Nicholson AISE PPT Ch02

8/8/2019 Nicholson AISE PPT Ch02

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Hamb u rgersper week

6 A

B

C

D U1

4

3

2

S of t drinksper week2 3 4 5 60

FIGURE 2-2: Indifference Curve


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6 A

B

C

E

D U1

4

3

2




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Points Below Indifference Curve

Figure 2-2: points such as F are below (to

the southeast) of given indifference curve.Point C is preferred to point F since Cprovides more of both goods.Because of transitivity, all points on U 1preferred to point F.Points on indifference curve are preferred topoints below it.


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6A

B

C

E

F DU1

4

3

2




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Slope of Indifference CurveFigure 2-2: from point A to point B, personwillingly gives up two hamburgers to gain

one soft drink, since consumer is equallyhappy at either point.

Slope of U 1: approximately -2 betweenpoints A and B: hamburgers decline bytwo units to gain one unit of soft drinks.


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Indifference Curves:M arginal Rate of Substitution

Marginal Rate of S u bstit u tio n (M RS):Rate at which individual will reduce

consumption of one good to get one moreunit of other good.M easured as negative of indifference curveslopeFigure 2-2: M RS between points A and B on U 1(approximately)-2.


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Diminishing M arginal Rate of Substitution

Fig. 2.3: On indifference curve U 1 ,consumer will only give up one hamburger

to gain one more soft drink between pointsB and C.

Between points C and D, consumer willgive up only hamburger to gain onemore soft drink.


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Diminishing M arginal Rate of Substitution

M RS diminishes along indifference curvemoving from left to right.

Reflects idea that consumers prefer balanced consumptionFigure 2.3: Point G reflects bundle that is

between points A and D.Since it is above U 1,point G preferable to anybundle on indifference curve.


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Indifference Curve M apsSince every hamburger/ soft drinkcombination must yield some level of

utility, every point must have one (and onlyone) indifference curve passing through it.Indi ff erence c u rve map shows utility anindividual obtains from all possibleconsumption options.

Figure 2- 4 shows three of infinite number of indifference curves in map.


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Labeling Indifference CurvesSince utility can not be measured, labelingindifference curves has no meaning

except to indicate that utility increasesfrom U 1 to U2 and then to U 3 in Figure 2- 4 .

In any indifference curve map, all we canassume is that utility increases as wemove to higher indifference curves.


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6A

B

C

G

DU1

4

3

2

S of t drinksper week2 3 4 60

FIGURE 2- 4 : Indifference Curve M apfor Hamburgers and Soft Drinks

5

5

U2

U3

H


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Illustrating Particular Preferences

Figure 2- 5 (a): good on vertical axis(smoke grinders) is useless, so consumer only gains utility from more of good onhorizontal axis (food).Figure 2- 5 (b); good on vertical axis is

economic bad (houseflies); consumer only gains utility from consuming less of bad.


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(a) A u seless g oo d

Sm o kegrinders

per week

U1 U2 U3

Foo d per week0 10

(b) An ec o no mic bad

Ho u se f liesper week

U1U2

U3

Foo d per week0 10

(c) Per f ect s u bstit u te

G all o nsof Exxo nper week

U1 U2 U3G allo ns of Mo bil

per week0

(d) Per f ect c o mplements

Rig h t s ho esper week

U4

U3

U1

U2

Le f t s ho esper week

0

1

2

3

4

1 2 3 4

FIGURE 2- 5 : Illustrations of Specific

Preferences


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Particular PreferencesFigure 2- 5 (c): two goods are perfectsubstitutes--consumer views them as

essentially the same;M

RS = 1

Figure 2- 5 (d): two goods are perfect

complements--they must be used together (like left and right shoes) to gain utility.


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Income and Utility: A Simple CaseWhen choosing to allocate incomebetween two goods (e.g., hamburgers and

soft drinks) consumer will:

Spend entire income on two goods, and

Choose combination of goods for which theM RS (marginal rate of substitution) betweenthe two goods equals the ratio of their prices.


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Income and Utility: A Simple Case

Since both goods (and only these goods)provide more utility with additionalconsumption, consumer will spend entireincome on these goods.

Only other alternative: throw incomeaway--does not increase utility.


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Equality of M RS with the Ratio or Prices

Suppose individual currentlyconsumes where M RS = 1.

Assume price of hamburgers is $1 andprice of soft drinks is $. 5 0.Yields a price ratio (P H/P S) of ($.5 0/$1) = .


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Equality of M RS with Price Ratios

Person could give up one hamburger (freeing $1) and purchase one soft drink

using $. 5 0.Since M RS =1, person would be just ashappy as before giving up burger, butwould now have additional $. 5 0 to spendcould thus increase utility.

