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Individual Demand. How Does the Best Affordable Bundle Change when the Prices or the Income Change . Optimal Consumer Choice. Assume consumer’s preferences over bundles of two goods, x and y, can be represented by a utility function U(x,y). The prices of the two goods are

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Individual demand

Individual Demand

How Does the Best Affordable Bundle Change when the Prices or the Income Change


Optimal consumer choice
Optimal Consumer Choice

  • Assume consumer’s preferences over bundles of two goods, x and y, can be represented by a utility function U(x,y).

  • The prices of the two goods are

  • Consumer’s income is I.

  • The optimal bundle will be a solution to the following problem:


Best affordable bundle
Best Affordable Bundle

  • Assuming convexity and “more-is-better” properties, plus some other technical assumptions, an interior solution will satisfy:

  • In words: the marginal rate of substitution between the two goods is equal to the ratio of prices and all the income is spent on purchases of the two goods.


Corner solutions perfect substitutes
Corner Solutions: Perfect Substitutes

y

  • If the goods are perfect substitutes, so that the marginal rate of substitution is constant no matter how much of each one of the goods the consumer has, the best affordable bundle may contain only one of the goods.

5

x


Marginal rate of substitution may not be well defined perfect complements
Marginal Rate of Substitution may not be well defined: Perfect Complements

  • If the goods are perfect complements, so that a consumer uses, say, 5 units of good y for every unit of good x, the best affordable bundle will always contain a fixed proportion of goods independent of the ratio of prices.

y

x


Income changes
Income Changes Perfect Complements

  • Income Expansion Path traces the changes in the composition of the best affordable bundle as the income changes

  • The Engel Curve is the relationship between the income and the amount of a good consumed


Income expansion path
Income Expansion Path Perfect Complements


Superior goods
Superior Goods Perfect Complements

As the consumer’s income increases, the quantity demanded increases


Superior and inferior goods
Superior and Inferior Goods Perfect Complements

A good is inferior if the quantity demanded falls with the consumer’s income


Income and tastes
Income and Tastes Perfect Complements


Price consumption path
Price Consumption Path Perfect Complements

  • Holding income and price of the second goodfixed, the Price Consumption Path for good one is the set of best affordable bundles as the price of this good varies.


Price consumption path1
Price-Consumption Path Perfect Complements


Individual demand curve
Individual Demand Curve Perfect Complements

  • The individual demand curve is the relationship that shows how much of a good the consumer wants to purchase when the price of this good varies and the rest of the prices and the income are held constant.



Income and substitution effects
Income and Substitution Effects Perfect Complements


The resulting demand
The resulting Demand Perfect Complements



Figure 3 13 giffen good
Figure 3.13 Giffen Good Perfect Complements


Compensating for price changes over compensation
Compensating for Price Changes: Perfect Complements“overcompensation”