demand analysis, estimation and forecasting_part1 (1)

7/31/2019 Demand Analysis, Estimation and Forecasting_part1 (1)

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7/12/12

DEMANDANALYSIS,ESTIMATION ANDFORECASTING


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DEMAND ANALYSIS

DEMAND: total quantity of a goodor service that customers are willingand able to purchase during a

specified period under a given setof economic conditions.

Direct demand vs. derived demand

Demand function vs. demand curve


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Determinants of demand

Own price

Prices of related goods Expectations of price changes

Consumer incomes

Tastes and preferences

Advertising expenditures

Industr vs. firm demand

DEMAND ANALYSIS

adviPopnYPQcar 443210 +++++=


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BASIS FOR DIRECTDEMAND

q

q

2

2

1

2

1

UU

pp =

a c


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q

q

2

a cb


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q

q

2

a c

d

Consumptionpath


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yqpqptosubjectqqUUMax =+=221121 ),(

)(),( 221121 qpqpyqqU += L

0

0

0

2211

22

2

11

1

==

==

==

qpqpyL

pUq

L

pUqL

),,(

),,(

),,(

21

2122

2111

ypp

yppqq

yppqq

=

=

=

2

2

1

1

p

U

p

U ==



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Totally differentiate first-order conditions:

22222121

11212111

22112211

dpdpdqUdqU

dpdpdqUdqU

dydpqdpqdqpdqp

=+=+

+=

0

2

1

2211

2

1

22212

12111

21

+

=

dpdp

dydpqdpq

dqdq

d

UUpUUp

pp

Using Cramers rule:

J

JdpJdpJdydpqdpqdq322221122211

1)( ++=

J

JdpJdpJdydpqdpq

dq

332231132211

2

)( ++=


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Let dy = dp2 = 0.

J

Jq

J

J

dp

dq 121

22

1

1 =

J

Jq

J

J

dp

dq 131

23

1

2 +

=

substitution effect vs. income effect


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)( 221121 qpqpyqq += L

0

0

0

2211

21

2

12

1

==

==

==

qpqpy

pqq

pqq

L

L

L

Totally differentiate FOCs:

-

-

221

112

22112211

dpdpdq

dpdpdq

dydpqdpqdqpdqp

=

=

+=

01

10

0

2

1

2211

2

1

2

1

21

+

=

dp

dp

dydpqdpq

dq

dq

d

p

p

pp

52100 21 === ppy

q1* =25q2* =10* = 5

2

2

2

21

2

2

1

1

pp

y

p

yq

p

yq

=

=

=


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J

Jq

J

J

dp

dq 121

22

1

1 +=

( )21

21

21

2

2

22 pp

pq

pp

p +

=

( ))5)(2(2

)5(

)25()5)(2(2

5)5( 2

+

=

5.12

25.625.6

=

=


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A consumers utility function isgiven by

.5221

2

2

2

1qqqqU ++=

Let p1 = 5, p2 = 10 and the consumers income for

the period 90.

a) Determine the quantities q1 and q2 which theconsumer should purchase in order to maximize hisderived utility.

b) Write the demand functionfor q1.c) Calculate the substitution and incomeeffects of a one unit change in p1.


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yxpxpxptosubject

xxxUMax

=++

+=

332211

321

)ln(

)()ln( 332211321 yxpxpxpxxx +++= L

0

01

01

01

332211

3

33

2

22

1

1

=+=

==

==

==

yxpxpxp

p

xx

pxx

px

L

L

L

L

1

***2-*13

13

2

12

1

1

pp

px

p

px

p

yx ====


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1002

U

21

21

=+

=

xxtosubject

xxMax

( )1002 21121 += xxxx L

01002

0

02

21

1

2

2

1

=+=

==

==

xx

xx

xx

L

L

L

25*250,1*)*,(,50*,25*2121

==== xxUxx

1012

U

21

21

=+

=

xxtosubject

xxMax

275,1125.275,1*)*,(,5.50*,25.25* 2121 === xxUxx

* is the marginal utility of income.


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DEMAND SENSITIVITY

XX

YY

=

Y

X

X

Y

=

XAverageXinChange

YAverageYinChange

/

/ElasticityArc =

2/)(

2/)(

12

12

12

12

XX

XX

YY

YY

+

+

=12

12

YY

XX

X

Y

+

+

=

Xd

Yd

ln

ln=

Y

X

dX

dY=


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PRICE ELASTICITY

Impact on total revenue

Maximum revenue and unitaryelasticity

Optimal pricing

P

MCP

11

=


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CROSS-PRICE ELASTICITY

Substitutes, complements,independents

Uses:

Formulating own pricing strategy and

analyzing risks associated with variousproducts

Assessing market competition


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INCOME ELASTICITY

Normal /superior goods vs. inferiorgoods

Inferior goods are countercyclicalgoods.

Normal goods may be:

- Noncyclical (0 < I < 1) : toiletries,

liquor, cigarettes


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EXAMPLE

Month No. of sportswatches sold Sports watchadvertisingexp

Sports watchprice Dress watchprice

July 4,500 10,000 26 50

August 5,500 10,000 24 50

September 4,500 9,200 24 50

October 3,500 9,200 24 46

November 5,000 9,750 25 50

December 15,000 9,750 20 50

January 5,000 8,350 25 50

February 4,000 7,850 25 50

March 5,500 9,500 25 55

April 6,000 8,500 24 51

May 4,000 8,500 26 51


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EXAMPLE

Analyze the sensitivity of demand forsports watch with respect to its ownprice and advertising expenditures.

Analyze the sensitivity of demand forsports watch with respect to theprice of dress watch.


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DEMAND ESTIMATION

PRICE

QUANTITY

p1

q

1

p2

p3

q

2

q

3


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IDENTIFICATIONPROBLEM

PRICE

QUANTITY

p1

q

1

p2

p3

q

2

q

3

D1

S1

D

2

S2

D3

S3


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DEMAND ESTIMATION

PRICE

QUANTITY

p1

q

1

p2

p3

q

2

q

3

S1

S2

S3


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METHODS OFESTIMATING DEMAND

Consumer interviews or survey

Experimental methods

Regression analysis

Deterministic vs. stochastic relationship

demand analysis, estimation and forecasting_part1 (1)

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