Chapter 04 Demand Analysis

8/3/2019 Chapter 04 Demand Analysis

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Demand AnalysisChapter 4


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The Basis for Consumer

Demand The ability of goods and services to

satisfy consumer wants is the basis for

consumer demand. Utility theory helps us understand the

basis for demand since it explains the

relationship between consumersatisfaction and the goods and servicesconsumed.


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Utility Functions

A mathematical representation of therelationship between total utility andthe consumption of goods and services.

Utility = f(Goods, Services) The utility function is shaped by

the tastes and preferences ofconsumers, and

the quantity and quality ofavailable products.


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Utility Functions The utility derived from consumption is

intangible.

Consumers reveal their preferencesthrough purchase decisions and providetangible evidence of the utility they

derive from various products.


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Marginal Utility Measures the added satisfaction derived

from one-unit increase in consumption

of a particular good or service, holdingconsumption of all other goods andservices constant.


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Total and Marginal Utility

Sandwiches per Meal, S Total Utility, UMarginal Utility,

MUS = U/S

MaximumAcceptable

Sandwich Price at

20 per MUS0 0 - -1 5 5 $1.002 9 4 0.803 12 3 0.604 14 2 0.405 15 1 0.206 15 0 0.00


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Total and Marginal Utility The marginal utility is diminishing as

consumption of sandwiches is

increasing. If each sandwich costs $1:

1st sandwich:

cost per unit of utility = 1/5 = 0.20 2nd sandwich:

cost per unit of utility = 1/4 = 0.25


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Total and Marginal Utility As a result of diminishing marginal utility, the

cost of each marginal unit of satisfaction

increases as we increase our consumption ofsandwiches.

Assume that the consumer has alternativeconsumption opportunities that would provideone additional unit of utility for 20.

Then, the consumer will be willing to increasethe consumption of sandwiches only if

sandwich prices were to fall.


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Total and Marginal Utility If the required price/marginal utility trade-off

for sandwiches is 20 per unit of satisfaction,

then the consumer will pay $1 for a singlesandwich. In order for the consumer to purchase one

more sandwich, the second sandwich should

cost only 80 (20 x 4 units of satisfaction). Similarly, in order for the consumer to

purchase the third sandwich, the thirdsandwich should cost only 60 (20 x 3 units

of satisfaction).


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The Law of Diminishing

Marginal UtilityAs an individual increases consumption

of a given product, the marginal utility

gained from consumption eventuallydeclines.

This law gives rise to a downward-sloping demand curve for all goodsand services.


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The Demand Curve

0

0,2

0,4

0,6

0,8

1

1,2

0 1 2 3 4 5 6 7

Quantity of Sandwiches

Price

($)


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Consumer Choice Products are frequently consumed as

part of a basket of goods and

services. Within this basket, products can be

substituted for each other.

The substitution occurs at differentdegrees for different pairs of products.


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Consumer Choice:

Total and Marginal UtilityGoods (Y) Services (X)

Quantity Total Utility

Marginal Utility

(MUY | X=4) Total Utility

Marginal Utility

(MUX | Y=1)

1 55 - 25 -

2 67 12 36 113 77 10 46 10

4 85 8 55 9

5 92 7 63 8

6 98 6 70 7

7 103 5 76 6

8 107 4 81 5

9 109 2 85 4

10 110 1 88 3


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Consumer Choice:

Indifference Curves E.g. A consumer can choose to buy a basket

with a high proportion of total expenditures

devoted to services or vice versa. For this consumer, a large number ofbaskets can be created that provide thesame level of util ity to the consumer. An indifference curve represents all

market baskets among which the consumer isindifferent about choosing.


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Indifference Curves

01234567

89

10

0 1 2 3 4 5 6 7 8 9 10QuantityofGoods(Y)

Quantity of Services (X)

U1 = 100 units U2 = 118 units


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Indifference Curves Indifference curves will never intersect

with each other.

Higher curves will represent higherlevels of utility.

The consumer will want to consume a

basket on a relatively higherindifference curve in order toincrease/maximize his/her utility.


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Marginal Rate of Substitution

The slope of each indifference curve equalsthe change in goods (Y) divided by the

change in services (

X). Marginal rate of substitution is the sloperelation that shows the change in theconsumption of Y (goods) necessary to offset

a given change in the consumption of X(services) if the consumers overall level ofutility is to remain constant.

MRS = Y / X = slope of an indifferencecurve


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MRS is not constant along an indifferencecurve.

