Chapter 4 Notes: Consumer Behavior

Chapter 4: Consumer Behavior

4.0 Introduction

• This chapter introduces a theory of consumer behavior to investigate why consumers make purchases.
• Consumers are assumed to "optimize" their utility given scarce resources.
• Consumer theory forms the basis for the "demand" side of the supply and demand model.

4.1 Consumers Preferences & The Concept of Utility

• Utility is a measure of how "satisfied" consumers are; a measure of happiness or well-being, not consumer income.

Utility Function

• Mathematical description of the relationship between actual consumption and the level of well-being.
• Represents consumers' preferences.
• Can take a variety of mathematical forms.
• Must conform to the four assumptions about preferences.

Utility with a Single Good

• Utility function is given by: $U(y) = \sqrt{y}$
• Marginal Utility (MU) is the slope of the total utility function: $MU_y = \frac{\triangle U}{\triangle y}$
• For example, if $U(y) = \sqrt{y}$, then $MU = \frac{1}{2\sqrt{y}}$

Principle of Diminishing Marginal Utility

• At some point, increased consumption of a good leads to a fall in the marginal utility of that good.
• As the quantity of y consumed increases ($Q<em>y \uparrow$), the marginal utility of y decreases ($MU</em>y \downarrow$).
• The graph of $U(y)$ is increasing but the gradient is decreasing.

Utility with More Than One Good

• Consider utility from seeing a movie in a theater (M) vs. watching a DVD (D):
  • $U = U(M, D)$
  • Utility might be represented by: $U = M^{0.8}D^{0.2}$. Movies consumed in the theater add more utility than those consumed at home [exponent on M in the theater (0.8) is larger than that on D movies at home (0.2)].

Marginal Utility

• Additional utility received from consuming an additional unit.
• The marginal utility of theater-movies and DVDs for this consumer is given by:
  • $MU<em>T = \frac{\triangle U(M,D)}{\triangle M} = U</em>M(M,D)$
  • $MU<em>D = \frac{\triangle U(M,D)}{\triangle D} = U</em>D(M,D)$
• With prescribed parameters ($U = T^{0.8}D^{0.2}$):
  • $MU_T = 0.8M^{-0.2}D^{0.2}$
  • $MU_D = 0.2M^{0.8}D^{-0.8}$

Comparing Consumption Outcomes

• Utility "rules" generate ordinal ranking of consumption bundles.

Ordinal Ranking

• Bundles can be ranked from best to worst.

Cardinal Ranking

• Can determine how much better one bundle is, compared to another.
  • Many questions can be answered with only an ordinal ranking (e.g., predicting what will be consumed).
  • There is no real-world measure of how much more a consumer likes bundle A compared to bundle B.

4.2 Indifference Curves

• Ordinal rankings are about relative outcomes.
• Some bundles are better than others; some are worse, some ranked equally (indifferent).
• A consumer is indifferent when he or she derives the same utility level from two or more bundles.
• Indifference curve plots out all of the consumption bundles that provide a consumer with the same level of utility or satisfaction.

Economic Assumption

• Consumers are rational and "optimize" consumption decisions given scarce resources.

Four Assumptions About Consumer Preferences:

1. Completeness and rankability
   • Consumers compare bundles of goods ranking them based on preference.
   • The consumer can rank any two bundles. For example baskets A and B:
     • Indifferent between, or equally happy with, bundles A and B (written A ≈ B).
     • Prefers bundle A to bundle B (written A ≻ B).
     • Prefers bundle B to bundle A (written B ≻ A).
2. For most goods, more is better than less
   • Non-satiation and "free disposal"
   • MU > 0
   • Preferences are (strongly) monotonic: a basket with more of at least one good and no less of the other good, is preferred to the original basket.
3. Transitivity
   • Imposes logical consistency on preferences. Consumer makes choices that are consistent with each other.
   • If A ≻ B and if B ≻ E, then A ≻ E.
4. The more a consumer has of a particular good, the less she is willing to give up of something else to get even more of that good
   • The idea behind this assumption is that consumers like variety.

Characteristics of Indifference Curves

• Derived from the four assumptions about consumer preferences:

  1. They can be drawn (completeness and rankability).
  2. Curves further from the origin represent higher utility (more is better).
  3. Curves never cross (transitivity).
  4. Convex to the origin (consumers like variety / diminishing marginal utility).

