CDAE Class 6 Sept. 13 Last class: 2.Preferences and choice Quiz 1 Today: Result of Quiz 1 2. Preferences and choice Next class: 2.Preferences and choice 3. Individual demand curves Quiz 2 (Chapter 2) Important date: Problem set 2: due Thursday, Sept. 20 Problems 2.1, 2.2, 2.4 and 2.10 (a and b only) from the textbook

Result of Quiz 1 N = 60 Range = 4 – 10 Average = Objectives of economics: explanation & prediction 2. Demand and supply functions (a) Graph (b) Equilibrium Q and P 3. Y is a nonlinear function of X 4. Derivatives 5. Profit maximization

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. e.g., Helen has $20 to buy candies (X) and/or soda (Y): P x X + P y Y < 20 where P x and Py are the corresponding prices In general: P 1 X 1 + P 2 X 2 + P 3 X 3 + …+ P n X n < I where I is the available income

2.7. Budget constraint (2) A graphic analysis of two goods (X and Y) -- Budget constraint  feasible (affordable) vs. infeasible (not affordable) regions e.g., 1X + 2Y < 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 Y Feasible (affordable) region a b c d Infeasible (not affordable) region X Slope of the budget line = -0.5 In general: slope = - P x / P y

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

Budget Constraint: an increase in P x Y Loss 50 L (P x = $1) L New (P x = $2) 25 0 X

Class exercise 2 (Tuesday, Sept. 11) Ms Johnson has $10 to buy beer and/or popcorns and the price of beer is $2 per bottle and the price of popcorn is $1 per bag. Draw a graph to show her budget constraint What is the slope of the budget line? What is the interpretation of the slope?

When one price rises price of pizza doubles: Px = $2 (up from $1) price of burritos and income unchanged slope of the new budget line: budget constraint swings in toward origin opportunity set shrinks

Changes in the Budget Constraint Y, Burritos per semester (a) Price of Pizza Doubles Loss X, Pizzas per semester

2.7. Budget constraint (3) Applications and special cases: -- Consumption quota -- China’s double price system -- Electricity pricing -- A minimum charge for taxi service -- A company requires its workers to purchase its product

2.8. Utility maximization 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

Class exercise 3 (Thursday, Sept. 13) 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)?

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

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