How do changes in disposable income affect government purchases and the government purchase function?

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The relationship between the two is somewhat indirect. If people have smaller disposable incomes, they will spend less money, reducing the amount of revenue raised through sales taxes. This has the greatest effects at the regional levels of government which rely mainly on sales and property taxes for revenue, unlike the federal government which is more reliant on other forms of taxation. This means that lower disposable income can reduce both local government revenue and expenditures. This means less money is available for spending on infrastructure and public services. Lack of consumer spending and reduced government spending can in combination lead to recession or economic contraction. 

To counter this, the government can engage in increased spending on things like infrastructure and public services to counter the deflationary spiral. Many economists think that increasing government purchasing, especially in the form of investment in infrastructure, is the best way to counter recessions and to meet inflation targets, assuming such spending does not increase government debt to unsustainable levels. 

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Changes to disposable income do indeed affect government purchasing power. Disposable income is defined as the amount left over after the government (federal, state, and local) has taken its share in taxes, so DPI has a backward affect on government spending. The more the government takes, the more it has to spend and the less disposable income individual households have to spend. The converse of this statement is also true -- the less the government takes, the less it has to spend (disregard deficit spending at this point) and the more disposable income an individual household has to spend. 

This is rather a trick question, because any change in the tax code (whether it is national or local government) increases purchasing power of either the government as the consumer or the individual. However, the government's purchasing power is affected by all the money it needs to spend on things like transfer payments. 

When people are out of work, they have little or no disposable income unless the government is spending tax revenue on transfer payments (unemployment, welfare, etc.). Hence the government's purchasing power is reduced by the amount of the transfer payments. 

So again, disposable income significantly affects government purchases and the government purchase function. Here is an example of how disposable income has a backward affect on the government's purchasing power. 

The lowest tax rate is 10%; the highest is 39.6%. If I work at McDonalds at minimum wage, my disposable income is my wages less the tax percentage (probably between 10 and 15%), not much for the government and my disposable income is pretty low. If I am the CEO of McDonalds, my tax rate is probably 39.6% or close to it. A lot for the government and my disposable income remains very high. 

Remembering the definition of disposable income will facilitate understanding of government purchasing power.

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In general, changes in people’s disposable income do not necessarily change the government purchase function or the level of government purchases.

In order to understand this, we must first be sure to understand that government purchases do not include transfer payments.  Therefore, welfare payments and unemployment insurance do not count.  This is important because transfer payments tend to be inversely related to disposable income levels.  When people get poorer, they tend to qualify for more transfer payments.

Government purchases are different.  These are goods and services that the government actually buys.  These purchases are authorized through the political process, not through market forces.  Therefore, government purchasing is typically independent of the level of disposable income in the economy.  For example, government purchasing went up with President Obama’s “stimulus package” in 2009.  It would have gone down (presumably) if Mitt Romney had been elected.  This would have happened for political reasons, not because of any sort of change in the amount of disposable income available to the public.

Therefore, we cannot say that government purchases are affected in any systematic and predictable way by disposable income levels.

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