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Usual Utility Maximization

In the context of usual utility maximization problems involving two goods, prove that:
a) All goods must have one net substitute.
b) An inferior good must have at least one gross substitute.

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This question hinges on the difference between net and gross substitutes, which in turn depends on the income and substitution effects. Recall that the consumer theory uses indifference curves to describe how consumers make choices. Given a certain amount of income, consumers allocate their money between two or more goods so as the maximize their utility (U=U(x1,x2)). The income constraint can be described mathematically as I = px1(x2) + px2(x2). In other words, the total available income is allocated between the two available goods.

The income effect describes how consumers react to an increase in purchasing power. For example, if the price of a good one normally buys falls, it leaves one with more money to buy other things. The substitution effect describes how consumers reallocate consumption of goods in response to changes in ...

Solution Summary

Proving that for all goods there must be one net substitute, and for inferior goods there must be one gross substitute. Exploration of the substitution and income effects.

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