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*May 05, 2012*

**Utility Functions Consumer Behavio****ur**

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Utility Functions: There are many algebraic representation of utility functions. Some of them are discussed below:

A) COBB DOUGLAS UTILITY FUNCTION :

U= X^aY^1-a

Here U represents the utility achieved

X and Y are the units of commodities consumed

a is a constant less than 1

**Example:** Consider a case of an individual who consumes two commodities rice and wine.

Then his utility function can be created as : U = rice^a wine ^1-a

B) PERFECT SUBSTITUTES: (Linear utility functions)

When an individual consumes two commodities which are perfect substitutes of each other then his utility function takes a linear form and can be represented as:

U= aX + bY

Where U = Utility achieved

X and Y are perfect substitutes of each other

a and b are the positive constants

**Example:** Suppose an individual consumes two commodities Coke and Pepsi which are considered to be perfect substitutes of each other. Then his utility function will take the form of:

U = a(Coke) + b(Pepsi)

Where a and b are positive constants

C) Perfect Complements ( Leontief utility function) : When an individual consumes two goods together in a fixed proportion then we get the following form of utility function:

U = Min(aX,bY)

U = Utility achieved

X and Y are perfect complement commodities

a and b are positive constants

**Example:** Suppose and individual consumes right shoe and left shoe. A pair of shoe is considered to be perfect complements and utility function of such an individual will take the following form:

U = min ( L , R)

Where L and R represent left and right shoe respectively.For further help in economics assignment please upload your economics assignment.