Key Concepts of Microeconomic Theory

Utility Maximization

• Individuals aim to maximize utility given a fixed income and market prices.
• The Marginal Rate of Substitution (MRS) should equate to the ratio of goods’ market prices.
• The model assumes people act like they perform these calculations, predicting behavior without actual computation.

Graphical Analysis

• Budget Constraint: Shows combinations of two goods that can be afforded.
  • Slope is determined by the ratio of prices.
• Utility Maximization: Occurs where an indifference curve is tangent to the budget line.
• Corner Solutions: Occur when one good is not consumed at all.

Mathematical Approach

• First-order conditions: Involve setting the partial derivatives to zero, ensuring the MRS equals the price ratio.
• Lagrange Multiplier (λ): Represents the marginal utility of income.
• Indirect Utility Function: Reflects utility in terms of prices and income.
• Lump Sum Principle: Taxes on income are more efficient than taxes on goods.

Expenditure Minimization

• Dual problem: Minimize expenditure for a given utility level.
• Expenditure Function: Shows minimal spending needed to achieve a utility level.
  • Properties: Homogeneous of degree one, concave in prices, nondecreasing with prices.

Income and Substitution Effects

Demand Functions

• Quantity demanded is a function of prices and income.
• Homogeneity: Demand is homogeneous of degree 0; proportional changes in prices and income leave demand unchanged.

Effects of Income Changes

• Normal Goods: Quantity demanded increases with income.
• Inferior Goods: Quantity demanded decreases with income.

Effects of Price Changes

• Substitution Effect: Change in consumption when price changes but utility is constant.
• Income Effect: Change in consumption due to change in real income from a price change.
• Giffen Goods: Inferior goods with a positive price-quantity relationship due to strong income effects.

Demand Curves

• Individual Demand Curve: Shows the relationship between price and quantity demanded, holding other factors constant.
• Compensated (Hicksian) Demand Curve: Reflects only substitution effects, holding utility constant.

Mathematical Analysis

• Slutsky Equation: Decomposes the effect of a price change into substitution and income effects.
  • Substitution effect always negative.
  • Income effect direction depends on whether the good is normal or inferior.

Demand Elasticities

• Price Elasticity: Measures responsiveness of quantity demanded to price changes.
  • Elastic, unit-elastic, and inelastic demand based on elasticity value.
• Income and Cross-Price Elasticities: Measure responsiveness to income changes and price changes of other goods.
• Relationships: Homogeneity, Engel aggregation, and Cournot aggregation describe interaction between different elasticities.

Consumer Surplus

• Consumer Welfare: Measured by changes in expenditure needed to maintain utility when prices change.
• Expenditure Function: Provides a basis for measuring welfare effects of price changes.