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The Hicksian demand function isolates the substitution effect by supposing the consumer is compensated with exactly enough extra income after the price rise to purchase some bundle on the same indifference curve. [2] If the Hicksian demand function is steeper than the Marshallian demand, the good is a normal good; otherwise, the good is inferior.
A synonymous term is uncompensated demand function, because when the price rises the consumer is not compensated with higher nominal income for the fall in their real income, unlike in the Hicksian demand function. Thus the change in quantity demanded is a combination of a substitution effect and a wealth effect.
where (,) is the Hicksian demand and (,) is the Marshallian demand, at the vector of price levels , wealth level (or income level) , and fixed utility level given by maximizing utility at the original price and income, formally presented by the indirect utility function (,).
It is also possible that the Hicksian and Marshallian demands are not unique (i.e. there is more than one commodity bundle that satisfies the expenditure minimization problem); then the demand is a correspondence, and not a function. This does not happen, and the demands are functions, under the assumption of local nonsatiation.
Roy's identity reformulates Shephard's lemma in order to get a Marshallian demand function for an individual and a good from some indirect utility function.. The first step is to consider the trivial identity obtained by substituting the expenditure function for wealth or income in the indirect utility function (,), at a utility of :
where (,) is the Hicksian demand for good , (,) is the expenditure function, and both functions are in terms of prices (a vector) and utility . Likewise, in the theory of the firm , the lemma gives a similar formulation for the conditional factor demand for each input factor: the derivative of the cost function c ( w , y ) {\displaystyle c ...
The substitution effect is the change that would occur if the consumer were required to remain on the original indifference curve; this is the move from A to B. The income effect is the simultaneous move from B to C that occurs because the lower price of one good in fact allows movement to a higher indifference curve.
In economics, the Hicks–Marshall laws of derived demand assert that, other things equal, the own-wage elasticity of demand for a category of labor is high under the following conditions: When the price elasticity of demand for the product being produced is high (scale effect). So when final product demand is elastic, an increase in wages will ...