Chapter 5 Market Demand

Individual Household’s Demands

Market Demand Network Externalities

Elasticities

Price Elasticity

Income Elasticity

Cross-Price Elasticity

Slutsky in Elasticities

Price Elasticity and Total Revenue

Outline and Conceptual Inquiries Deriving the Market Demand Understanding Network Externalities Would you purchase a fax machine if no one else had one? Application: Network Externalities in Consumption of International MultiIngredient Foods Did you purchase a pet rock, an Elmo, Power Ranger shoes or Pokémon cards? Application: Why Technology Adoption has a Bandwagon Effect Elasticity Dissected Units of Measurement Deriving a Unit-Free Measure of Responsiveness Why a Logarithmic Representation? Price Elasticity of Demand What is your demand for living? Application: Impact of an Airport on Travelers’ Expenditures © Michael E. Wetzstein, 2012

Relationship between Price Elasticity and Total Revenue Why do farmers always seem to complain about the prices they receive or their yields? Application: How to Adjust Prices: US versus French Wine Producers

Price Elasticity and the Price Consumption Curve Income Elasticity of Demand Cross-Price Elasticity of Demand Slutsky Equation in Elasticities Appendix to Chapter 5 Behavioral Economics Do stock and commodity traders suffer from loss aversion? What will provide you with more satisfaction a diamond necklace or a family vacation?

Summary 1. Assuming individual households’ demand curves are independent of each other, the market demand curve for a commodity is determined by horizontally summing these individual household demand curves. 2. Network externalities exist when an individual household’s demand for a commodity is dependent on other households’ level of consumption. Positive (negative) network externalities exist when one household’s value for a commodity increases (decreases) as other households purchase the item. 3. Elasticity is a measure of how responsive one variable is to a change in another variable. As a unit-free measurement, it is a standardized measurement of this responsiveness. 4. Elasticity is determined by weighting the derivative associated with the variables, which results in a measure of the percentage change in one variable to a percentage change in another variable. As a percentage change measurement, elasticity can be expressed in logarithmic form. 5. Elasticity is classified in terms of its responsiveness. This responsiveness is called elastic (inelastic) if the percentage change of the dependent variable is greater (less) than the percentage change in the independent variable. Unitary elasticity results when the percentage changes are equal. 6. The change in total revenue from a price change is dependent on the elasticity of demand. If demand is elastic (inelastic), price and total revenue move in the opposite (same) direction. Unitary elasticity results in total revenue remaining constant for any price change. 7. Income elasticity of demand measures the percentage change in quantity to a percentage change in income. Cross-price elasticity of demand measures the percentage change in quantity to a percentage change in the price of a related commodity. 8. The Slutsky equation in elasticity form indicates how the price elasticity of demand can be disaggregated into the substitution and income effects. The relative size of the income effect © Michael E. Wetzstein, 2012

depends on the proportion of total expenditure devoted to the commodity. 9. (Appendix) Behavior economics is a field of economics that relaxes assumptions on economic behavior by incorporating finding from related disciplines.

Key Concepts aggregate demand bandwagon effect behavioral economics cross-price elasticity elastic elasticity elasticity of demand

Key Equations ε11 = ξ11 − α1η1 The Slutsky equation in elasticity form indicates how the price elasticity of demand can be disaggregated into the substitution and income components.

© Michael E. Wetzstein, 2012

income elasticity market demand perfectly elastic demand perfectly inelastic demand positive network externalities total expenditures total revenue

TEST YOURSELF Multiple Choice 1. Market demand is derived by summing a. Vertically individual demand curves b. Vertically individual utility functions c. Horizontally individual demand curves d. Horizontally individual indifference curves and then deriving the aggregate demand. 2. When positive network externalities are present a. The value one household places on a commodity increases as other households purchase it b. The summation of individual household demands for a commodity will overestimate the market demand c. It is not possible to derive the market demand curve d. Both a and b. 3. If we express the elasticity of y with respect to x in logarithmic form, it becomes a.

b.

c.

d. 4. The elasticity of y with respect to x is defined as a.

b.

c.

d.

