. What would be the impact of allowing tax cuts to expire on aggregate output, Y? And why is that - answer the question with economic theory behind, not according to your opinion, political party’s view or normative statement. (Assuming all else equal.)

Depending on where you are in the semester and what topics you have been over at this point, the question could be answered in a couple of different ways.
The most basic way is to write you GDP equation, and economy wide savings equation:

Y = C + I + G where C = (income minus taxes and savings)

Investment + private savings = government spending + taxes

With a balanced budget, government spending would equal taxes, and investment would equal private savings.

Since taxes are effectively rising by $200 billion.  This is going to lower income by the amount of the tax increase of $200 billion.  Since people save roughly 1/3 of their income (stated in the question by a marginal propensity to consume of 2/3) C is only going to decrease by 2/3 of this amount, and likewise private savings will lower by 1/3 of this amount:

Private savings goes down 1/3*200B = 66.67B

Public savings will go up by 200B because that is the amount of the tax increase, and there is no mention of an increase in government spending.

National savings, which is government savings (public savings)  plus private savings will be the sum of these two changes:

200 – 66.67 = 133.33

Finally, what happens to investment?  If we assume that the savings equation holds, then the increase in national savings has to go somewhere.  In this case it will go to investment, so investment will rise by an amount equal to the increase in national savings, or 133.33.

But what happens to aggregate output, Y?  Typically if we have a tax increase, aggregate demand will shift left immediately because of the reduction in consumption going on in the economy.  But because the money went from consumers to the government, and then is loaned out to businesses, the increase in investment will slowly shift aggregate demand back to where it was originally.

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