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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.)
The costate variables () can be interpreted as Lagrange multipliers associated with the state equations. The state equations represent constraints of the minimization problem, and the costate variables represent the marginal cost of violating those constraints; in economic terms the costate variables are the shadow prices.
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 accelerator effect in economics is a positive effect on private fixed investment of the growth of the market economy (measured e.g. by a change in gross domestic product (GDP)). Rising GDP (an economic boom or prosperity) implies that businesses in general see rising profits, increased sales and cash flow, and greater use of existing capacity.
However, the size of this multiplier effect is likely to be diminished by two considerations: first, an upward push that the new spending gives to interest rates, which diminishes spending on goods such as physical capital and consumer durables; and second, an upward push that the spending gives to the general price level, which diminishes the ...
As has been discussed, the multiplier relies on the MPC (marginal propensity to consume). The use of the term MPC here is a reference to the MPC of a country (or similar economic unit) as a whole, and the theory and the mathematical formulae apply to this use of the term.
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.
For example, in economics the optimal profit to a player is calculated subject to a constrained space of actions, where a Lagrange multiplier is the change in the optimal value of the objective function (profit) due to the relaxation of a given constraint (e.g. through a change in income); in such a context is the marginal cost of the ...