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# Income and Substitution Effects with Different Utility Functions

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.
Go through the following three steps at your own pace:
Initial price: the best affordable bundle (A) is shown for a given unit price of the commodity on the horizontal axis and the consumer's income.
Increased price: the best affordable bundle (B) is now superimposed after increasing the price of the commodity on the horizontal axis, everything else being equal.
Compensated income: the best affordable bundle (C) is now superimposed while keeping the increased price constant and changing the income so as to leave the consumer indifferent with the initial bundle A.
The income effect, defined as the horizontal difference between points B and C, is then highlighted in blue. The substitution effect, defined as the horizontal difference between points A and C, is then highlighted in red.
You can also alter the parameter governing the shape of the indifference curves to test whether and how income and substitution effects vary. This exercise is particularly useful when dealing with the CES utility function since it allows you to verify one of its properties, namely it can generate Cobb–Douglas, Leontieff, and linear utility functions as special cases.

### 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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