<P> In economics, the fiscal multiplier (not to be confused with monetary multiplier) is the ratio of a change in national income to the change in government spending that causes it . More generally, the exogenous spending multiplier is the ratio of a change in national income to any autonomous change in spending (private investment spending, consumer spending, government spending, or spending by foreigners on the country's exports) that causes it . When this multiplier exceeds one, the enhanced effect on national income is called the multiplier effect . The mechanism that can give rise to a multiplier effect is that an initial incremental amount of spending can lead to increased income and hence increased consumption spending, increasing income further and hence further increasing consumption, etc., resulting in an overall increase in national income greater than the initial incremental amount of spending . In other words, an initial change in aggregate demand may cause a change in aggregate output (and hence the aggregate income that it generates) that is a multiple of the initial change . </P> <P> The existence of a multiplier effect was initially proposed by Keynes student Richard Kahn in 1930 and published in 1931 . Some other schools of economic thought reject or downplay the importance of multiplier effects, particularly in terms of the long run . The multiplier effect has been used as an argument for the efficacy of government spending or taxation relief to stimulate aggregate demand . </P> <P> In certain cases multiplier values less than one have been empirically measured (an example is sports stadiums), suggesting that certain types of government spending crowd out private investment or consumer spending that would have otherwise taken place . This crowding out can occur because the initial increase in spending may cause an increase in interest rates or in the price level . In 2009, The Economist magazine noted "economists are in fact deeply divided about how well, or indeed whether, such stimulus works", partly because of a lack of empirical data from non-military based stimulus . New evidence came from the American Recovery and Reinvestment Act of 2009, whose benefits were projected based on fiscal multipliers and which was in fact followed--from 2010 to 2012--by a slowing of job loss and private sector job growth . </P> <P> The other important aspect of the multiplier is that to the extent that government spending generates new consumption, it also generates "new" tax revenues . For example, when money is spent in a shop, purchases taxes such as VAT are paid on the expenditure, and the shopkeeper earns a higher income, and thus pays more income taxes . Therefore, although the government spends $1, it is likely that it receives back a significant proportion of the $1 in due course, making the net expenditure much less than $1 . Indeed, in theory, it is possible, if the initial expenditure is targeted well, that the government could receive back more than the initial $1 expended . </P>

What is the equation for the spending multiplier the tax multiplier