Multiplier (economics)

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

In this system, money is created whenever a bank gives out a new loan.

This is because the loan, when drawn on and spent, mostly finishes up as a deposit back in the banking system and is counted as part of money supply.

This process continues multiple times, and is called the multiplier effect.

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 tax rates, causes German GDP to increase by €150, then the spending multiplier is 1.5.

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: 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.

As we are concentrating on the income-expenditure side, let us assume I(r) = 0 (or alternatively, constant interest), so that: Now, assuming away government and foreign sector, aggregate demand at time t is: assuming goods market equilibrium (so

respectively, then substituting these in: or, rearranging and rewriting as a second order linear difference equation: The solution to this system then becomes elementary.

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.

[citation needed] The three most known multiplier formula are as depicted, where: The general method for calculating short-run multipliers is called comparative statics.

That is, comparative statics calculates how much one or more endogenous variables change in the short run, given a change in one or more exogenous variables.

The comparative statics method is an application of the implicit function theorem.

[2] The general method for calculating impulse response functions is sometimes called comparative dynamics.

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.

[3] 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,[4] 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.