Deriving Hicksian (compensated) Demand Using the Slutsky Equation

Deriving Hicksian (compensated) Demand Using the Slutsky Equation

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Derivation of Hicksian Demand Function using the Slutsky Equation.

In this video, I offer a derivation of the Slutsky Equation (an equation that decomposes the Marshallian demand curve's price effect into income and substitution effects). The video intuitively motivates the Slutsky Identity by relating the utility maximization problem to the expenditure minimization problem.

The Slutsky equation (or Slutsky identity) in economics, named after Eugen Slutsky, relates changes in Marshallian (uncompensated) demand to changes in Hicksian (compensated) demand, which is known as such since it compensates to maintain a fixed level of utility. The equation demonstrates that the change in the demand for a good, caused by a price change, is the result of two effects:

Effect One - a substitution effect, the result of a change in the relative prices of two goods; and

Effect Two - an income effect, the effect of a change in price resulting in a change in the consumer's purchasing power.

Learn how to derive a demand function form a consumer's utility function. In this problem there is no utility function, only the consumers optimal demand for one of the two goods.

This video introduces the Cobb-Douglas utility function for two goods and demonstrates some of its properties.

I demonstrate how to compute marginal rate of substitution for Cobb Douglas utility. I use the resulting expression to show why Cobb Douglas indifference curves have constant slope along rays out of the origin.

I also demonstrate how to solve for consumer demand using the Cobb-Douglas utility function. After deriving Cobb-Douglas demand, I show that the alpha share parameter in Cobb-Douglas utility functions actually represents the consumer's expenditure share on that good.

This video uses calculus to compute MRS, but after that, the rest is just algebra. If you are a viewer who doesn't know calculus, you can take me at my word, skip the computation of MRS, and the rest of the video can still be worthwhile.

Economics Playlist

Derivation of Marshallian Demand Functions from Utility Functions:    • Derivation of Marshallian Demand Functions...  

Derivation of Marshallian Demand Functions from Utility Functions (II):    • Derivation of Marshallian Demand Functions...  


Derivation of Hicksian Demand Functions from Utility Functions:
   • Derivation of Hicksian Demand Function fro...  

Deriving Marshallian and Hicksian Demand Functions (compensated and uncompensated demand):
   • Deriving Marshallian and Hicksian Demand F...  

Derivation of a Generalised (n-good) Marshallian Demand Function from Utility Function.
   • Derivation of a Generalised (n-good) Marsh...  

Deriving Hicksian (compensated) Demand Using the Slutsky Equation:
   • Deriving Hicksian (compensated) Demand Usi...  

Deriving Marshallian Demand From a Stone-Geary Utility Function:
   • Deriving Marshallian Demand from Stone-Gea...  

I hope it helps :)