nhi 111 Lecture4

Microeconomics Lecture 4 Notes

Objectives

  • Understanding Comparative Statics

  • Deriving a demand curve from indifference curves and budget lines

  • Deriving an ‘Engel curve’ relating income and optimal choice

  • Classifying types of goods: normal versus inferior goods, 'ordinary goods', and 'Giffen goods'

Comparative Statics

  • Comparative statics involves the process of comparing two equilibria without analyzing the dynamics of transition.

  • Changes in equilibrium can result from:

    • Own price changes

    • Cross price changes

    • Income changes

Own Price Changes

Own Price Effects

  • The own price effect is the impact of a change in the price of a good on its quantity demanded.

  • A decrease in the price of good x raises the quantity demanded, but consumption of x may not necessarily increase.

  • Changes in the budget constraint represent how it rotates with price changes.

Diagram Details: Own Price Change Effects

  1. A visual representation of the effects of price changes is depicted with quantities and indifference curves.

    • If the price of x decreases:

    • Move from point x1 to x2 along the budget constraint from Budget Constraint 1 (BC1) to Budget Constraint 2 (BC2).

  2. Under the assumption of fixed prices of good y (p2) and income (y).

Ordinary Goods

  • Ordinary goods are those for which the quantity demanded increases as the price decreases (i.e., maintaining a downward-sloping demand curve).

Giffen Goods

  • Giffen goods are characterized by a rise in quantity demanded as the own price increases.

  • This situation typically occurs under specific conditions related to consumer behavior and necessity versus luxury desires.

  • An example from history includes the Irish potato famine, where rising potato prices led to increased consumption because individuals could not afford other luxuries.

Price-Consumption Curve

  • The price-consumption curve reflects the set of utility-maximizing bundles as the price changes, keeping other factors equal.

  • Traces movements along the demand curve as prices fluctuate, establishing the relationship to the ordinary demand curve.

Special Cases with Cobb-Douglas Preferences

  • In cases where preferences adhere to a Cobb-Douglas utility function, the demand functions for commodities 1 and 2 can be expressed as:
    U(x_1, x_2) = x_1^a x_2^b

  • The ordinary demand functions can be derived, leading to specific behaviors in price offer curves and demand characteristics.

Perfect Complements and Perfect Substitutes

  • Perfect Complements: Utility is defined in terms of both goods being consumed together. The ordinary demand functions reflect this relationship where demand decreases for one when the price increases for the other.

    • Utility function: U(x_1, x_2) = ext{min}(x_1, x_2)

  • Perfect Substitutes: Consumers replace one good with another at constant rates, leading to a different set of demand equations that shift according to their relative prices.

Income Changes

How Income Changes Affect Demand

  • Changes in income affect demand differently for normal and inferior goods:

    • Normal goods: Demand increases as income increases.

    • Inferior goods: Demand decreases as income increases.

  • The Engel curve plots the relationship between quantity demanded and income, revealing the nature of goods as normal or inferior.

Engel Curve

  • The Engel curve is a graphical representation of the relationship between quantity demanded and income.

  • For normal goods, the Engel curve slopes upward, while it slopes downward for inferior goods.

Shapes of Engel Curves

  • Normal goods, luxuries, and necessities each exhibit distinct patterns in the Engel curve:

    • Luxuries: Fraction of income spent increases as income increases.

    • Necessities: Fraction of income spent decreases as income increases.

Cross Price Effects

Effects of Price Changes on Other Goods

  • Cross price effects include:

    • Gross Substitutes: An increase in the price of one good leads to an increase in demand for a substitute good.

    • Gross Complements: More expensive pricing of one good decreases demand for a complementary good.

    • Unrelated goods show no effect when the price of one changes.

Cross-Price Demand Functions

  • For perfect complements, the equations indicate that increasing the price of one good will lead to a lower quantity demanded of the other, while in Cobb-Douglas scenarios, interactions between goods can be more complex.