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CDAE 254 - Class 5 Sept. 12 Last class: 1. Introduction Class exercise

CDAE 254 - Class 5 Sept. 12 Last class: 1. Introduction Class exercise 2. Utility and choice Quiz 1 Today: Result of Quiz 1 2. Utility and choice Class exercise 2 Next class: Utility and choice Important date: Problem set 1 due today.

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CDAE 254 - Class 5 Sept. 12 Last class: 1. Introduction Class exercise

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  1. CDAE 254 - Class 5 Sept. 12 • Last class: • 1. Introduction • Class exercise • 2. Utility and choice • Quiz 1 • Today: • Result of Quiz 1 • 2. Utility and choice • Class exercise 2 • Next class: • Utility and choice • Important date: • Problem set 1 due today

  2. N = 47 Range = 4.5 –- 10 Average = 8.81 1. Two goals (objectives) of economics: explanation & prediction 2. Supply and demand functions: (a) Draw the supply and demand lines (b) Derive the equilibrium P* and Q* 3. Y = 2 + 0.2X – 0.01X2 Y is a nonlinear function of X 4. Derive derivatives 5. Profit function  q* that maximizes the profit Result of Quiz 1

  3. 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

  4. 2.3. Utility (3) What is a utility function? Given the three assumptions about rational choice, a consumer is able to rank alternative bundles in the order of her or his preferences. The ordinal ranking expressed in a mathematical equation is called a utility function: Utility = U (X1, X2, ……, Xn)

  5. 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:

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

  7. 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 -- Should have negative slopes -- Diminishing MRS: the value of MRS decreases when X increases --Balanced bundles are preferred to unbalanced bundles

  8. Impossible Indifference Curves B , Burritos per semester e b 1 I a 0 I Z , Pizzas per semester

  9. Impossible Indifference Curves B , Burritos per semester b a I Z , Pizzas per semester

  10. Impossible Indifference Curves B , Burritos per semester b a I Z , Pizzas per semester

  11. 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

  12. 2.5. Marginal utility and MRS (2) Marginal utility and MRS U= U(X, Y)

  13. 2.6. Special utility functions (1) Perfect substitutes (2) Perfect complements (3) A useless good (4) An economic bad

  14. straight line indifference curves Perfect substitutes

  15. 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

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

  17. 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

  18. Horizontal or vertical indifference curves A useless good

  19. Utility decreases when the quantity increases An economic bad

  20. 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. 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. Class exercise 2(Tuesday, Sept. 12)

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