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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.
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 ...
A Cobb-Douglas utility function (see Cobb-Douglas production function) with two goods and income generates Marshallian demand for goods 1 and 2 of = / and = /. Rearrange the Slutsky equation to put the Hicksian derivative on the left-hand-side yields the substitution effect:
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 is akin to the result that the price derivatives of the expenditure function give the Hicksian demand functions. The additional step of dividing by the wealth derivative of the indirect utility function in Roy's identity is necessary since the indirect utility function, unlike the expenditure function, has an ordinal ...
The relationship between the utility function and Marshallian demand in the utility maximisation problem mirrors the relationship between the expenditure function and Hicksian demand in the expenditure minimisation problem. In expenditure minimisation the utility level is given and well as the prices of goods, the role of the consumer is to ...
In economics, deadweight loss is the loss of societal economic welfare due to production/consumption of a good at a quantity where marginal benefit (to society) does not equal marginal cost (to society) – in other words, there are either goods being produced despite the cost of doing so being larger than the benefit, or additional goods are not being produced despite the fact that the ...
Hicks decomposition, Hicksian decomposition, Hicksian decomposition of demand-> concept in economics. See Slutsky equation and Hicksian demand function; Gains from production, Gains from specialization-> This is the term for the benefits that occur due to the shift in supply after trade takes place