Chapter 6: Demand. Watanabe Econ Demand 1 / 61. Watanabe Econ Demand 2 / 61. Watanabe Econ Demand 3 / 61
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1 Econ Microeconomic Analysis Chapter : Demand Instructor: Hiroki Watanabe Spring 1 Watanabe Econ Demand 1 / 1 1 Introduction Overview Income Changes Own-Price Changes Cross-Price Changes Inverse Demand 7 Now We Know Watanabe Econ Demand / 1 1 Introduction Overview Comparative Statics Endogenous & Exogenous Variables Overview Income Changes Own-Price Changes Cross-Price Changes Inverse Demand Watanabe Econ Demand / 1 7 Now We Know
2 Overview Chpt : Categories and definitions. Chpt 8: Price change demand. Chpt 1: Price change welfare. Watanabe Econ Demand / 1 Comparative Statics Discussion 1.1 (Consumer Reaction to Situational Changes) Listen to Marketplace Audio Clip. With the tools we have learned so far, propose a way to measure or predict "a big dent in volunteerism" triggered by the increasing gas price. Watanabe Econ Demand / 1 Comparative Statics Definition 1. (Comparative Statics) Variables predetermined outside the model are called exogenous variables. Variables whose values are determined in the model are called endogenous variables. Comparative statics analyzes the change in equilibrium values ( etc, endogenous C variables) corresponding to the change in one particular parameter (p T etc, exogenous variables). Watanabe Econ Demand / 1
3 Comparative Statics Ceteris paribus: hold everything else still. Why can t we move multiple parameters at the same time like in the real world? Prediction becomes less clear-cut: 1 p C : ceteris paribus C :. p C : while p T : 1 C : indefinite. Watanabe Econ Demand 7 / 1 Endogenous & Exogenous Variables Endogenous & exogenous variables: 1 Given ( ), p and m, UMP predicts which Liz will choose. UMP does not predict the movement of p, m and change in tastes ( ). Watanabe Econ Demand 8 / 1 1 Introduction Overview Marshallian Demand Function Review Terms & Graphs Income Changes Own-Price Changes Cross-Price Changes Inverse Demand Watanabe Econ Demand 9 / 1 7 Now We Know
4 Marshallian Demand Function Definition.1 (Marshallian Demand Function) Marshallian demand function tells us the optimal bundle at each given price and income, denoted by φ(p, m) = φ 1 (p, m) φ. (p, m) Watanabe Econ Demand 1 / 1 Review Fact. (Change in Parameters) Change in price causes rotation to the budget constraint. Change in income causes parallel shifts to the budget constraint. Watanabe Econ Demand 11 / 1 Terms & Graphs Lots of definitions to learn today to describe and classify different types of commodities. Watanabe Econ Demand 1 / 1
5 Terms & Graphs Definition. (Demand s Response to Parametric Changes (Terms)) Exogenous Variable φ C (p, m) φ C (p, m) m normal income inferior p C Giffen LOD p T substitute complement Watanabe Econ Demand 1 / 1 Terms & Graphs Definition. (Demand s Response to Parametric Changes (Graph)) on C - T on C -parameter m income expansion path Engel curve p C price offer curve demand curve Watanabe Econ Demand 1 / 1 1 Introduction Overview Income Changes Normal & Income-Inferior Goods Income Expansion Path Example 1: Cobb-Douglas Example : Perfect Substitutes Example : Perfect Complements Own-Price Changes Cross-Price Changes Watanabe Econ Inverse Demand Demand 1 / 1 7 Now We Know
6 Normal & Income-Inferior Goods Definition.1 (Normal & Income-Inferior Goods) φ C (p, m) φ C (p, m) m normal income inferior p C Giffen LOD p T substitute complement Watanabe Econ Demand 1 / 1 Normal & Income-Inferior Goods Indifference Curves Budget Line (High m) Budget Line (Low m) Tea x T (cups) Cheese x C (slices) Watanabe Econ Demand 17 / 1 Normal & Income-Inferior Goods Budget Line (High m) Budget Line (Low m) Freshly Baked Cheesecake x (slices) Store Bought Stale Cheesecake x 1 (slices) Watanabe Econ Demand 18 / 1
