Neoclassical Theory of Consumption
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1 Neoclassical Theory of Consumption Economics II: Microeconomics VŠE Praha September 2009 Micro (VŠE) Consumption theory 09/09 1 / 24
2 Economics II: Microeconomics Consumers: Firms: People. Households. Applications. Internal Organisation. Industrial Organisation. Equilibrium: Holds. Does not hold. Micro (VŠE) Consumption theory 09/09 2 / 24
3 Microeconomics Consumers: Firms: People. Now Households. Applications. Internal Organisation. Industrial Organisation. Equilibrium: Holds. Does not hold. Micro (VŠE) Consumption theory 09/09 3 / 24
4 Neoclassical theory of consumption Basics PEOPLE CHOOSE THE BEST THINGS THEY CAN AFFORD. Micro (VŠE) Consumption theory 09/09 4 / 24
5 Neoclassical theory of consumption Basics PEOPLE CHOOSE THE BEST THINGS THEY CAN AFFORD. Micro (VŠE) Consumption theory 09/09 5 / 24
6 Neoclassical theory of consumption Basics THE BEST THINGS: De nition Consumtion bundle is a complete list of the goods & services that are involved in the choice problem that is investigated. (say, X and Υ). Fact Notation: Strict preference: Indi erence: Alternative notation: Weak preference: X Υ X Υ X Υ Micro (VŠE) Consumption theory 09/09 6 / 24
7 Neoclassical theory of consumption Basics Relationship between,,and Lemma if X Υ and Υ X then? if X Υ but not Υ X then? Micro (VŠE) Consumption theory 09/09 7 / 24
8 Neoclassical theory of consumption Basics Relationship between,,and Lemma if X Υ and Υ X then X Υ if X Υ but not Υ X then X Υ Micro (VŠE) Consumption theory 09/09 8 / 24
9 Neoclassical theory of consumption Homo-economicus The economic agent (or economic human) Micro (VŠE) Consumption theory 09/09 9 / 24
10 Neoclassical theory of consumption Homo-economicus The economic agent (or economic human) Rational Micro (VŠE) Consumption theory 09/09 9 / 24
11 Neoclassical theory of consumption Homo-economicus The economic agent (or economic human) Rational Egoist (or self-interested) Micro (VŠE) Consumption theory 09/09 9 / 24
12 Neoclassical theory of consumption Rationality Axiom 1 st Axiom: Complete preferences Either of X Y Y X X Y jorj Either of X Y Y X both Example Buridan s ass... 2 nd Axiom: Re exive preferences X X jorj X X Micro (VŠE) Consumption theory 09/09 10 / 24
13 Neoclassical theory of consumption Rationality Axiom 3 rd Axiom: Transitive preferences If X Y and Y Z then X Z If X Y and Y Z then X Z or If X Y and Y Z then X Z Example The Dutch-booking... Micro (VŠE) Consumption theory 09/09 11 / 24
14 Indi erence curves e = (15, 25) d = (10, 15) e c a I 1 indi erece curve Micro (VŠE) Consumption theory 09/09 12 / 24
15 Indi erence curves I 0 : a e I 1 : b e Q : Do the axioms hold? Question : (a) I 0 I 1 I 2 ; (b) I 0 I 1 I 2 ; or (c) I 2 I 1 I 0 Micro (VŠE) Consumption theory 09/09 13 / 24
16 Indi erence curves Proposition Indi erence curves representing distinct levels of preference cannot cross. Proof. Otherwise the transitivity axiom is violated. I 0 : a e I 1 : b e Q : Do the axioms hold? Micro (VŠE) Consumption theory 09/09 14 / 24
17 Indi erence curves I 0 : a e I 1 : b e Q : Do the axioms hold? Question : (a) I 0 I 1 I 2 ; (b) I 0 I 1 I 2 ; or (c) I 2 I 1 I 0 Micro (VŠE) Consumption theory 09/09 15 / 24
18 Indi erence curves Psych. Assumptions Axiom 4 th Axiom: Insatiable (monotonic) preferences If X Y then X Y If X > Y then X Y 5 th Axiom: Convex preferences (w) If X Y then αx + (1 α) Y X where α 2 (0, 1) (s) If X Y then αx + (1 α) Y X Question : (a) I 0 I 1 I 2 ; (b) I 0 I 1 I 2 ; or (c) I 2 I 1 I 0 Micro (VŠE) Consumption theory 09/09 16 / 24
19 Indi erence curves: No-No-No Cases Micro (VŠE) Consumption theory 09/09 17 / 24
20 Indi erence curves: Special Cases Micro (VŠE) Consumption theory 09/09 18 / 24
21 Marginal rate of substitution De nition Marginal rate of substitution (MRS) is the rate at which the consumer is just willing to substitute one good for the other - MRS is the (absolute of the) slope of an indi erence curve at a particular point: x 2 x 1 or dx 2 dx 1 Micro (VŠE) Consumption theory 09/09 19 / 24
22 Diminishing Marginal Rate of Substitution Micro (VŠE) Consumption theory 09/09 20 / 24
23 Next lecture Further studies in Neoclassical Theory! Thank you! Micro (VŠE) Consumption theory 09/09 21 / 24
24 Utility measure of happiness cardinal utility ordinal utility De nition Utility function: A way of assigning a number to every possible consumption bundle, such taht more preferred bundles get assigned larger numbers. Micro (VŠE) Consumption theory 09/09 22 / 24
25 Utility Theorem of Debreu Theorem Given the assumptions of Rationality and Monotonicity, 9u () s.t. (x 1, x 2 ) (y 1, y 2 ) () u (x 1, x 2 ) > u (y 1, y 2 ). Proof. Do not need for this course. Micro (VŠE) Consumption theory 09/09 23 / 24
26 Utility Monotonic transforations Lemma Any monotonic transformation of the original utility function is a utility function representing the same preferences. Proof. 1. Suppose u () is the utility function representing the preferences P. (x 1, x 2 ) P (y 1, y 2 ) () u (x 1, x 2 ) > u (y 1, y 2 ) (1) 2. And suppose that f (u) is a monotonic transformation of u (). u (x 1, x 2 ) > u (y 1, y 2 ) () f (x 1, x 2 ) > f (y 1, y 2 ) (2) 3. From (1) and (2) follows: (x 1, x 2 ) P (y 1, y 2 ) () f (x 1, x 2 ) > f (y 1, y 2 ) (3) Micro (VŠE) Consumption theory 09/09 24 / 24
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