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Cobb-Douglas Formulation of Marshallian and Hicksian Demand Functions

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This Demonstration shows the relationships of iso-utility and iso-expenditures for the goods and in the Cobb–Douglas formulation for Marshallian and Hicksian levels of consumption. Both compensated and uncompensated income are considered. Let and be the number of units of the goods. Then the Cobb–Douglas utility form is:

[more]

,

with scalar factor for utility , and preference share parameters and . is normalized to 1.

Marshallian consumption 1 (blue curve and blue line): maximization of with optimal consumption , subject to uncompensated income , where and are the original prices.

Hicksian consumption (blue curve and green line): minimization of compensated income with optimal consumption , subject to original utility .

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Marshallian consumption 2 (red curve and red line): maximization of with optimal consumption , subject to uncompensated income , where and are the changed prices. (January 2023)
Contributed by: Carlos Angulo
Open content licensed under CC BY-NC-SA

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This Demonstration is based on forthcoming work that develops further mathematical analysis from an idea in [1]. The purpose is to explore how changes in the system parameters lead to changes in the equilibrium states. Hicksian substitution and income effects are represented in the following plots: (1) blue curve and blue line (original Marshallian consumption); (2) red curve and red line (final Marshallian consumption); and (3) blue curve and green line (Hicksian consumption).

References

[1] K. Sydsæter, P. Hammond, A. Strøm and A. Carvajal, Essential Mathematics for Economic Analysis, 6th ed., Hoboken, NJ: Pearson, 2021.

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