7 Income Expansion Path Definition. (Income Expansion Path & Engel Curve) on C - T on C -parameter m income expansion path Engel curve p C price offer curve demand curve Watanabe Econ Demand 19 / 1 Income Expansion Path Tea x T (cups) 1 Indifference Curves Budget Line (Low m) Budget Line (Intermediate m) Budget Line (High m) Cheese x C (slices) Watanabe Econ Demand / 1 Income Expansion Path Engel Curve Income m ($) Cheese x C (slices) Watanabe Econ Demand 1 / 1
8 Example 1: Cobb-Douglas Example. (Cobb-Douglas Utility Function) Liz s preferences are represented by ( C, T ) = C T. MRS at ( C, T ) is T C. The price is given by p = (p C, p T ) = (1, 1) and she has $m. Find her Engel curve. Watanabe Econ Demand / 1 Example 1: Cobb-Douglas φ(m, p = (1, 1)) = φ C (m, p), φ T (m, p) = m, m. Engel curve for cheesecakes at p = (1, 1): m = C. Watanabe Econ Demand / 1 Example 1: Cobb-Douglas 9 Indifference Curves 8 Budget Line (Low m) Budget Line (Intermediate m) 7 Budget Line (High m) Tea x (cups) T Cheese x C (slices) Watanabe Econ Demand / 1
9 Example 1: Cobb-Douglas Engel Curve 7 Income m ($) Cheese x C (slices) Watanabe Econ Demand / 1 Example : Perfect Substitutes Example. (Perfect Substitutes) Consider a bundle of six-packs and bottles of Corona (, 1 ). Suppose p = (p, p 1 ) = (1, ). MRS at (, 1 ) is while the relative price is. Watanabe Econ Demand / 1 Example : Perfect Substitutes Indifference Curves Budget Line (m=) Budget Line (m=) Budget Line (m=) Bottles x Six Packs x Watanabe Econ Demand 7 / 1
10 Example : Perfect Substitutes Engel Curve Income m ($) 1 1 Six Packs x Watanabe Econ Demand 8 / 1 Example : Perfect Substitutes Engel Curve Income m ($) 1 1 Bottles x 1 Watanabe Econ Demand 9 / 1 Example : Perfect Complements Example. (Perfect Complements) Consider a bundle (cereal, milk)= ( C, M ). Liz says she can t have cereals without milk and the only time she has milk is when she eats her cereals. Liz s preferred cereal-milk ratio is 1 to 1. (p C, p M ) = (, ). What do Liz s Engel curves look like? (curve? flat?) Consider m = and m = 8 for example. Watanabe Econ Demand / 1
11 Example : Perfect Complements Indifference Curves Budget Line (m=). Budget Line (m=8). Milk x (oz) M Cereals x C (oz) Watanabe Econ Demand 1 / 1 Example : Perfect Complements 1 Engel Curve 1 1 Income m ($) Cereals x C (oz) Watanabe Econ Demand / 1 1 Introduction Overview Income Changes Own-Price Changes Law of Demand & Giffen Good Price Offer Curve & Demand Curve Example 1: Perfect Complements Example : Perfect Substitutes Example : Cobb-Douglas Cross-Price Changes Watanabe Econ Inverse Demand Demand / 1 7 Now We Know
12 Law of Demand & Giffen Good Definition.1 (LOD & Giffen Goods) φ C (p, m) φ C (p, m) m normal income inferior p C Giffen LOD p T substitute complement Prada shoes: If they re cheap and everyone s wearing them, then... Watanabe Econ Demand / 1 Price Offer Curve & Demand Curve Definition. (Price Offer Curve & Demand Curve) on C - T on C -parameter m income expansion path Engel curve p C price offer curve demand curve Watanabe Econ Demand / 1 Price Offer Curve & Demand Curve Indifference Curves Budget Line (p C =) 7 Budget Line (p C =) Tea x (cups) T Cheesecakes x C (slices) Watanabe Econ Demand / 1
13 Price Offer Curve & Demand Curve 8 Demand Curve 7 Price p ($/slice) C Cheesecakes x C (slices) Watanabe Econ Demand 7 / 1 Price Offer Curve & Demand Curve 1 Budget Line (p C =) 1 Budget Line (p =) C 1 Budget Line (p =1) C Tea x T (cups) Cheesecakes x C (slices) Watanabe Econ Demand 8 / 1 Price Offer Curve & Demand Curve Price p ($/slice) C 1 1 Cheesecakes x C (slices) Watanabe Econ Demand 9 / 1
14 Example 1: Perfect Complements Example. (Perfect Complements) Consider a bundle (cereal, milk)= ( C, M ). Liz s preferred cereal-milk ratio is 1 to 1. Normalize p M = 1 and let m =. What does Liz s Marshallian demand function look like? Watanabe Econ Demand / 1 Example 1: Perfect Complements 1 Note C = M. m p φ(p, m) = C + p M m. p C + p M Watanabe Econ Demand 1 / 1 Example 1: Perfect Complements Indifference Curves Budget Line (low p C ) 18 1 Budget Line (high 1 p ) C 1 Milk x M (oz) Cereals x C (oz) Watanabe Econ Demand / 1
