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In microeconomics, the expenditure function represents the minimum amount of expenditure needed to achieve a given level of utility, given a utility function and the prices of goods. Formally, if there is a utility function u {\displaystyle u} that describes preferences over n goods, the expenditure function e ( p , u ∗ ) {\displaystyle e(p,u ...
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. Then the multiplier is M.
Formally, the expenditure function is defined as follows. Suppose the consumer has a utility function defined on commodities. Then the consumer's expenditure function gives the amount of money required to buy a package of commodities at given prices that give utility of at least ,
Chapter 10 introduces the famous 'multiplier' through an example: if the marginal propensity to consume is 90%, then 'the multiplier k is 10; and the total employment caused by (e.g.) increased public works will be ten times the employment caused by the public works themselves' (pp. 116f). Formally Keynes writes the multiplier as k=1/S'(Y).
Average propensity to consume (APC) (as well as the marginal propensity to consume) is a concept developed by John Maynard Keynes to analyze the consumption function, which is a formula where total consumption expenditures (C) of a household consist of autonomous consumption (C a) and income (Y) (or disposable income (Y d)) multiplied by marginal propensity to consume (c 1 or MPC).
The end result is a magnified, multiplied change in aggregate production initially triggered by the change in investment, but amplified by the change in consumption i.e. the initial investment multiplied by the consumption coefficient (Marginal Propensity to consume).
The other important aspect of the multiplier is that to the extent that government spending generates new consumption, it also generates "new" tax revenues. For example, when money is spent in a shop, purchases taxes such as VAT are paid on the expenditure, and the shopkeeper earns a higher income, and thus pays more income taxes.
Whereas Marshallian demand comes from the Utility Maximization Problem, Hicksian Demand comes from the Expenditure Minimization Problem. The two problems are mathematical duals, and hence the Duality Theorem provides a method of proving the relationships described above. The Hicksian demand function is intimately related to the expenditure ...