# Income and Substitution Effects with Different Utility Functions

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This Demonstration shows the income and substitution effects for the commodity on the horizontal axis as its unit price increases for a variety of utility functions. These range from standard textbook Cobb-Douglas, Leontieff (perfect complements), and linear (perfect substitutes) to constant elasticity of substitution (CES) utility functions, and utility functions having a satiation point or generating a Giffen demand.

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Contributed by: Massimiliano Landi (August 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Beside utility functions that are seen in undergraduate microeconomics courses, some other utility functions, generating a Giffen demand, are also shown so as to visualize the difference in sign and magnitudes of income and substitution effects. You can select the utility functions from the menu; initially a utility is randomly chosen. The utility functions are:

Cobb–Douglas:

Leontieff (perfect complements):

Linear (perfect substitutes):

Bliss point:

Giffen goods (1):

Giffen goods (2):

Constant elasticity of substitution (CES):

Giffen goods (1) is characterized by a zero substitution effect [1] whereas Giffen goods (2) has a negative substitution effect that nevertheless is counterbalanced by a positive income effect [2].

References

[1] P. N. Sørensen, "Simple Utility Functions with Giffen Demand," *Economic Theory*, 31, 2007 pp. 367–370.

[2] M. Landi, "Single Peakedness and Giffen Demand," MIMEO, Singapore Management University, 2011.

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