CDAE 254 - Class 6 Sept. 13

Last class:2. Preferences and choiceQuiz 1

Today:Result of Quiz 1

2. Preferences and choice

Next class:2. Preferences and choice3. Individual demand curvesQuiz 2 (Chapter 2)

Important date:Problem set 2: due Thursday, Sept. 20Problems 2.1, 2.2, 2.4 and 2.10 (a and b only) from the textbook

Result of Quiz 1Result of Quiz 1

N = 60 N = 60 Range = 4 – 10 Average = 8.06Range = 4 – 10 Average = 8.06

1. 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 choice2.1. 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): 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

2.7. Budget constraint (2) A graphic analysis of two goods (X and Y)

-- Budget constraint feasible (affordable) vs. infeasible (not affordable) regionse.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

Y

Feasible (affordable) region

50

25

20

10

100 30

a

b

c

d

Infeasible (not affordable) region

X

Slope of the budget line = -0.5In general: slope = - Px / Py

Budget Constraint: an increase in income

Y

Gain

100

Lnew (I = $100)

L (I = $50)

50

25

500X

A change in income does not change the slope of the budget line

Budget Constraint: an increase in Px

Y

Loss

50

L (Px = $1)

LNew

(Px = $2)

25

250X

Class exercise 2Class exercise 2(Tuesday, Sept. 11)(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 constraintWhat is the slope of the budget line?What is the interpretation of the slope?

When one price risesWhen one price rises

price of pizza doubles: Px = $2 (up from $1)

price of burritos and income unchangedslope of the new budget line:budget constraint swings in toward originopportunity set shrinks

Changes in the Budget Constraint

Y, Burritosper semester

(a) Price of Pizza Doubles

Loss

50

25

250

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 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

MRSP

P

Y

X

Utility maximization

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

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