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The government purchases function is the relationship between income in the economy on the one hand and government purchases on the other. In general, we expect that there is actually very little relation between these two. We expect that the government will make purchases without regard to the amount of income in the economy.
The purchases that the government makes do not typically depend on the amount of income that is in the economy or the amount of tax revenues that the government takes in. Our government has consistently shown that it is willing to borrow in order to spend, thus making it so that the government purchases are independent of income or tax revenues. So, we should not say that the government purchases function will rise when tax revenues rise.
Instead, we should say that the government purchases function will rise when circumstances demand it. For example, when the 9/11 terrorist attacks occurred, the US government greatly increased spending on matters relating to security and eventually went to war, thus causing the purchasing function to rise even faster. This increase was driven by events, not by tax revenues. This is typical. So, we can say that the government purchases function will rise if something happens to make the government need to spend more money.
Social Security spending would not cause the government purchases function to rise. Social Security payments are transfer payments, not payment for work being done in the present. Therefore, these payments are not part of government purchases.
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