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In microeconomics, a consumer's Marshallian demand function is the quantity he/she demands of a particular good as a function of its price, his/her income, and the prices of other goods, a more technical exposition of the standard demand function. It is a solution to the utility maximization problem of how the consumer can maximize his/her utility for given income and prices. 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 his/her 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. Although Marshallian demand is in the context of partial equilibrium theory, it is sometimes called Walrasian demand as used in general equilibrium theory.
According to the utility maximization problem, there are L commodities with price vector p and choosable quantity vector x. The consumer has income I, and hence a budget set of affordable packages
where ⟨ p , x ⟩ {\displaystyle \langle p,x\rangle } is the inner product of the price and quantity vectors. The consumer has a utility function
The consumer's Marshallian demand correspondence is defined to be
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