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Not to be confused with the "Multiplier effect" of a Transformer.

In economics, a multiplier is a factor of proportionality that measures how much an endogenous variable changes in response to a change in some exogenous variable.

For example, suppose variable x changes by 1 unit, which causes another variable y to change by M units. Then the multiplier is M.

Common uses

Two multipliers are commonly discussed in introductory macroeconomics.

Money multiplier

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In 12 months 2013, c ommercial retails, shoebox residences and mass market properties continued to be the celebrities of the property market. Models are snapped up in report time and at document breaking prices. Builders are having fun with overwhelming demand and patrons need more. We feel that these segments of the property market are booming is a repercussion of the property cooling measures no.6 and no. 7. With additional buyer's stamp responsibility imposed on residential properties, buyers change their focus to commercial and industrial properties. I imagine every property purchasers need their property funding to understand in value. In monetary microeconomics and banking, the money multiplier measures how much the money supply increases in response to a change in the monetary base.

The multiplier may vary across countries, and will also vary depending on what measures of money are considered. For example, consider M2 as a measure of the U.S. money supply, and M0 as a measure of the U.S. monetary base. If a $1 increase in M0 by the Federal Reserve causes M2 to increase by $10, then the money multiplier is 10.

Fiscal multipliers

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. Multipliers can be calculated to analyze the effects of fiscal policy, or other exogenous changes in spending, on aggregate output.

For example, if an increase in German government spending by €100, with no change in taxes, causes German GDP to increase by €150, then the spending multiplier is 1.5. Other types of fiscal multipliers can also be calculated, like multipliers that describe the effects of changing taxes (such as lump-sum taxes or proportional taxes).

Keynesian and Hansen-Samuelson multipliers

Keynesian economists often calculate multipliers that measure the effect on aggregate demand only. (To be precise, the usual Keynesian multiplier formulas measure how much the IS curve shifts left or right in response to an exogenous change in spending.)

American Economist Paul Samuelson credited Alvin Hansen for the inspiration behind his seminal 1939 contribution. The original Samuelson multiplier-accelerator model (or, as he belatedly baptised it, the "Hansen-Samuelson" model) relies on a multiplier mechanism that is based on a simple Keynesian consumption function with a Robertsonian lag:

$C_t=C_0+c{Y}_{t-1}$

$1/(1-c(1-t)+m)$

so present consumption is a function of past income (with c as the marginal propensity to consume). Here, t is the tax rate and m is the ratio of imports to GDP. Investment, in turn, is assumed to be composed of three parts:

$I_t=I_0+I(r)+b(C_t-C_{t-1})$

The first part is autonomous investment, the second is investment induced by interest rates and the final part is investment induced by changes in consumption demand (the "acceleration" principle). It is assumed that b > 0. As we are concentrating on the income-expenditure side, let us assume I(r) = 0 (or alternatively, constant interest), so that:

$I_t=I_0+b(C_t-C_{t-1})$

Now, assuming away government and foreign sector, aggregate demand at time t is:

$Ytd=C_t+I_t=C_0+I_0+c{Y}_{t-1}+b(C_t-C_{t-1})$

assuming goods market equilibrium (so $Y_t=Ytd$), then in equilibrium:

$Y_t=C_0+I_0+c{Y}_{t-1}+b(C_t-C_{t-1})$

But we know the values of $C_t$ and $C_{t-1}$ are merely $C_t=C_0+c{Y}_{t-1}$ and $C_{t-1}=C_0+c{Y}_{t-2}$ respectively, then substituting these in:

$Y_t=C_0+I_0+c{Y}_{t-1}+b(C_0+c{Y}_{t-1}-C_0-c{Y}_{t-2})$

or, rearranging and rewriting as a second order linear difference equation:

$Y_t-(1+b)c{Y}_{t-1}+bc{Y}_{t-2}=(C_0+I_0)$

The solution to this system then becomes elementary. The equilibrium level of Y (call it $Y_p$, the particular solution) is easily solved by letting $Y_t=Y_{t-1}=Y_{t-2}=Y_p$, or:

$(1-c-bc+bc)Y_p=(C_0+I_0)$

so:

$Y_p=(C_0+I_0)/(1-c)$

The complementary function, $Y_c$ is also easy to determine. Namely, we know that it will have the form $Y_c=A_1{r}_{1}t+A_2{r}_{2}t$ where $A_1$ and $A_2$ are arbitrary constants to be defined and where $r_1$ and $r_2$ are the two eigenvalues (characteristic roots) of the following characteristic equation:

$r^2-(1+b)cr+bc=0$

Thus, the entire solution is written as $Y=Y_c+Y_p$

Opponents of Keynesianism have sometimes argued that Keynesian multiplier calculations are misleading; for example, according to the theory of Ricardian equivalence, it is impossible to calculate the effect of deficit-financed government spending on demand without specifying how people expect the deficit to be paid off in the future. Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.

General method

The general method for calculating long-run multipliers is called comparative statics. That is, comparative statics calculates how much one or more endogenous variables change in the long run, given a permanent change in one or more exogenous variables. The comparative statics method is an application of the Implicit Function Theorem.

Dynamic multipliers can also be calculated. That is, one can ask how a change in some exogenous variable in year t affects endogenous variables in year t, in year t+1, in year t+2, and so forth. A graph showing the impact on some endogenous variable, over time (that is, the multipliers for times t, t+1, t+2, etcetera), is called an impulse-response function. The general method for calculating impulse response functions is sometimes called comparative dynamics.

History

Illustration of the original visualisation of the tableau économique by Quesnay, 1758.

The Tableau économique (Economic Table) of François Quesnay (1758), which laid the foundation of the Physiocrat school of economics is credited as the "first precise formulation" of interdependent systems in economics and the origin of multiplier theory. In the tableau économique, one sees variables in one period (time t) feeding into variables in the next period (time t+1), and a constant rate of flow yields geometric series, which computes a multiplier.

The modern theory of the multiplier was developed in the 1930s, by Kahn, Keynes, Giblin, and others, following earlier work in the 1890s by the Australian economist Alfred De Lissa, the Danish economist Julius Wulff, and the German-American economist N. A. J. L. Johannsen.

Critiques

Economist Robert Barro believes that the Keynesian multiplier is close to zero. For every dollar the government borrows and spends, spending elsewhere in the economy falls by almost the same amount.

See also

• Complex multiplier
• Multiplier uncertainty