© Michael E. Wetzstein, 2012

5. If demand is perfectly inelastic, a. The demand curve is a horizontal line b. Any change in price causes an infinite change in quantity demanded c. Quantity demanded is unaffected by changes in price d. The demand curve has a negative slope. 6. The price elasticity of demand for banana bread is estimated to be −0.55. This implies that the demand is a. Inelastic b. Perfectly inelastic c. Perfectly elastic d. Elastic. 7. Suppose the market demand for root beer can be represented by Q1 = 240 – 12p1. Which of the following is true? a. The price elasticity of demand is unitary b. Demand is elastic at relatively high prices, but becomes inelastic as the price declines c. The demand is perfectly inelastic d. The price elasticity of demand is inelastic. 8. The total revenue elasticity εTR,p is equal to a. 1 + ε11 b. 1/ε11 c. 1 + 1/ε11 d. 1 − ε11. 9. Suppose the demand for blueberries is inelastic. As the price increases, quantity demand will __________ and total revenue will __________. a. Decline; decline b. Decline; remain the same c. Decline; rise d. Rise; rise. 10. Along a linear demand curve, total revenue is maximized when a. Demand is perfectly elastic b. Price is maximized c. Demand is unitary elastic d. Demand is perfectly inelastic. 11. Demand will be more elastic when a. The commodity in question has few substitutes b. A longer time is available to adjust to price changes c. The commodity accounts for a small proportion of total expenditure d. All of the above. © Michael E. Wetzstein, 2012

12. The income elasticity for an automobile is estimated to be 2. This implies that an automobile is a(n) a. Inferior and a necessary good b. Normal and a necessary good c. Normal and a luxury good d. Inferior and a Giffen good. 13. Suppose a 10 percent increase in the price of bananas leads to a rise of 8 percent in the quantity of apples demanded. This indicates the cross-price elasticity for apples and bananas is a. 0.8 and the two commodities are gross substitutes b. 1.25 and the two commodities are gross complements c. 0.8 and the two commodities are gross complements d. 1.25 and the two commodities are gross substitutes. 14. Suppose the demand function for x1 = 2Ip2/(5p1). The cross-price elasticity for x1 is a. 1 and the two commodities are gross substitutes b. ½ and the two commodities are gross substitutes c. 1 and the two commodities are gross complements d. ½ and the two commodities are gross complements. 15. The Slutsky equation in elasticity form is ε11 = ξ11 – α1η1. In this equation, ξ11 represents the a. Income elasticity with respect to x1 b. Price elasticity of demand for x1 c. The cross-price elasticity of demand between x1 and x2 d. The substitution elasticity of demand for x1.

© Michael E. Wetzstein, 2012

Short Answer 1. Explain why we expect the market demand curve to have a negative slope. 2. Compare positive and negative network externalities and their effects on the market demand curve. 3. Why is it important to know if demand is elastic or inelastic in order to determine how total revenue responds to price changes? 4. List the factors that determine the price elasticity of demand. 5. Comment on the following statement: “In order for a commodity to be a luxury good, it must be a normal good.” 6. Explain how the sign of the cross-price elasticity can tell us whether two commodities are gross complements or substitutes.

© Michael E. Wetzstein, 2012

Problems 1. Suppose Brian, B, and Sara, S, are the only two consumers in the market for Q1. Their demand functions are

Let Brian’s income IB = 50 and Sara’s income IS = 90. Derive the market demand for Q1. Will it have a negative slope? Is it convex? 2. Suppose Brian’s demand depends on whether Sara purchases x1, while Sara’s demand is unaffected by Brian’s demand for x1:

With the same incomes as in Problem 1, derive the market demand for x1. How does this market demand function compare with the demand function in Problem 1? Explain. 3. Suppose the demand for pizza can be represented by Q1 = 190 – 10p1. Find the price elasticity of demand at the following prices: $6, $9, $12, and $15. 4. Suppose the price elasticity of demand for lettuce is −½. If a drought leads to a higher price of lettuce, what will happen to total expenditures on lettuce? Explain. 5. Suppose the price elasticity of demand for e-books is −1.2. The cross-price elasticity between e-books and notepads is −1.5. If the price of notepads declines by 15 percent, what will be the price of e-books to keep quantity demanded unchanged? 6. Suppose the demand for x1 is x1 = 9Ip2/(7p1). Calculate the own-price elasticity of demand ε11, the income elasticity of demand η1, and the cross-price elasticity of demand ε12. Is the commodity normal or inferior? Are x1 and x2 gross complements or substitutes? 7. Suppose a household’s utility function is a. Derive the demand function for x1. b. Suppose the market consists of 100 individuals with these identical preferences. Derive the market demand function for Q1 and its price elasticity. 8. Eugene’s income elasticity for popcorn is 0.8 and he spends 10 percent of his income on popcorn. If his price elasticity of demand for popcorn is −1.3, what is his substitution price elasticity?

© Michael E. Wetzstein, 2012