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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. For example, suppose variable x changes by k units, which causes another variable y to change by M × k units.
This equation implies that if Y rises by 10, then net investment will equal 10×2 = 20, as suggested by the accelerator effect. If Y then rises by only 5, the equation implies that the level of investment will be 5×2 = 10. This means that the simple accelerator model implies that fixed investment will fall if the growth of production slows.
The multiplier–accelerator model can be stated for a closed economy as follows: [3] First, the market-clearing level of economic activity is defined as that at which production exactly matches the total of government spending intentions, households' consumption intentions and firms' investing intentions.
The complex multiplier is the multiplier principle in Keynesian economics (formulated by John Maynard Keynes).The simplistic multiplier that is the reciprocal of the marginal propensity to save is a special case used for illustrative purposes only.
In economics, the consumption function describes a relationship between consumption and disposable income. [ 1 ] [ 2 ] 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 .
The money multiplier is normally presented in the context of some simple accounting identities: [1] [2] Usually, the money supply (M) is defined as consisting of two components: (physical) currency (C) and deposit accounts (D) held by the general public. By definition, therefore: = +.
The MPS plays a central role in Keynesian economics as it quantifies the saving-income relation, which is the flip side of the consumption-income relation, and according to Keynes it reflects the fundamental psychological law. The marginal propensity to save is also a key variable in determining the value of the multiplier.
The costate equation is related to the state equation used in optimal control. [ 1 ] [ 2 ] It is also referred to as auxiliary , adjoint , influence , or multiplier equation . It is stated as a vector of first order differential equations