The Consumer’s Optimization Problem

Post on 26-Jan-2016

54 views 0 download

description

The Consumer’s Optimization Problem. Individual consumption decisions are made with the goal of maximizing total satisfaction from consuming various goods and services. Consumer Theory. Assumes buyers are completely informed about: Range of products available Prices of all products - PowerPoint PPT Presentation

Transcript of The Consumer’s Optimization Problem

5-1

The Consumer’s Optimization Problem

• Individual consumption decisions are made with the goal of maximizing total satisfaction from consuming various goods and services

5-2

Consumer Theory

• Assumes buyers are completely informed about:• Range of products available

• Prices of all products

• Capacity of products to satisfy

• Their income

5-3

Indifference Curves

• Locus of points representing different bundles of goods, each of which yields the same level of total utility

• Negatively sloped & convex

5-4

Properties of Consumer Preferences

• Completeness• For every pair of consumption bundles, A and B, the

consumer can say one of the following:• A is preferred to B• B is preferred to A• The consumer is

indifferent between A and B

5-5

Properties of Consumer Preferences

• Transitivity• If X is preferred to Y, and Y is preferred to Z,

then X must be preferred to Z

5-6

Properties of Consumer Preferences

• Nonsatiation• More of a good is always preferred to less

5-7

Utility

• The benefits consumers obtain from the goods and services they consume is called utility.

• A utility function shows an individual’s perception of the utility level attained from consuming each conceivable bundle of goods

5-8

Marginal Utility

• Addition to total utility attributable to the addition of one unit of a good to the current rate of consumption, holding constant the amounts of all other goods consumed

• MU= Changes in Total Utility /

Change in No of Units Consumed MU U X

5-9

Constrained Utility Maximization (Figure 5.8)

A•

I

C•

•B

II

R

T

Quantity of burgers

Qu

anti

ty o

f piz

zas

0 8020 10040 60

10

20

30

40

50

7010 9030 50

•E

III

•DIV

45

15

5-10

Marginal Rate of Substitution

• MRS shows the rate at which one good can be substituted for another while keeping utility constant• Negative of the slope of the indifference curve

• Diminishes along the indifference curve as X increases & Y decreases

• Ratio of the marginal utilities of the goods

X

Y

MUYMRS

X MU

5-11

How to get MRS Formula

• U = ƒ(XY) (Here, U= Utility; X,Y= 2 goods)

by differentiation,

dU= ƒ1dX + ƒ2dY Here, ƒ1= ΔU/ ΔX = MUx

ƒ2= ΔU/ ΔY = MUy

as per indifference curve, U remains constant. So, U = 0

→ ƒ1dX + ƒ2dY = 0

→ ƒ1dX = - ƒ2dY

→ ƒ1 / ƒ2 = - dX/dY

as indifference curve is neutral, so….

IdX/dYI = I ƒ1 / ƒ2 I = MUx/ MUy

So, MRSxy = MUx/ MUy

5-12

Slope of an Indifference Curve & the MRS (Figure 5.3)

Quantity of good X

Qu

an

tity

of

go

od

Y

0

I

C (360,320)

600

800

A

B

T

T’

360

320

5-13

MRS = slope of indifference curve = slope of tangent line

5-14

The slope is 35/35 = 1

5-15

MRS = − ΔY /ΔX = 5 /10 = 1 2

5

10

5-16

5

10

Before, − ΔY /ΔX = 5/10 or 1/ 2, After, − ΔX/ ΔY = 10/5 or 2

10:5 or 2:1

5-17

5-18

Consumer’s Budget Line

• Shows all possible commodity bundles that can be purchased at given prices with a fixed money income

X YM P X P Y

X

Y Y

PMY X

P P

or

5-19

Consumer’s Budget Constraint (Figure 5.5)

5-20

Typical Budget Line (Figure 5.6)

Quanti

ty o

f Y

Quantity of X

X

Y Y

PMY X

P P

A

B

Y

MP

X

MP

5-21

Shifting Budget Lines (Figure 5.7)

Panel B – Changes in price of X

200

100A

B

250

D

R

N

120

240

Qu

anti

ty o

f Y

Quantity of X

Panel A – Changes in money income

Qu

anti

ty o

f Y

Quantity of X

A

B

100F

Z

80

160

200

125

C

5-22

The following figure shows a portion of a consumer’s indifference map. Theconsumer faces the budget line ZL, and the price of Y is $20.

The consumer's income = $__________. The price of X is $_____________.

600

20

5-23

The following figure shows a portion of a consumer’s indifference map. Theconsumer faces the budget line ZL, and the price of Y is $20.

The equation for the budget line ZL is Y = ______________________.

30 - 1x

30/ 30

5-24

The following figure shows a portion of a consumer’s indifference map. Theconsumer faces the budget line ZL, and the price of Y is $20.

What combination of X and Y would the consumer choose? Why?

15X and 15Y

5-25

The following figure shows a portion of a consumer’s indifference map. Theconsumer faces the budget line ZL, and the price of Y is $20.

The marginal rate of substitution at the combination in part c is __________.

MRS=PMRS=Pxx / P / PYY

= 20 / 20= 20 / 20 = 1= 1

5-26

The following figure shows a portion of a consumer’s indifference map. Theconsumer faces the budget line ZL, and the price of Y is $20.

If the budget line pivots to ZM, the consumer chooses _______ units of good X and _________ units of good Y.

10

15

5-27

The following figure shows a portion of a consumer’s indifference map. Theconsumer faces the budget line ZL, and the price of Y is $20.

Along budget line ZM, the price of X is $_________ and the price of Y is$________.30

20

5-28

The following figure shows a portion of a consumer’s indifference map. Theconsumer faces the budget line ZL, and the price of Y is $20.

The new MRS is equal to __________.MRS= 30/ 20 =1MRS= 30/ 20 =1

5-29

The figure below shows a portion of a consumer’s indifference map, and a budget line. The consumer’s income is $1,200 and the price of Y is $6.

Using the given budget line, what is one point on the consumer’s demand for X?(Both Price & Quantity)

Px = $1,200/200 = $6 and X = 100

5-30

The figure below shows a portion of a consumer’s indifference map, and a budget line. The consumer’s income is $1,200 and the price of Y is $6.

Pivot the budget line and derive two other points on the consumer’s demand for X.

At A, Px = $1,200/100 = $12 and X = 50

At B, Px = $1,200/200 = $6 and X = 100

At C, Px = $1,200/300 = $4 and X = 150

5-31

Market Demand

• Market demand is a list of prices and the quantities consumers are willing and able

• to purchase at each price in the list, other things being held constant.

• Marketdemand is derived by horizontally summing the demand curves for all the individuals in the market.

5-32

Derivation of Market Demand

Quantity demanded

Price Consumer 1 Consumer 2 Consumer 3Market

demand

$6

2

1

5

4

3

3

1213

5

8

10

0

7

10

1

3

5

0

6

8

0

1

4

3

2531

6

1219

5-33

Derivation of Market Demand Figure (5.10)