• Note:

  • Parallel
  • Downward sloping
  • As move down gradient diminishes

A Consumers Indifference Curves CANNOT Cross

• Bundles D and F are on the same indifference curve, therefore Joe must be indifferent between them.
• If an indifference curve through bundle F intersects the original curve it implies Joe is indifference between points E and F as well as between points F and D.
• If Joe ranks bundle F = E and F = D then should rank E = D. But E is on a higher curve than D so is preferred. This is Inconsistent!!!!!!

Tradeoffs along an Indifference Curve

• Bundle A to bundle B, apartment size increases by 250sq ft, no. of friends falls by 5 to leave utility unchanged.
• Bundle B to bundle C, apartment size increases by 250sq ft, no. of friends falls by 3 to leave utility unchanged.
• As apartment size gets larger, Jo is less willing to trade off the number of friends for additional apartment size.

The Marginal Rate of Substitution (MRS)

• Indifference curves describe tradeoffs.
  • How much of one good you are willing to give up for one more unit of another good?
• Indifference curve slope shows this tradeoff.
• We call this slope the marginal rate of substitution ($MRS_{XY}$).
• Describes the rate at which one is willing to trade off or substitute exactly 1 unit of good X for more of good Y, and be equally well off.

The Marginal Rate of Substitution and Marginal Utility

• As you move down an indifference curve, you experience a diminishing marginal rate of substitution.

The Marginal Rate of Substitution and Marginal Utility

• Change in the level of utility: $\triangle U = MU<em>{lattes} \times \triangle Q</em>{lattes} + MU<em>{burritos} \times \triangle Q</em>{burritos}$
• Along an indifference curve, the change in utility is zero. So:
  • $0 = MU<em>{lattes} \times \triangle Q</em>{lattes} + MU<em>{burritos} \times \triangle Q</em>{burritos}$
• Rearranging:
  • $-MU<em>{burritos} \times \triangle Q</em>{burritos} = MU<em>{lattes} \times \triangle Q</em>{lattes}$

The Marginal Rate of Substitution and Marginal Utility

• As move from point A to point B:
  • $Q<em>{lattes} \uparrow \rightarrow MU</em>{lattes} \downarrow$
  • $Q<em>{burritos} \downarrow \rightarrow MU</em>{burritos} \uparrow$
• Law of diminishing marginal utility
• $\frac{MU<em>{lattes}}{MU</em>{burritos}} = \frac{\downarrow}{\uparrow} = \downarrow$
• $MRS = \frac{\triangle Y}{\triangle X} = - \frac{MU<em>X}{MU</em>Y}$

The Marginal Rate of Substitution and Marginal Utility

• The MRS between two goods is equal to the inverse of the goods' marginal utilities.
• Steeper curves imply the consumer is willing to give up a lot of Y to get one unit of X, or could trade 1 unit of X for a lot of good Y.
• Flatter curves imply the consumer would require a large increase in good X to give up one unit of the good Y, or could trade 1 unit of Y for a lot of good X.

The Curvature of Indifference Curves: Substitutes and Complements

• Indifference curve shape depends on the relationship between products.
  • Relatively straight indifference curves - goods are more easily substitutable.
  • Indifference curves more convex to the origin - goods that are more complementary to one another.

Perfect Substitutes

• Goods that the consumer will trade at a fixed rate and receive the same level of utility (MRS is constant).

Perfect Complements

• Goods that the consumer must consume in a fixed proportion.

Indifference Curves for Perfect Substitutes

• Here consumers preferences for 3-oz and 12-oz bags of tortilla chips.
• This consumer should be willing to trade one 12-oz bag for four 3-oz bags no matter how much of each he or she has. MRS is constant in this case.

Indifference Curves for Perfect Complements

• Preferences for right and left shoes.
• Most consumers will prefer to consume these goods in constant proportion.
• Adding another right shoe will not increase utility. The consumer needs another left shoe as well if utility is to increase.

The Same Consumer Can Have Indifference Curves with Different Shapes

• Initially, for low levels of utility ($U_A$), bananas and strawberries might be substitutes.
• As utility increases ($U_B$), the consumer might prefer a variety of fruit in their diet more than initially.