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

- Common uses
- Fiscal multipliers
- Keynesian and Hansen–Samuelson multipliers
- General method
- History
- See also
- References

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

Two multipliers are commonly discussed in introductory macroeconomics.

Commercial banks create money, especially under the fractional-reserve banking system used throughout the world. 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. After putting aside a part of these deposits as mandated bank reserves, the balance is available for the making of further loans by the bank. This process continues multiple times, and is called the **multiplier effect**.

The multiplier may vary across countries, and will also vary depending on what measures of money are being 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.

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. 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 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. Investment, in turn, is assumed to be composed of three parts:

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:

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

assuming goods market equilibrium (so ), then in equilibrium:

But we know the values of and are merely and respectively, then substituting these in:

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

The solution to this system then becomes elementary. The equilibrium level of Y (call it , the particular solution) is easily solved by letting , or:

so:

The complementary function, is also easy to determine. Namely, we know that it will have the form where and are arbitrary constants to be defined and where and are the two eigenvalues (characteristic roots) of the following characteristic equation:

Thus, the entire solution is written as

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 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.

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.^{ [1] } A graph showing the impact on some endogenous variable, over time (that is, the multipliers for times *t*, *t*+1, *t*+2, etc.), is called an impulse-response function. ^{ [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. Johannsen.^{ [5] }

**Keynesian economics** are the various macroeconomic theories and models of how aggregate demand strongly influences economic output and inflation. In the Keynesian view, aggregate demand does not necessarily equal the productive capacity of the economy. Instead, it is influenced by a host of factors – sometimes behaving erratically – affecting production, employment, and inflation.

In microeconomics, **supply and demand** is an economic model of price determination in a market. It postulates that, holding all else equal, in a competitive market, the unit price for a particular good, or other traded item such as labor or liquid financial assets, will vary until it settles at a point where the quantity demanded will equal the quantity supplied, resulting in an economic equilibrium for price and quantity transacted. It forms the theoretical basis of modern economics.

The **IS–LM model**, or **Hicks–Hansen model**, is a two-dimensional macroeconomic tool that shows the relationship between interest rates and assets market. The intersection of the "investment–saving" (IS) and "liquidity preference–money supply" (LM) curves models "general equilibrium" where supposed simultaneous equilibria occur in both the goods and the asset markets. Yet two equivalent interpretations are possible: first, the IS–LM model explains changes in national income when the price level is fixed in the short-run; second, the IS–LM model shows why an aggregate demand curve can shift. Hence, this tool is sometimes used not only to analyse economic fluctuations but also to suggest potential levels for appropriate stabilisation policies.

**Nicholas Kaldor, Baron Kaldor**, born **Káldor Miklós**, was a Cambridge economist in the post-war period. He developed the "compensation" criteria called Kaldor–Hicks efficiency for welfare comparisons (1939), derived the cobweb model, and argued for certain regularities observable in economic growth, which are called Kaldor's growth laws. Kaldor worked alongside Gunnar Myrdal to develop the key concept Circular Cumulative Causation, a multicausal approach where the core variables and their linkages are delineated. Both Myrdal and Kaldor examine circular relationships, where the interdependencies between factors are relatively strong, and where variables interlink in the determination of major processes. Gunnar Myrdal got the concept from Knut Wicksell and developed it alongside Nicholas Kaldor when they worked together at the United Nations Economic Commission for Europe. Myrdal concentrated on the social provisioning aspect of development, while Kaldor concentrated on demand-supply relationships to the manufacturing sector. Kaldor also coined the term "convenience yield" related to commodity markets and the so-called theory of storage, which was initially developed by Holbrook Working.

* The General Theory of Employment, Interest and Money* of 1936 is a book by English economist John Maynard Keynes. It caused a profound shift in economic thought, giving macroeconomics a central place in economic theory and contributing much of its terminology – the "Keynesian Revolution". It had equally powerful consequences in economic policy, being interpreted as providing theoretical support for government spending in general, and for budgetary deficits, monetary intervention and counter-cyclical policies in particular. It is pervaded with an air of mistrust for the rationality of free-market decision making.

The **marginal propensity to save** (**MPS**) is the fraction of an increase in income that is not spent and instead used for saving. It is the slope of the line plotting saving against income. For example, if a household earns one extra dollar, and the marginal propensity to save is 0.35, then of that dollar, the household will spend 65 cents and save 35 cents. Likewise, it is the fractional decrease in saving that results from a decrease in income.

In economics, the **marginal propensity to consume** (**MPC**) is a metric that quantifies induced consumption, the concept that the increase in personal consumer spending (consumption) occurs with an increase in disposable income. The proportion of disposable income which individuals spend on consumption is known as propensity to consume. MPC is the proportion of additional income that an individual consumes. For example, if a household earns one extra dollar of disposable income, and the marginal propensity to consume is 0.65, then of that dollar, the household will spend 65 cents and save 35 cents. Obviously, the household cannot spend *more* than the extra dollar.

In economics, a **model** is a theoretical construct representing economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified, often mathematical, framework designed to illustrate complex processes. Frequently, economic models posit structural parameters. A model may have various exogenous variables, and those variables may change to create various responses by economic variables. Methodological uses of models include investigation, theorizing, and fitting theories to the world.

In economics, the **consumption function** describes a relationship between consumption and disposable income. The concept is believed to have been introduced into macroeconomics by John Maynard Keynes in 1936, who used it to develop the notion of a government spending multiplier.

