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lect04__Utility_Maximization

# lect04__Utility_Maximization - Utility maximization In...

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37 Utility maximization In general, a consumer will reach the highest level of satisfaction at a point where the slope of the budget line equals the slope of the indifference curve. All bundles on the budget line are on a lower indifference curve than E. At E the budget line and indifference curve have one point in common. There is a tangency at E between the budget line and indifference curve. Given this budget line, E is the optimal choice of consumption for this person. Different consumers, with different preferences can have different optimal choices for the same budget line. X 1 X 2 U 1 U 2 E

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38 If the consumer does not choose to consume one of the goods, there may not be a tangency at the optimal consumption bundle. This is what is known as a corner solution. In the diagram below, E is the consumption bundle that maximizes the consumer's utility. How do we find E? U X 1 X 2 This consumer chooses only X 2 X 1 X 2 U 1 U 2 E
39 At E two important conditions hold: Equation 1: MU 1 /MU 2 =P 1 /P 2 (at E the budget line and indifference curve are tangent) Equation 2: P 1 X 1 +P 2 X 2 =I (the consumer spends all of her income on X 1 and X 2 ) Solving for the consumption bundle E is just an algebra problem - 2 equations in 2 unknowns, X 1 and X 2 . When we solve for X 1 and X 2 with P 1 , P 2 and I unspecified, we solve for the entire demand functions. To obtain a particular solution, substitute in the appropriate values for P 1 , P 2 and I.

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40 Example 1: a. What are the demand functions for the utility function U=X 1 X 2 ? b.
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lect04__Utility_Maximization - Utility maximization In...

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