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CDAE 254 - Class 5 Sept. 11 Last class: 2. Preferences and choice Today:

CDAE 254 - Class 5 Sept. 11 Last class: 2. Preferences and choice Today: 2. Preferences and choice Quiz 1 (Chapter 1) Next class: Preferences and choice Important date: Problem set 2: due Thursday, Sept. 20. 2. Utility and choice 2.1. Basic concepts

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CDAE 254 - Class 5 Sept. 11 Last class: 2. Preferences and choice Today:

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  1. CDAE 254 - Class 5 Sept. 11 • Last class: • 2. Preferences and choice • Today: • 2. Preferences and choice • Quiz 1 (Chapter 1) • Next class: • Preferences and choice • Important date: • Problem set 2: due Thursday, Sept. 20

  2. 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

  3. 2.2. Assumptions about rational choice: A and B are two bundles of goods and services: (1) Completeness: A  B or B  A or A  B (2) Transitivity of preferences If A  B and B  C, then A  C (3) Economic goods: More is better

  4. 2.4. Indifference curve and substitution (1) What is an indifference curve? A curve that represents all the combinations of goods or services that provide the same level of utility. (2) A graphical presentation (3) Marginal rate of substitution (MRS): The negative of the slope of an indifference curve: MRS = Interpretation:

  5. Marginal Rate of Substitution Y , Burritos per semester a 8 – 3 b 5 1 – 2 c 3 1 d – 1 2 1 I 0 3 4 5 6 X , Pizzas per semester

  6. 2.4. Indifference curve and substitution (4) Indifference curve maps (5) Indifference curves do not intersect (6) An indifference curve should be “thin” (7) Convex indifference curve -- Diminishing MRS: MRS decreases when X increases -- Relatively balanced bundles are preferred to relatively unbalanced bundles

  7. 2.5. Marginal utility and MRS (1) Marginal utility: Change in utility associated with a one-unit change in the consumption of a good, holding other goods unchanged. e.g., Utility = U(X1, X2, …, Xn) Economic goods: MU > 0 Economic bads: MU < 0 A useless product: MU = 0

  8. 2.5. Marginal utility and MRS (2) Marginal utility and MRS U= U(X, Y)

  9. 2.6. Special utility functions (1) Perfect substitutes (2) Perfect complements (3) A useless good (4) An economic bad

  10. Perfect substitutes • straight line indifference curves

  11. Perfect Substitutes Coke, Cans per week 4 3 2 1 1 2 3 4 I I I I 0 1 2 3 4 Pepsi, Cans per week

  12. Perfect complements • right-angle indifference curves • MRS = 0 (Coffee-Cream)

  13. Perfect Complements Ice cream, Scoops per week e c 3 3 I b d 2 2 I a 1 1 I 0 1 2 3 Pie, Slices per week

  14. A useless good • Horizontal or vertical indifference curves

  15. An economic bad • Utility decreases when the quantity increases

  16. Practice problem Mr. Smith does not watch any TV without popcorn and he eats popcorn only when he watches TV. Draw an indifference curve to show his preference for popcorn and watching TV.

  17. 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): Px X + Py Y < 20 where Px and Py are the corresponding prices In general: P1 X1 + P2 X2 + P3 X3 + …+ Pn Xn< I where I is the available income

  18. 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 < 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

  19. Budget Constraint 1 X + 2 Y < 50 Y a 25 Infeasible (not affordable) region b 20 c 10 Feasible (affordable) region d X 0 10 30 50 Slope of the budget line = -0.5 In general: slope = - Px / Py

  20. Budget Constraint: an increase in income Y 50 new (I = $100) L 25 Gain L (I = $50) X 0 50 100 A change in income does not change the slope of the budget line

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

  22. 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?

  23. 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

  24. Changes in the Budget Constraint (a) Price of Pizza Doubles Y , Burritos per semester 25 Loss 0 25 50 X , Pizzas per semester

  25. 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

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