Individual demand
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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

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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

  • 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


Superior goods

Superior Goods

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


Superior and inferior goods

Superior and Inferior Goods

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


Income and tastes

Income and Tastes


Price consumption path

Price Consumption Path

  • 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


Individual demand curve

Individual Demand Curve

  • 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.


Figure 3 7 demand curve for good 1

Figure 3.7 Demand Curve for Good 1


Income and substitution effects

Income and Substitution Effects


The resulting demand

The resulting Demand


Income and substitution effects work in opposite directions

Income and Substitution Effects Work in Opposite Directions


Figure 3 13 giffen good

Figure 3.13 Giffen Good


Compensating for price changes over compensation

Compensating for Price Changes:“overcompensation”


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