D

ECO1014_Topic_5_Week_5_Theory_Lecture__1_

Course Overview

  • Course Title: Consumer Theory II

  • Instructor: Dr. Eric Golson

  • Institution: University of Surrey

  • Academic Year: 2024-25

  • Contact: e.golson@surrey.ac.uk

Course Structure

  • Outline of Week 5:

    • Consumer Optimization: Comparative Statics

    • Income and Substitution Effects

    • Marginal Rate of Substitution (MRS) and Marginal Utilities

    • Essential Reading: Begg et al., Chapter 5

Review of Previous Week

  • Indifference Curves Representation:

    • Consumers’ preferences can be represented by indifference curves.

    • Three Axioms of Preferences:

      • Completeness

      • Transitivity

      • Local Nonsatiation

  • Marginal Rate of Substitution (MRS):

    • Calculated as the slope of the indifference curve (MRS = dy/dx).

  • Budget Constraint:

    • Represents the limits of consumption choices based on income.

    • Equivalent to the Production Possibility Frontier (PPF).

    • Optimal consumption occurs when the budget constraint is tangent to the indifference curve.

Optimization - Numerical Example

  • Utility Function Example: U(x, y) = xy

    • Price of Good x (Px) = 2

    • Price of Good y (Py) = 4

    • Consumer's Total Income = 80

  • Implications:

    • The utility function indicates the consumer values goods x and y significantly.

    • Both goods must be consumed to derive utility—these are not perfect complements.

  • Visual Representation:

    • Need to find budget constraint and indifference curve for analysis.

Budget Constraint Calculation

  • Budget Constraint Formula: 2x + 4y = 80

    • Rearranged: y = 20 - 0.5x

  • Indifference Curve Calculation:

    • U = xy

    • Rearranged: y = U/x

MRS Calculation

  • At optimum: MRS must equal the slope of the budget constraint.

  • Slope Calculation: Budget constraint slope = -0.5

    • MRS definition:

      • Represents how much of good y the consumer is willing to sacrifice for an additional unit of good x.

    • MRS= dy/dx = -y/x

  • From the optimum conditions:

    • y = 1/2 x

    • Substituting into budget constraint leads to optimal quantities: x* = 20, y* = 10.

Marginal Utility

  • Definition: Marginal utility indicates the gain in utility from increasing the consumption of a good slightly.

  • Relationship Between MRS and Marginal Utility:

    • Along an indifference curve, total change in utility must equal zero with partial derivatives.

  • Marginal Utility Equations:

    • MUx = ∂U/∂x (Marginal utility of x)

    • MUy = ∂U/∂y (Marginal utility of y)

    • Along the indifference curve, 0 = MUx * dx + MUy * dy implies:

      • dy/dx = - MUx / MUy

Comparative Statics

  • Examines how changes in exogenous variables affect consumer behavior.

    • Focus on changes to income and goods' prices.

  • Income Effects: Normal vs. Inferior Goods:

    • Normal Goods: Consumption increases as income rises.

    • Inferior Goods: Consumption decreases as income rises.

Income and Substitution Effects

  • Law of Demand: Inversely relates price changes to quantity demanded.

    • Effects to consider:

      • Income Effect: Changes in purchasing power due to price changes.

      • Substitution Effect: Changes in consumption patterns in response to relative price changes.

  • Graphical Analysis: Demonstrates shifts in consumption decisions due to price changes.

Transfers: Cash vs. Kind

  • Consumers benefit more from cash transfers than free goods due to flexibility in spending choices.

Course Recap and Future Topics

  • Current Concepts: Opportunity Costs, Demand and Supply, Market Equilibrium, Surplus, Elasticities, Consumer Theory (indifference curves, budget constraints, optimization).

  • Next Week: Introduction to Aggregate Demand and Output.