Microeconomics I Chapter 1 Theory of Demand Ali Mazyaki, Ph.D. Institute for Management and Planning Studies (IMPS)
Agenda 1- Preference and Choice 1-1- Choice set 1-2- Preference 1-3- Rationality 1-4- Utility function 2- Consumer choice 2-1- Commodities 2-2- The consumption set 2-3- Competitive Budgets 2-4- Demand function 2-5- Comparative statics 2-6- The weak axiom of revealed preferences 3- Classical demand theory 3-1- Basics 3-2- Preference and utility 3-3- The utility maximization problem 4- Aggregate demand هتفرشیپ درخ داصتقا1 ،یکیزم ،92 - 1391 2/17/2014 2
1- Preference and Choice حیجرت و باختنا "Consumption" is the genuine of any economic modeling. Precise definition and practical theorizing of this concept is of upmost importance in economics. Use mathematics: Formalizing the concept using mathematical instruments has several advantages: It provides us a precise language that bans any misinterpretation. This is 1. an invaluable usage of mathematics in economics letting us talk in a flawless understandable way. – However, one should be aware of the important fact that we do not study mathematics here and all the mathematical formulas have to be interpreted and understood through some logical constructs. 2. Formalizing our understanding is very useful for verification of our ideas. To criticize economic conjectures one need to be clear and the language we normally use in our everyday life is not quite suitable for achieving this clarity. هتفرشیپ درخ داصتقا1 ،یکیزم ،92 - 1391 2/17/2014 3
1- Preference and Choice 1-1- Choice set • How do individuals choose from a set of opportunities? • What can we conclude from observed choices? Objective: formulation of a theory that may be applied to a host of conceivable choice problems. • Consider a "set of possible alternatives” and call it Consumption Set (Choice Set) X: – X is a representation of all alternatives that a consumer may conceive – Primitive characteristic of the individual: preference relations that summarize his tastes – We impose rationality axioms on preferences and then analyze what this implies for choosing element(s) out of X هتفرشیپ درخ داصتقا1 ،یکیزم ،92 - 1391 2/17/2014 4
1- Preference and Choice 1-2- Preference • To formalize this concept we use preference relation ≽ which is a binary relation on the set of alternatives X: ≽⊂ 𝑌 × 𝑌. • Having the above definition we may define: 𝑦 ≻ 𝑧 ⇔ 𝑦 ≽ 𝑧 𝑐𝑣𝑢 𝑜𝑝𝑢 𝑧 ≽ 𝑦 𝑦 ∼ 𝑧 ⇔ 𝑦 ≽ 𝑧 𝑏𝑜𝑒 𝑧 ≽ 𝑦 • Read ≽ : "at least as good as" ای “یبوخ هب لقادح“ • Read ≻ : "strictly preferred to“ ای “زا تسا رتهب ًادیکا“ • Read ∼ : "is indifferent with“ ای “اب تسا توافت یب“ 5 هتفرشیپ درخ داصتقا1 ،یکیزم ،92 - 1391 2/17/2014
1- Preference and Choice 1-3- Rationality Now we may define one of the first fundamental definitions in economics which is normally referred to as rationality . However, in some textbooks (Jehle & Reny) it is assumed as the standard assumption of preferences. The preference relation ≽ is called rational if it is complete and transitive: لماک ندوب 1. 𝐷𝑝𝑛𝑞𝑚𝑓𝑢𝑓𝑜𝑓𝑡𝑡: ∀𝑦, 𝑧 ∈ 𝑌 𝑓𝑗𝑢ℎ𝑓𝑠 𝑦 ≽ 𝑧 𝑝𝑠 𝑧 ≽ 𝑦 2. 𝑈𝑠𝑏𝑜𝑡𝑗𝑢𝑗𝑤𝑗𝑢𝑧: ∀𝑦, 𝑧, 𝑨 ∈ 𝑌 𝑗𝑔 𝑦 ≽ 𝑧 𝑏𝑜𝑒 𝑧 ≽ 𝑨 ⇒ 𝑦 ≽ 𝑨 یلاقتنا ندوب هتفرشیپ درخ داصتقا1 ،یکیزم ،92 - 1391 2/17/2014 6
1- Preference and Choice 1-3- Rationality Exercise: Show that if the weak preference relation ≽ of a consumer is rational, then: i. ≻ is irreflexive and transitive ii. ∼ is reflexive, transitive and symmetric iii. If 𝑦 ≻ 𝑧 ≽ 𝑨 ⇒ 𝑦 ≻ 𝑨 Note that ≻ and ∼ are not rational (why?) هتفرشیپ درخ داصتقا1 ،یکیزم ،92 - 1391 2/17/2014 7
1- Preference and Choice 1-3-1- Discussion of basic rationality assumptions Completeness: It eliminates the lack of ability to compare Comparing alternatives can be difficult if we have little experience with them (e.g. climate change) We neglect the (time) costs of comparing alternatives Cost of being rational may make “being rational” irrational!; in fact, we set “the cost of thinking” zero which is not very troublesome هتفرشیپ درخ داصتقا1 ،یکیزم ،92 - 1391 2/17/2014 8
