Lecture 6 Consumer Choice

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1 Lecture 6 Consumer Choice Business 5017 Managerial Economics Kam Yu Fall 2013

2 Outline 1 Rational Choice Consumption Decisions Market Demand 2 Consumers Responsiveness Price Applications Income Substitutes and Complements 3 Lagged Demands, Network Effects, and Rational Addiction Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

3 Rational Choice Consumption Decisions Recap of Rational Behaviours In Lecture 2, we assume that a rational consumer behaves according to some rules: 1 Completeness: Given two choices, a consumer is able to decide she prefers one or the other, or she is indifferent between them. 2 Transitivity: If a consumer prefers A to B and B to C, then she must prefer A to C. 3 More is Better: There is always something that a consumer wants more. That is, we are never totally satisfied with what we have. From these assumptions, economists use a mathematical trick to represent a consumer s welfare by a utility function. Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

4 Rational Choice Consumption Decisions Utility Functions A utility function relates a consumption bundle to a number. Example: Assume that Anna buys only two goods, Coke (c) and hot dog (h). A consumption bundle is a list of the quantities of the goods, (c, h). The utility function f is f (c, h) = u, where u is a number indicating the utility level. Suppose that f (2, 1) = 49, that is, two Cokes and one hot dog give the utility level of 49. On the other hand, f (1, 2) = 55. Since 55 > 49, hungry Anna prefers one Coke and two hot dogs (1, 2) to two Cokes and one hot dog (2, 1). Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

5 Rational Choice Consumption Decisions Marginal Utility Suppose Anna has one Coke and two hot dogs, with utility f (1, 2) = 55. What if we buy her one more Coke? Her utility will increase, say, to f (2, 2) = 64. Given that she s already had (c, h) = (1, 2), the extra utility of one more Coke is = 9. We call this the marginal utility of Coke when she has consumed one already. As Anna buys more Cokes or hot dogs, utility from the additional consumption becomes smaller and smaller. This is called diminishing marginal utility. Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

6 Rational Choice Consumption Decisions Marginal Utilities at the Cafeteria Anna s marginal utilities may look like this: Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

7 Rational Choice Consumption Decisions Optimal Consumption Bundle Given the prices of the goods (P c, P h ) and the budget of consumption, how does a consumer make the optimal choice? A necessary condition is this: At the optimal bundle, the ratio of marginal utilities (MU) between two goods is equal to their price ratio, that is, MU c = P c. MU h P h Rearranging the above equation, we get MU c P c = MU h P h. (1) This means that the last penny spent on each good gives the same utility. Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

8 Rational Choice Consumption Decisions Two Hot Dogs with a Medium Diet Coke Please Why does Equation (1) have to hold at the optimal bundle? Imagine it does not, say MU c P c > MU h P h. This means that the last penny spent on Coke gives a higher marginal utility than that of hot dog. The consumer can be better off by shifting the last penny spent on hot dog to Coke. The opposite is true if the inequality goes in the other direction. Conclusion: utility is maximized when equality holds. Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

9 Rational Choice Consumption Decisions Law of Demand What if on the next day the Cafeteria increase the price of Coke? Since P c is now higher, at the old optimal bundle, MU c P c < MU h P h. Now Anna is better off by spending less on Coke and more on hot dog. In other words, quantity demanded for Coke will goes down. We have proven the law of demand for one consumer. Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

10 Rational Choice Market Demand What About the Market Demand Curve? At any given price, we need to add up the quantity demanded from all the consumers: Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

11 Price Price Elasticity of Demand Prices and quantities have units attached to them, like $ per cup of Coke, $ per hot dog, etc. Sometimes we want the consumers response in price changes expressed in a dimensionless number. Own price elasticity of demand: % change in quantity demanded E d = % change in price = Q/Q P/P = Q P P Q 1 P = (slope of the demand curve) Q Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

12 Price Some Elasticities Technically, E d is always negative because of the law of demand. Thus a lot of economists only care about the absolute value, E d, that is, the value without the negative sign. Some results from empirical studies: Good or Service Elasticity Cigarettes 0.42 Salmon 2.47 Gasoline 0.50 Chicken 1.67 Peak hour bus services 0.23 Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

13 Price Some Definitions The elasticity of demand measures the degree the responsiveness of the consumers. Three distinct cases: 1 inelastic: 0 E d < 1 2 unitary elastic: E d = 1 3 elastic: E d > 1 Some extreme cases: When a good or service is needed at a certain quantity no matter what the price is, the demand curve is vertical and E d = 0. In a perfect competitive market, each producer faces a horizontal demand curve. That is, demand is perfectly elastic, E d. Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

