CDAE Class 4 Sept. 6 Last class: 1.Introduction 2.Preferences and choice Class exercise 1 Today: 2. Preferences and choice Next class: 2.Preferences and choice Quiz 1 Important date: Problem set 1: due today

Class exercise 1 (Tuesday, Sept. 4) 1. Derive the derivatives: (a) Y = 10(b) Y = X + 0.1X 2 2. If a company’s profit function is profit = – q – 0.01 q 2 (a) What should be the profit-maximizing production level (q*)? (b) What is the maximum profit?

3. 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

2.2. 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

Assumption 1: Completeness A consumer can rank any two bundles of goods only one of following is true: a consumer prefers Bundle A to Bundle B prefers Bundle B to Bundle A is indifferent between A and B

Assumption 2: Transitivity consumer's preference over bundles is consistent: if consumer prefers Bundle A to Bundle B and Bundle B to Bundle C then consumer prefers Bundle A to Bundle C

Assumption 3: More is better more of a good is better than less of it good: commodity for which more is preferred to less at least at some levels of consumption bad: something for which less is preferred to more (e.g., pollution)

Bundles of Pizzas and Burritos Lisa Might Consume B, Burritos per semester (a) Ranking Regions Z, Pizzas per semester d a b e c f A B

2.3. Utility (1) What is utility? The pleasure or satisfaction that a consumer obtains from his or her activities. (2) How to measure utility? -- No unit for utility (happiness) -- Ordinal comparison of alternative choices

2.3. Utility (3) What is a utility function? G iven 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 (X 1, X 2, ……, X n )

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:

Marginal Rate of Substitution B, Burritos per semester – –2 – Z, Pizzas per semester a b c d I

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 b alanced bundles are preferred to relatively unbalanced bundles

B, Burritos per semester Z, Pizzas per semester I 1 I 0 a b e

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

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

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(X 1, X 2, …, X n ) Economic goods: MU > 0 Economic bads: MU < 0

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

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

Perfect substitutes straight line indifference curves

Coke, Cans per week Perfect Substitutes 1234 Pepsi, Cans per week I 1 I 2 I 3 I 4

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

Ice cream, Scoops per week Perfect Complements 123 Pie, Slices per week I 1 I 2 I 3 a d ec b