1- Preference and Choice 1-3-1- Discussion of basic rationality assumptions Transitivity: It is useful to make the decisions independent from other factors Intensity of preferences may be depicted by defining many alternatives Problem of “just perceptible differences”: Agent may be indifferent between just perceptible differences of colors for painting a room. However, as we repeat this the agent may prefer starting to final color هتفرشیپ درخ داصتقا1 ،یکیزم ،92 - 1391 2/17/2014 9
1- Preference and Choice 1-3-1- Discussion of basic rationality assumptions Framing: The 2002 Nobel laureates Daniel Kahneman (together with Vernon L. Smith) integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty. Kahneman and Tversky (1984) show that framing is very important specially when outcomes are uncertain. هتفرشیپ درخ داصتقا1 ،یکیزم ،92 - 1391 2/17/2014 10
1- Preference and Choice 1-3-1- Discussion of basic rationality assumptions Framing: Problem of framing (manner of presenting alternatives matters for choice) Prices in store 1: € 125 for stereo and € 15 for calculator Salesman tells you that one of them costs € 5 less in store 2, which is located 20 minutes away In experiments, fraction that would travel to other store is much higher, if discount is on calculator by contrast, the same individuals express indifference to the following question Because of a stock out you must travel to the other store to get the two items, but you will receive € 5 off on either item as compensation. Do you care on which item the rebate is given? This violates transitivity هتفرشیپ درخ داصتقا1 ،یکیزم ،92 - 1391 2/17/2014 11
1- Preference and Choice 1-3-1- Discussion of basic rationality assumptions Framing: x: travel to other store and € 5 discount on calculator y: travel to other store and € 5 discount on stereo z: buy both items at first store first two choices reveal: 𝑦 ≻ 𝑧 𝑏𝑜𝑒 𝑨 ≻ 𝑧 third choice reveals: 𝑦 ∼ 𝑧 but: maybe we have misspecified the choice alternatives individuals do also care about making good bargains, often understood as price reductions in % perception for first two choices: discount on individual product perception for third choice: discount on bundle of goods هتفرشیپ درخ داصتقا1 ،یکیزم ،92 - 1391 2/17/2014 12
1- Preference and Choice 1-3-1- Discussion of basic rationality assumptions Aggregation of preferences : We often take households as the primitive of our analysis preferences of mom: ≻ 𝐵 preferences of dad: ≻ 𝐶 preferences of child: ≻ 𝐷 Majority-rule votes produces cyclical household preferences (i.e. Condorcet Paradox): 𝑦 ≻ 𝐵 𝑧 ≻ 𝐵 𝑨 𝑧 ≻ 𝐶 𝑨 ≻ 𝐶 𝑦 𝑨 ≻ 𝐷 𝑦 ≻ 𝐷 𝑧 Check that in the majority voting x is strictly preferred to y and y is strictly preferred to z. While z is strictly preferred to x which is a violation of transitivity. هتفرشیپ درخ داصتقا1 ،یکیزم ،92 - 1391 2/17/2014 13
1- Preference and Choice 1-3-1- Discussion of basic rationality assumptions Bounded rationality: changes in taste x: smoke 1 cigarette a day y: abstinence (initial situation) z: heavy smoking Preferences in initial situation: 𝑦 ≻ 𝑧 ≻ 𝑨 Once the individual has started smoking, preferences change to: 𝑨 ≻ 𝑦 ≻ 𝑧 “Change -of- taste” models are important for analyzing addictive behavior in “behavioral economics” (see for example O'Donoghue, T. and M. Rabin 2001 who define several selves for an individual, one of them is rational and the other is not!) Heidhues Kőszegi (2010 ), using the same “bounded rationality” with the notion of “naiveté”, model “over borrowing” as a reason for financial crisis. هتفرشیپ درخ داصتقا1 ،یکیزم ،92 - 1391 2/17/2014 14
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