Answer to Question #186056 in Macroeconomics for Fayaz Ahmad

Question

derive and explain the marshallian and hicksian demand curves using the indifference curve approach

Answer 1

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The Marshallian and Hickson demands are two approaches to almost the same problem: how to get value we want with the money we have.

We must also look at the Lagrangian functions where we obtain the first derivatives.

This brings us to the most important distinction between the two forms of demand: The relationship between the price of a good and the quantity demanded is depicted by Marshallian demand curves. Hickson demand curves depict the relationship between a good's price and the quantity supplied, considering that some other products' prices and our degree of utility remain static. We simply cannot be as satisfied if we do not maintain equal purchasing power.

Marshallian and Hickson demand curves meet where the quantity demanded is equal for both sides of the consumer choice problem.

Consumer wealth is higher with Hickson demand curves than with Marshallian demand curves for prices above this equilibrium point, since Hickson demand curves presume real wealth remains unchanged to maintain utility constant. Only nominal wealth is assumed to be equal in Marshallian demand.

For prices below this level, the reverse is true: Marshallian demand implies that the consumer is better off as nominal wealth stays constant but price levels fall (negative inflation). Since Hickson demand assumes constant real wealth, the person is worse off. This is why Marshallian demand curves are more 'stable': they take into account both rent and substitution effects.

For an individual problem, these are obtained from the first order conditions of the Lagrangian for either a primal or dual demand problem.

Formally:

Marshallian demand $(dX1)$ is a function of the price of$X1$ , the price of $X2$  (assuming two goods) and the level of income or wealth($m):$

$X^*=dX1(PX1, PX2, m)$ .

Hickson demand $(hX1)$ is a function of the price of $X1,$ the price of $X2$  (assuming two goods) and the level of utility we opt for$(U)$ :$X^*=hX1(PX1,PX2,U)$