From left to right, MRS usually declines asthe amount of substitution increases.

MRS declines because of the law of

diminishing marginal utility.


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Marginal Rate of Substitution When we move from a left-hand-side point to

a right-hand-side point on a given

indifference curve:

the loss in utility associated with a reductionin Y is equal to U = MUYx Y.

the gain in utility associated with an increasein X is equal to U = MUX x X.


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Marginal Rate of Substitution Along an indifference curve, the utility level

does not change.

Therefore, the absolute value of the changein utility for reducing Y needs to be equal tothe change in utility for increasing X.

So, the following must be true:

MUY x Y = (MUX x X ) The absolute value of the changes in utility

must be the same and the signs must beopposite in order for TU to stay constant.


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When MUYx Y = (MUX x X ) is true, thefollowing must also be true:

MRSXY= Slope of an indifference curve

The slope of the indifference curve is determinedby the ratio of the marginal utilities derived fromeach product.

X

Y

MU

MU

Y

X=


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Consumer Choice:Budget Lines

The second important determinant ofthe consumer choice is the existence of

a budget constraint.Abudget l ine represents all

combinations of products that can be

purchased for a fixed dollar/liraamount:


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Consumer Choice:Budget Lines

Total Budget = Spending + Spendingon Goods on Services B = PY Y + PX X

The expression for the budget line becomes:

XP

P

P

BY

Y

X

Y

=


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Budget Line

0123456

789

10

0 2 4 6 8 10 12 14 16 18 20

Budget = $1,000 Budget = $1,500 Budget = $2,000

U1 = 100 units U2 = 118 units


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Decrease in Price of Y

0123456789

1 0

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

B udge t = $ 1 , 5 0 0 , P Y = $ 2 5 0 U 1 = 1 0 0 un it s

U 2 = 1 1 8 un it s B udge t = $ 1 ,5 0 0 , P Y =

B udge t = $ 1 ,5 0 0 , P Y = $ 1 5 0


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Effect of Price Changes Consumer is affected in two ways:

1. Income Effect: With the same budget, a pricedecrease allows higher consumption (higherindifference curve) and a price increase causeslower consumption (lower indifference curve).

Change in the quantity demanded as a result of achange in the consumers real income (real incomechanges as result of a change in the price level)


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Effect of Price Changes2. Substitution Effect: With the samebudget, a price increase makes the productrelatively more expensive and shifts the

overall consumption away and moretowards the cheaper product (movementalong the indifference curve).

Change in the quantity demanded that isthe result of only a change in the relativeprices of goods, given a constant realincome.


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Effect of Price Changes3. Total Effect: Total effect is the sum ofincome and substitution effects.


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Effect of Price Changes

Price of X decreases

Nominal income is the same.Same combination can be bought

by spending less of the nominal

income.Consumer has money left to

purchase more of X or Y.Consumers real income has

increased.

Income effect is the change in thecombination due to the new real

income.Consumer can move to a higher

indifference curve.

Nominal income is the same.If the real income were kept at the

original level, what is the combinationthat the consumer would buy?Substitution effect is the change in

the combination due to the new price

ratio, under the original real income.

Consumer would choose anotherpoint on the same indifference curve.


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Decrease in Price of Y

012345

6789

1 01 1

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

B udge t = $ 1 ,5 0 0 , P Y = $ 2 5 0 U 1 = 1 0 0 un i t s

U 2 = 1 1 8 un it s B udge t = $ 1 ,5 0 0 , P Y =


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Optimal Consumption

Optimal consumption will occur whenutility for the consumer is maximized.

Utility is maximized when a consumerchooses a basket of products on thehighest indifference curve possible, for

a given budget expenditure.


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Consumer Choice:Budget Constraint and Utility

The budget constraint will impose alimit on the level of utility a consumer

can derive from consumption of thebasket of products.

The highest indifference curve a

consumer can reach will be determinedby the budget constraint.