Only way utility cannot be increasedfurther: when M RS = price ratio.


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Showing Utility M aximization Graphically

Individuals b u dget c o nstraint is limit that

persons income places on combinationsof goods and services consumer can buy.

Figure 2- 6 : individual has a fixed amountof income to spend on two goods, X andY.


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Budget Constraint from Figure 2- 6If all income is spent on X, X max can bepurchased.

If all income is spent on Y, Y max can bepurchased.

The line joining X max and Y max representsvarious mixed bundles of goods X and Y thatconsumer can purchase using all income.


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Qu antity of Yper week

Yma x

Qu antity of Xper week0 Xma x

FIGURE 2- 6 : Individuals BudgetConstraint for Two Goods


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Qu antity of Yper week

Yma x

No t a ffo rdable

Inc o me

Affo rdable

Qu antity of Xper week0 Xma x

FIGURE 2- 6 : Individuals BudgetConstraint for Two Goods


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Budget ConstraintBudget lines downward slope reflects factthat more X can be purchased only if lessY is purchased.

If Y is expensive relative to X, budget linewill be relatively flat (Y on vertical axis).

If Y is relatively inexpensive compared toX, budget line will be relatively steep.


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Budget Constraint Algebra

Assume individual has I dollars of incometo spend on goods X and Y.

Suppose price of X is P x and price of Y isP Y.

Total amount spent on X and Y are P xXand P YY ,respectively.


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Budget Constraint Algebra

Solving equation 2.3 for Y, to express it inthe standard form for linear equation, wehave

[2.4] 1

Y Y

X X Y

!


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Budget Constraint AlgebraEquation 2. 4 shows that if all incomespent on Y, I/P Y will be purchased, and if

all income is spent on X, I/P X will bepurchased.

The slope of budget line (-PX/P

Y)

represents o pp o rtunity c o st of X in termsof foregone Y.


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Utility M aximizationIndividual can afford all bundles of X and Ythat fall within budget constraint representedby shaded area in Figure 2- 6 .

Point A is affordable, but not all of theconsumers income would be spent.

Point B is affordable, but is not on the highestindifference curve that the consumer canreach, so some utility is wasted.


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4 1


B

A

Inc o me

U1 S of t drinksper week0

FIGURE 2- 7 : Graphic Demonstrationof Utility M aximization


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4 2


B

A

DInc o me

U1 S of t drinksper week0

FIGURE 2- 7 : Graphic Demonstrationof Utility M aximization

U3


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Utility M aximization

Fig. 2. 7 : Point D is on higher indifferencecurve than C, but is not affordable given

the budget constraint.

Point C, where the consumer chooses X *,Y* is the affordable point that lies on(tangent to) highest indifference curve, sorepresents utility maximization.


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Utility M aximization At point C, all income is spent. At point C, indifference curve U 2 lies

tangent to budget line, so

or curveceindifferenof lopeconstraint budgetof lope !

. MRS P P

Y

X

!


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Using The M odel of Choice

Utility maximization model explainsnumber of common observations.

Figure 2- 8 provides illustration of whypeople with same income choose to spend

in different ways.


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(a) Hu ngry J o e


8

0 4

(b) T h irsty Teresa

Inc o me2

16

(c) Ex tra-t h irsty E d

U0

U1U2

S of t drinks

per week20

F IG UR E 2-8 : Differences in PreferencesResult in Differing Choices

S of t drinks

per week

S of t drinks

per week



U0U0

U1

U1U2U2

Inc o meInc o me


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Using the M odel of ChoiceFigure 2- 9 shows four indifference curvemaps with budget constraint and utility-maximizing choice labeled E.

Panel (a) shows that people will not buyuseless goods; (b) shows they will not buybads.Panel (c) shows that people will buy leastexpensive of two perfect substitutes; (d)shows that perfect complements will bepurchased together.


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(a) A u seless g oo d

Sm o kegrinders

per week

U1

E

E

E

E

U2 U3

Foo d per week

Inc o me

Inc o me

Inc o me

Inc o me

0 10

(b) An ec o no mic bad

Ho u se f liesper week

U1U2

U3

Foo d per week0 10

(c) Per f ect s u bstit u te

G allo nsof Exxo nper week

U1 U2 U3G all o ns of Mo bil

per week0

(d) Per f ect c o mplements

Rig h t s ho esper week

U3

U1

U2

Le f t s ho esper week

0

2

2

FIGURE 2- 9 : Utility-M aximizingChoices for Special Types of Goods

Nicholson AISE PPT Ch02

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