14 Price Straight-Line Demand Curve Elasticity along a straight-line demand curve: Although the demand curve has the same slope everywhere, P and Q are different at different points. Elastic range: The upper part has high prices and small quantities, therefore demand is elastic (E d > 1). Inelastic range: The lower part has low prices and large quantities, therefore demand is inelastic (E d < 1). Unitary elasticity: The two parts are separated by a point with E d = 1. Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

15 Price Straight-Line Demand Curve Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

16 Applications Maximizing Revenue Question: A firm facing a downward sloping demand curve wants to pay down debt and need cash, the business managers wants to maximize sales revenues (R = PQ). What price should she set? At one extreme, price is set too high and quantity demanded is zero. At the other extreme a zero price will sell a lot of goods but no revenue as well. Answer: The manager should set the price at the level such that E d = 1. Why? At a point in the elastic range, E d > 1 so that a 1% price cut will trigger a more than 1% increase in sales. Revenue increases. At a point in the inelastic range, E d < 1 so that a 1% price hike will trigger a less than 1% decrease in sales. Revenue increases. Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

17 Applications Need Cash? Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

18 Applications Fat Tax Some U.S. state governments are consider a fat tax on fatty food and sugary drink as a tool to reduce the obesity rate. The effectiveness of the tax critically depends on the elasticity of demand on those food. Empirical studies have found that the estimated E d for soda beverages ranges from 0.78 to Other studies suggest that a fat tax has small impacts on the average weight of Americans. Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

19 Applications Easy Ways to Lose Weight? Stay in School Economists Jay Bhattacharya and Neeraj Sood find that obesity has something to do with studying. Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

20 Income Income and Demand Instead of price, we can find the relation between income and quantity demanded for a good or service, assuming that price remains the same. Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

21 Income Engel Curve The Engel curve can slope upward (normal goods), downward (inferior goods), or vertical (table salt). they can even change direction: a good can be normal at low income level but becomes inferior at high income level, can you give an example? Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

22 Income Income Elasticity of Demand % change in quantity demanded E i = % change in income = Q/Q M/M = Q M M Q = Classification of goods: inferior goods: E i < 0 necessities: 0 E i 1 luxuries: E i > 1 1 (slope of the Engel curve) Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28 M Q

23 Income Luxury, Normal, and Inferior Goods Observations during the 2008 recession: Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

24 Substitutes and Complements Substitutes and Complements Two goods are substitutes if the price of one good goes up result in an increase in demand for the other good. Examples: Zippers and buttons Butter and margarine Natural gas and fuel oil Pork and chicken Two goods are complements if the price of one good goes up result in an decrease in demand for the other good. Examples: Movie tickets and restaurant meals Lettuce and salad dressing Blue-ray players and HDTV Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

25 Substitutes and Complements Cross-Price Elasticity of Demand The cross-price elasticity of two goods X and Y is defined as E XY = % change in quantity demanded for X % change in price of Y = Q X /Q X P Y /P Y = Q X P Y P Y Q X Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

26 Lagged Demands, Network Effects, and Rational Addiction Lagged Demands Definition: Consumption is intertemporal in nature. Demand of a good in the future depends on the current demand. This applies to products that are addictive or habitual. Firms have different pricing strategies in selling these product. They often offer a very low price for new customers and charge the normal price after a kick-in period. Examples: Tobacco companies tried to often free cigarettes to new smokers. Cable, digital phone, and Internet services providers offer low price packages for the first six months. Subprime mortgage lenders offered low teaser rates for the first two years. In business, this leads to the problem of asset specificity. For example, utility companies usually sign long-term contracts with mining companies before building a coal-fired power plant near a mine. Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

27 Lagged Demands, Network Effects, and Rational Addiction Network Effects Definition: The value of a product depends on the total number of users. The effect occurs most commonly in IT products which rely on networking: telephone, telex, fax, the Internet, Skype, Facebook. Firms face the critical mass problem in product development. The value of a smartphone depends on the number of apps available. But software developers do not want to write apps for systems with few users. Economist Edward Glaeser suggests that people want to live in big cities because of the positive network externality of knowledge and idea exchanges. Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

28 Lagged Demands, Network Effects, and Rational Addiction World Mobile Phone Market Kam Yu (LU) Lecture 6 Consumer Choice Fall / 28

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