Last class: Today: Next class: Important date: 2. Utility and choice CDAE 254 - Class 7 Sept. 19 Last class: 2. Utility and choice Today: 3. Individual demand curve Quiz 2 (Chapter 2) Next class: Individual demand curve Important date: Problem set 2 due Tuesday, Sept. 26 Problems 2.1, 2.2, 2.4 and 2.10 (a and b only) from the textbook

2. Utility and choice 2.1. Basic concepts 2.2. Assumptions about rational choice 2.3. Utility 2.4. Indifference curve and substitution 2.5. Marginal utility and MRS 2.6. Special utility functions 2.7. Budget constraints 2.8. Utility maximization 2.9. Applications

2.7. Budget constraint (1) Budget constraint: total expenditure should be less than or equal to the available income. (2) A graphic analysis of two goods (X and Y) -- Budget constraint  feasible (affordable) vs. infeasible (not affordable) regions e.g., 1X + 2Y < 50 -- What is the slope of the budget line? Slope = - (I/Py) / (I/Px) = - Px / Py -- Impacts of a change in income (I) -- An increase in income expand the feasible region -- A decrease in income reduce the feasible region -- Impacts of a change in one price (e.g, an increase in Px) -- Impacts of a change in both prices

Budget Constraint 1 X + 2 Y < 50 25 Infeasible (not affordable) region b 20 c 10 Feasible (affordable) region d 10 30 X 50 Slope of the budget line = -0.5 In general: slope = - Px / Py

Budget Constraint: an increase in income Y 50 L new (I = $100) 25 Gain L (I = $50) X 50 100 A change in income does not change the slope of the budget line

Budget Constraint: an increase in Px Y 25 L ( P = $1) x Loss L New ( P = $2) x X 25 50

2.8. Utility maximization 2.8.1. A graphical analysis -- Budget constraint -- Indifference curves -- Utility maximization problem -- Solution: Slope of the budget constraint is equal to the slope of the indifference curve: What will happen if the two are not equal? For example, MRS = -1 and Px/Py = 1/2 = 0.5 MRS = -0.3 and Px/Py = 1/2 = 0.5

Utility maximization optimum bundle, e, where highest indifference curve touches the budget line

2.8. Utility maximization 2.8.2. Graphical analysis – corner solutions -- What is a corner solution? -- Possible reasons for corner solutions (a) Due to constraints (e.g., relative prices) (b) Due to preference (e.g., religion reason) -- Business and policy applications

2.8.3. A mathematical analysis 2.8. Utility maximization 2.8.3. A mathematical analysis Maximize U = U (X, Y) subject to Px X + PyY < I

2.9. Applications 2.9.1. Food stamp program in the U.S. (1) How does it work? (2) Economic analysis: income vs. food subsidies (3) Justifications for food subsidies

Food Stamps Versus Cash Subsidy All other goods per month Budget line with cash Y + 100 f C e Y I 3 d I 2 I 1 B Budget line with food stamps A Original budget line 100 Y Y + 100 Food per month

2.9. Applications 2.9.2. Special cases of utility maximization -- X and Y are perfect substitutes -- X and Y are perfect complements -- X is a useless good -- X is an economic bad -- Consumption quota -- China’s double price system -- Electricity pricing -- A a minimum charge for taxi service -- A company requires its workers to purchase its product

Chapter 2: Review questions -- What are the two groups of factors that determine individual demand? -- What are the three assumptions about rational choice? -- How to explain the concept of utility and utility function? -- How to explain an indifference curve and how to draw it? -- What is MRS and how to calculate it? -- What is the relation between MRS and marginal utilities? -- How to draw indifference curves for special goods? -- How to draw and interpret a budget constraint? -- What are the impacts of a change in income or price(s)? -- What is the condition for utility maximization? -- What will the consumer do if the condition for utility maximization is mot met? -- How to graphically explain each of the special cases of utility maximization problems?

Class Exercise 1. Kevin has $20 to watch movies ($5 each) and rent DVDs ($2 each). Plot Kevin’s budget constraint 2. At the point where the budget line, 2 X + 3 Y = 18, crosses an indifference curve, the MRS = -2. How should the consumer change her consumption of X and Y to maximize her utility (i.e., increase X and decrease Y or decrease X and increase Y)?

Take-home exercise (Tuesday, Sept. 19) While city B faces a likely shortage of electricity in the summer and a surplus of electricity in the winter, the following pricing policy has been proposed: Summer (June to Sept): $0.10 per unit for the first 200 units and then $0.14 for each additional unit Winter (Dec. to March): $0.10 per unit for the first 200 units and then $0.08 for each additional unit Other months: $0.10 per unit How will the proposed policy affect Mr. A who consumes about 500 units per month, Mrs. B who consumes about 150 units per months, and Ms. C who consumes about 200 units per month?