Fiscal multiplier

This article is about the effect of spending on national income. For the multiplier effect in banking, see Fractional-reserve banking.

In economics, the multiplier effect refers to the idea that the initial amount of money spent by the government leads to an even greater increase in national income. In other words, an initial change in aggregate demand causes a change in aggregate output for the economy that is a multiple of the initial change.

It is particularly associated with Keynesian economics; some other schools of economic thought reject, or downplay the importance of multiplier effects, particularly in the long run. The multiplier has been used as an argument for government spending or taxation relief to stimulate aggregate demand.

Definition

The basic formula for the economic multiplier, in macroeconomics, is $\Delta Y \over \Delta I$, or the change in equilibrium GDP divided by the change in investment (i.e. the initial increase in spending).

Examples

For example: a company spends $1 million to build a factory. The money does not disappear, but rather becomes wages to builders, revenue to suppliers etc. The builders will have higher disposable income as a result, so consumption, hence aggregate demand will rise as well. Suppose further all of the recipients of new factory spending in turn spend it.

The increase in the gross domestic product is the sum of the increases in net income of everyone effected. If the builder receives $1 million and pays out $800,000 to sub contractors, he has a net income of $200,000 and a corresponding increase in disposable income (the amount remaining after taxes).

This process proceeds down the line through subcontractors and their employees, each experiencing an increase in disposable income to the degree the new work they perform does not displace other work they are already performing. Each participant who experiences an increase in disposable income then spends some portion of it on final (consumer) goods, according to his or her marginal propensity to consume, which causes the cycle to repeat an arbitrary number of times, limited only by the spare capacity available.

The idea is that the net increase in disposable income by all parties throughout the economy will be greater than the original investment. When that is the case, the government can increase the gross domestic product during a recession by an amount that is greater than an increase in the amount it spends.

Another example is when a tourist visits somewhere they need to buy the plane ticket, catch a taxi from the airport to the hotel, book in at the hotel, eat at the restaurant and go to the movies or tourist destination. The taxi driver needs petrol (gasoline) for his cab, the hotel needs to hire the staff, the restaurant needs attendants and chefs, and the movies and tourist destinations need staff and cleaners.

Applications

The multiplier effect is a tool used by governments to attempt to stimulate aggregate demand. This can be done in a period of recession or economic uncertainty. The money invested by a government creates more jobs, which in turn will mean more spending and so on.

It must be noted that the extent of the multiplier effect is dependent upon the marginal propensity to consume and marginal propensity to import. Also that the multiplier can work in reverse as well, so an initial fall in spending can trigger further falls in aggregate output.

The concept of the economic multiplier on a macroeconomic scale can be extended to any economic region. For example, building a new factory may lead to new employment for locals, which may have knock-on economic effects for the city or region.

Various Multiplier Estimates

Note: In the following examples the multiplier is the right-hand-side equation without the first component.

• y is original output (GDP)
• $b_{C}$ is marginal propensity of consumption (MPC)
• $b_{T}$ is original income tax rate
• $b_{M}$ is marginal propensity to import
• $\Delta y$ is change in income (equivalent to GDP)
• $\Delta a_{T}$ is change in lump-sum tax rate
• $\Delta b_{T}$ is change in income tax rate
• $\Delta G$ is change in government spending
• $\Delta T$ is change in aggregate taxes
• $\Delta I$ is change in investment
• $\Delta X$ is change in exports

Standard Lump-sum Tax Equation

$\Delta y=\Delta a_{T}*{\frac {-b_{C}}{1-b_{C}(1-b_{T})+b_{M}}}$

Note: only $\Delta a_{T}$ is here because if this is a change in lump-sum tax rate then $\Delta b_{T}$ is implied to be 0.

Standard Income Tax Equation

$\Delta y=\Delta b_{T}*{\frac {-b_{C}*y}{1-b_{C}(1-b_{T})+b_{M}}}$

Note: only $\Delta b_{T}$ is here because if this is a change in income tax rate then $\Delta a_{T}$ is implied to be 0.

Standard Government Spending Equation

$\Delta y=\Delta G*{\frac {1}{1-b_{C}(1-b_{T})+b_{M}}}$

Standard Investment Equation

$\Delta y=\Delta I*{\frac {1}{1-b_{C}(1-b_{T})+b_{M}}}$

Standard Exports Equation

$\Delta y=\Delta X*{\frac {1}{1-b_{C}(1-b_{T})+b_{M}}}$

Balanced-Budget Government Spending Equation

$\Delta y=\Delta G*1$

$\Delta y=\Delta T*1$

Statistics

United States of America

Estimation has found "textbook" values of multipliers are overstated. The following tables has assumptions about monetary policy along the left hand side. Along the top is whether the multiplier value is for a change in government spending (ΔG) or a tax cut (-ΔT).

Monetary Policy Assumption	ΔY/ΔG	ΔY/(-ΔT)
Interest Rate Constant	1.93	1.19
Money Supply Constant	0.6	0.26

The above table is for the fourth quarter under which a permanent change in policy is in force.

History

The multiplier was initially developed by Ralph George Hawtrey in 1931.

External links

• Multiplier Effect by bank lending