Hicksian demand curves show the relationship between the price of a good and the quantity demanded of it assuming that the prices of other goods and our level of utility remain constant,
while Marshallian demand curves simply show the relationship between the price of a good and the quantity demanded of it.
Hicksian demand functions are often convenient for mathematical manipulation because they do not require income or wealth to be represented. However, Marshallian demand functions of the form x ( p , m ) that describe demand given prices p and income m are easier to observe directly.
Whereas Marshallian demand comes from the Utility Maximization Problem, Hicksian Demand comes from the Expenditure Minimization Problem.
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