# Relationship between hicksian marshallian demand function

### Supplementary Materials 7b

If we work with a generic utility function (we do not know its mathematical . It is the relation between marshallian demand function and indirect utility function A compensated (Hicksian) demand curve shows the relationship between the. want to derive the Slutsky equation, which gives the relationship between the derivatives of Marshallian and Hicksian demand (decomposing. would produce a Hicksian demand curve or compensated demand curve (see usually called the Marshallian demand curve if there is need to distinguish it . accurately and graphically the difference in size between the CV and EV.) x. £y.

It will only be the talk of the town if you buy a very expensive brand of computers. Because PCs are in great demand in our society, prices of computers have risen.

### Difference Between Hicks and Slutsky | Difference Between | Hicks vs Slutsky

However, since people are searching for cheaper brands, the prices of computers have also decreased. This also compares to holidays. For example, when Christmas is near, the prices for fruits, hams, and pastas increase. Our mothers are very wise because they know that the prices of hams and pastas are still low when December is not yet around.

Several microeconomics theories and functions are able to explain the situation. Some of these are the Hicks demand function and the Slutsky Equation. The differences between Hicks and Slutsky are the following. This is named after John Richard Hicks. He was an economist of British origin, and he was considered to be one of the most influential economists that had great contributions during the 20th century.

Hicksian demand functions are connected to the Marshallian demand functions which are then fundamentally related by the Slutsky equation. Marshallian demand functions originated from the Utility Maximization Problem while Hicksian demand functions come from the Expenditure Minimization Problem.

## Difference Between Hicks and Slutsky

Hicksian demand functions are closely related to expenditure functions. This microeconomic equation was named after Eugen Slutsky.

Eugen Slutsky was a known Russian economist, statistician, and political economist. Suppose the initial equilibrium of the consumer is at point R where the budget line PQ is tangent to the indifference curve I1, and OA of good X is bought by the consumer in the tipper diagram.

Let the price of X fall. As a result, the budget line PQ extends to PQ3 and the consumer is at a higher point of equilibrium T on the indifference curve I3.

The movement from R to T is the price effect which includes both the substitution effect and the income effect.

**Deriving Marshallian and Hicksian Demand Functions (Compensated and Uncompensated Demand)**

This is shown by the D3 curve in the lower portion of the figure. This is the uncompensated or ordinary or Marshallian demand curve which shows that when the price of good X falls from P to P1 its quantity demanded increases from OA to OD.

The Hicksian Compensated Demand Curve: Since the compensated demand curve is based on the substitution effect of a change in the price of good X, we carry the above analysis further and derive the Hicks substitution effect. Let us take away the increase in the real income of the consumer due to the fall in the price of X equal to PM of good Y and Q1 N of X good by drawing a compensated budget line MN parallel to the budget line PQ1.

This line MN is tangent to the original indifference curve I1, at point H.

### Hicksian demand function - Wikipedia

The movement from point R to H on the I1, curve is the substitution effect which traces out the demand curve D1, in the lower portion of the figure when the demand for X increases from OA to OB with the fall in its price from P to P1. The Slutsky Compensated Demand Curve: In order to derive the Slutsky substitution effect, let us take away the increase in the apparent real income of the consumer equal to PMX of Y and Q1N1 of X by drawing the Slutsky compensated budget line M1N1, parallel to PQ which passes through the original point R on the I1, curve where he will buy the same quantity OA of X.

But since the price of X has fallen, he will buy more of it so that he moves to point S on the higher indifference curve I2, which is tangent to the budget line M1N1 Thus the movement from R to S traces out the Slutsky compensated demand curve D2 in the lower part of the figure.

A perusal of the compensated demand curve D1 of Hicks and D2 of Slutsky shows that the curve D2 is more elastic than D1. This is because the total expenditure on the purchase of good X is greater in the Slutsky approach than in the Hicks approach. While the conventional demand curves D3 is more elastic than even the Slutsky demand curve D2.