15 1 Example 1: Perfect Complements 8 Demand Curve φ C (p, m)=m/(p C +p M ) 7 Price p ($/slice) C Cereals x C (oz) Watanabe Econ Demand / 1 Example : Perfect Substitutes Example. (Perfect Substitutes) Consider a bundle of six-packs and bottles of Corona (, 1 ). Normalize p 1 = 1 and let m =. What does Liz s Marshallian demand function look like? Watanabe Econ Demand / 1 Example : Perfect Substitutes Bottles x Indifference Curves Budget Line (p =) Budget Line (p =) 8 7 Budget Line (p =1) Six Packs x Watanabe Econ Demand / 1
16 Example : Perfect Substitutes 1 Demand Curve (p >) Price p ($/six pack) Demand Curve (p =) 1 Demand Curve (p <): φ ()=/p Six Packs x Watanabe Econ Demand / 1 Example : Cobb-Douglas Example. (Cobb-Douglas Utility Function) Liz s preferences are represented by ( C, T ) = C T. MRS at ( C, T ) is T C. The price is given by p = (p C, p T ) = (p C, 1) and she has $1. What does Liz s Marshallian demand function look like? Watanabe Econ Demand 7 / 1 Example : Cobb-Douglas 1 7. Indifference Curves Budget Line (p C =1) Budget Line (p C =) Tea x (cups) T Cheesecakes x C (slices) Watanabe Econ Demand 8 / 1
17 Example : Cobb-Douglas Demand Curve φ C (p, m)=m/(p C ). Price p ($/slice) C Cheesecakes x C (slices) Watanabe Econ Demand 9 / 1 1 Introduction Overview Income Changes Own-Price Changes Cross-Price Changes Inverse Demand 7 Now We Know Watanabe Econ Demand / 1 Discussion 1.1 : how does the increase in the gas price affect Liz s spending on community services ( "purchase" of volunteering work). Definition.1 (Substitutes & Compliments) 1 A cheesecake is a complement to tea if increase in the price of tea leads to decrease in cheesecake consumption. A cheesecake is a substitute to tea if increase in the price of tea leads to increase in cheesecake consumption. Bottles & six-packs of Corona? Cereal & milk? Cobb-Douglas utility? Watanabe Econ Demand 1 / 1
18 Example. : φ C (m = 1, p C, p T ) = 1/p C is independent of the price of tea.. Demand Curve φ C (p, m)=m/(p C ) Price p ($/slice) C Cheesecakes x C (slices) Watanabe Econ Demand / 1 1 Introduction Overview Income Changes Own-Price Changes Cross-Price Changes Inverse Demand 7 Now We Know Watanabe Econ Demand / 1 Definition.1 (Inverse Demand Function) Inverse demand function D( C ) assigns the price at which the amount C will be selected, given p T and m. Watanabe Econ Demand / 1
19 Watanabe Econ Demand / 1 Watanabe Econ Demand / 1 So? Normalize p T = 1. Tangency condition: p C = MRS( C, T ). D( C ) = p C = MRS( C, T ) Inverse demand function denotes the marginal willingness to pay at each C given p T and m. Watanabe Econ Demand 7 / 1
20 Marginal Willingness to Pay (cups/slice) Inverse Demand D C (x )=m/(x C ) C Cheesecakes x C (slices) Watanabe Econ Demand 8 / 1 1 Introduction Overview Income Changes Own-Price Changes Cross-Price Changes Inverse Demand 7 Now We Know Watanabe Econ Demand 9 / 1 Characterize commodities by changing situational background. Income changes and associated graphs. Own-price changes and associated graphs. Cross-price changes. Meaning of the inverse demand function. Watanabe Econ Demand / 1
21 Index ceteris paribus, 7 Cobb-Douglas utility function,, 7 comparative statics, complement, 1, 1 demand curve, endogenous variables,, 8 Engel curve, 19, exogenous variables,, 8 Giffen good, 1, income expansion path, 19 income-inferior good, 1, 1 law of demand, 1, LOD, see law of demand Marshallian demand function, 1,,, 7 normal good, 1, 1 perfect complements,, perfect substitutes,, φ, see Marshallian demand function price offer curve, substitute, 1, 1 tangency condition, 7 Watanabe Econ Demand 1 / 1
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