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Elasticity Percentage relationship between two

variables:

elasticity = % change in A/ % change in B Price elasticity shows the sensitivity of

demand to changing prices:

price elasticity = % change Q / % change in P


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Price Elasticity

Mathematically,

% change in Q = Quantity / Initial Quantity

and,

% change in P = Price / Initial Price Therefore,

Pin%

Qin%

P

P

Q

Q=


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Arc Elasticity Measures the sensitivity of Q to changes in

P over a range of price values:

12

21

21

12

21

12

21

12

PP

PP

QQ

QQEp

)/2P(P

PP

)/2Q(Q

QQEp

+

+

=

+

+

=


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Arc Elasticity E.g. If the price of a product rises

from $11 to $12, the quantity

demanded falls from 7 to 6 units. Thearc elasticity of demand over this pricerange is:

1.7712)/2(11

1112

7)/2(6

76Ep =

+

+

=


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Arc Elasticity We use averages in the denominators because:

1. If we had used the beginning values (Q=7,

P=$11), Ep would equal to -1.57.2. If the price decreases from $12 to $11, then Qincreases from 6 to 7. If we use beginning values(Q=6, P=$12), this time Ep equals -2.0.

3. It looks like we have a different sensitivitydepending on whether we have a price increaseor a price decrease.

Using averages avoids this ambiguity.


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Point Elasticity Measures the sensitivity of Q to changes in P

when the change is very small:

where dQ/dP is the derivative of Q withrespect to P.

1

1

Q

Px

dP

dQEp =


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Point Elasticity

E.g. Q = 18 - P

When Q = 6 and P = 12,

Ep = -1 x (12/6) = -2

Note that when the demand curve islinear, (dQ/dP) is constant along thedemand curve. However, Ep changes as Qand P values change.


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Point Elasticity E.g. Q = 100 - P2

When Q = 75 and P = 5,

Ep = -2P x (5/75) = -50 / 75 = -0.67

E.g. Q = 100 / P1.7

When Q = 10 and P = 3.875, Ep = ?Rewrite the demand equation:

log Q = log 100 - 1.7 log P


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Elasticity Definitions |Ep| > 1 relatively elastic demand

(% in Q > % in P)

0 < |Ep| < 1 relatively inelastic demand(% in Q < % in P)

|Ep| = 1 unitary elasticity(% in Q = % in P)

|Ep| = perfect elasticity(% in Q >> % in P since % in P = 0)

|Ep| = 0 perfect inelasticity(% in Q = 0)


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Determinants of Elasticity

Ease of substitution

Proportion of total expenditures

Durability of product Possibility of postponing purchase

Possibility of repair Used product market


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Demand Elasticity and Revenue

(TR = Q x P) Price increase:

|Ep| > 1 (% decrease in Q > % increase in P)

TR is decreasing.

0 < |Ep| < 1 (% decrease in Q < % increase in P) TR is increasing.

|Ep| = 1 (% decrease in Q = % increase in P) TR does not change.


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Demand Elasticity and Revenue

(TR = Q x P) Price decrease:

|Ep| > 1 (% increase in Q > % decrease in P)

TR is increasing.

0 < |Ep| < 1 ( % increase in Q < % decrease in P) TR is decreasing.

|Ep| = 1 (% increase in Q = % decrease in P) TR does not change.


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Price Quantity Arc Elasticity Revenue

18 0 0

17 1 -35.0 1716 2 -11.0 32

15 3 -6.2 45

14 4 -4.1 56

13 5 -3.0 65

12 6 -2.3 72

11 7 -1.8 77

10 8 -1.4 809 9 -1.1 81

8 10 -0.9 80

7 11 -0.7 77

6 12 -0.6 72

5 13 -0.4 65

4 14 -0.3 56

3 15 -0.2 45

2 16 -0.2 32

1 17 -0.1 17

0 18 0 0


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02468

101214161820

0 2 4 6 8 10 12 14 16 18 20

Demand Elasticity

0

20

40

60

80

0 2 4 6 8 10 12 14 16 18 20

Total Revenue

Inelastic

ElasticUnitary


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Demand and Marginal Revenue

Ep = -1

Inelastic

Elastic

MR

D

P

Q


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Demand and Revenue Demand Curve: P = a - bQ

Total Revenue: PxQ = aQ - bQ2

Marginal Revenue: dTR/dQ = a - 2bQ

Note that the demand curve and themarginal revenue curve share the y-intercept.

Marginal revenue curve has twice the slope


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Cross-Elasticity of Demand Shows the impact on the quantity

demanded of a particular product created by

a price change in a related product(substitutes or complements):

Ex > 0 for substitutes.

Ex < 0 for complements.

B

B

A

A

P

P

Q

Q

Ex=


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Income Elasticity of Demand Sensitivity of quantity demanded to changes in the

consumers income:

EY> 1.0 for superior goods.

0 EY 1.0 for normal goods.

Y

Y

Q

QEY =

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Chapter 04 Demand Analysis