In economics, **comparative statics** is the comparison of two different economic outcomes, before and after a change in some underlying exogenous parameter.

In monetary economics, a **money multiplier** is one of various closely related ratios of commercial bank money to central bank money under a fractional-reserve banking system. It relates to the *maximum* amount of commercial bank money that can be created, given a certain amount of central bank money. In a fractional-reserve banking system that has legal reserve requirements, the total amount of loans that commercial banks are allowed to extend is equal to a multiple of the amount of reserves. This multiple is the reciprocal of the reserve ratio minus one, and it is an economic multiplier. The actual ratio of money to central bank money, also called the money multiplier, is lower because some funds are held by the non-bank public as currency. Also, in the United States most banks hold excess reserves.

In statistics, and particularly in econometrics, the **reduced form** of a system of equations is the result of solving the system for the endogenous variables. This gives the latter as functions of the exogenous variables, if any. In econometrics, the equations of a structural form model are estimated in their theoretically given form, while an alternative approach to estimation is to first solve the theoretical equations for the endogenous variables to obtain reduced form equations, and then to estimate the reduced form equations.

In statistics, econometrics, epidemiology and related disciplines, the method of **instrumental variables** (**IV**) is used to estimate causal relationships when controlled experiments are not feasible or when a treatment is not successfully delivered to every unit in a randomized experiment. Intuitively, IVs are used when an explanatory variable of interest is correlated with the error term, in which case ordinary least squares and ANOVA give biased results. A valid instrument induces changes in the explanatory variable but has no independent effect on the dependent variable, allowing a researcher to uncover the causal effect of the explanatory variable on the dependent variable.

A **balanced budget** is a budget in which revenues are equal to expenditures. Thus, neither a budget deficit nor a budget surplus exists. More generally, it is a budget that has no budget deficit, but could possibly have a **budget surplus**. A *cyclically* balanced budget is a budget that is not necessarily balanced year-to-year, but is balanced over the economic cycle, running a surplus in boom years and running a deficit in lean years, with these offsetting over time.

* Foundations of Economic Analysis* is a book by Paul A. Samuelson published in 1947 by Harvard University Press. It is based on Samuelson's 1941 doctoral dissertation at Harvard University. The book sought to demonstrate a common mathematical structure underlying multiple branches of economics from two basic principles: maximizing behavior of agents and stability of equilibrium as to economic systems. Among other contributions, it advanced the theory of index numbers and generalized welfare economics. It is especially known for definitively stating and formalizing qualitative and quantitative versions of the "comparative statics" method for calculating how a change in any parameter affects an economic system. One of its key insights about comparative statics, called the correspondence principle, states that stability of equilibrium implies testable predictions about how the equilibrium changes when parameters are changed.

The **AD–AS** or **aggregate demand–aggregate supply model** is a macroeconomic model that explains price level and output through the relationship of aggregate demand and aggregate supply.

**Luigi L. Pasinetti** is an Italian economist of the post-Keynesian school. Pasinetti is considered the heir of the "Cambridge Keynesians" and a student of Piero Sraffa and Richard Kahn. Along with them, as well as Joan Robinson, he was one of the prominent members on the "Cambridge, UK" side of the Cambridge capital controversy. His contributions to economics include developing the analytical foundations of neo-Ricardian economics, including the theory of value and distribution, as well as work in the line of Kaldorian theory of growth and income distribution. He has also developed the theory of structural change and economic growth, structural economic dynamics and uneven sectoral development.

The **Cambridge capital controversy**, sometimes called "**the capital controversy**" or "**the two Cambridges debate**", was a dispute between proponents of two differing theoretical and mathematical positions in economics that started in the 1950s and lasted well into the 1960s. The debate concerned the nature and role of capital goods and a critique of the neoclassical vision of aggregate production and distribution. The name arises from the location of the principals involved in the controversy: the debate was largely between economists such as Joan Robinson and Piero Sraffa at the University of Cambridge in England and economists such as Paul Samuelson and Robert Solow at the Massachusetts Institute of Technology, in Cambridge, Massachusetts.

The **wage unit** is a unit of measurement for monetary quantities introduced by Keynes in his 1936 book *The General Theory of Employment, Interest and Money*. A value expressed in wage units is equal to its price in money units divided by the wage of a man-hour of labour.

The **monetary/fiscal policy debate**, otherwise known as the **Ando–Modigliani/Friedman–Meiselman debate**, was the exchange of viewpoints about the comparative efficiency of monetary policies and fiscal policies that originated with a work co-authored by Milton Friedman and David I. Meiselman and first published in 1963, as part of studies submitted to the Commission on Money and Credit.

- ↑ James Hamilton (1994),
*Time Series Analysis*, Chapter 1, page 2. Princeton University Press. - ↑ Helmut Lütkepohl (2008), 'Impulse response function'.
*The New Palgrave Dictionary of Economics*, 2nd. ed. - ↑ The multiplier theory, by Hugo Hegeland, 1954, p. 1
- ↑ The Economic record, by the Economic Society of Australia and New Zealand, 1962, p. 74 Donald Markwell,
*Keynes and Australia*, Reserve Bank of Australia, 2000, pages 34-7. http://www.rba.gov.au/publications/rdp/2000/pdf/rdp2000-04.pdf - ↑ The origins of the Keynesian revolution, by Robert William Dimand, p. 117

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