Explain why a $100 reduction in taxes does not have the same impact on output and employment as a $100 increase in government spending.

A tax cut of $100 does not have the same impact as a $100 increase in government spending because there is not the same initial increase in GDP.  That is, a $100 increase in government spending increases GDP by $100 right away whereas the $100 tax cut does not. 

When the government increases spending by $100, it buys goods or services from individuals with that $100.  This $100 is directly applied to GDP because it takes the form of a government purchase of new goods or services.  The multiplier then takes effect as people who get money for providing goods and services to the government turn around and spend that money.  If we use this information to derive the multiplier mathematically, we find that the equation for the multiplier is 1/(1-MPC) where MPC is the marginal propensity to consume.

When the government decreases taxes by $100, there is no direct effect on GDP.  The government is refraining from taking money instead of actually paying it out to buy goods and services.  This does not increase GDP.  The tax cut first increases GDP when taxpayers spend some of the money saved to buy goods and services.  They will only spend some of it, though, because they will want to save the rest.  Therefore, the multiplier has to be lower than the government expenditures multiplier. 

So, the tax cut does not increase GDP as much as the government spending does.  This is because government spending counts towards GDP whereas a tax cut does not.