MULTIOBJECTIVE CONSUMER CHOICE MODELLING BASED ON DEPENDING-ON-CONTEXTPREFERENCE

Presenting author: Evgenij OzhegovNRU HSE - Perm

Dept. of Applied mathematics and social system modellingMCDM 2011, 14.06.2011

Outline

• Generalization of the knowledge about recent consumer

choice modelling approaches;

• Consideration of particular models;

• Formulating of the multiobjective problem of consumer

choice;

• Empirical issue of using such model.

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Structure of consumer choice models• By the number of consumers models are divided on:

• Individual demand models• Aggregated demand models

• In terms of time factor:• Static models• Dynamic models

• By the number of consumer choice criteria:• Singlecriterion models• Multicriteria models

• By the homogeneity of the products:• Models with homogeneous products• Models with heterogeneous products

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Classical rational demand

• ) – set of consumer products, where – amount of

consumed product i.

• means that better (strongly preffered) than

• - not worse (weakly preffered)

• - equvivalent

• Rational strong preference coherent, antireflexive,

transitive, asimmetric.

• Weak preference reflexive, coherent, transitive.4

Classical rational demand

• The utility function introduced as the function which:

• .

• Consumer choice problem is choosing the most prefered set

for each budget constraint B, defined by the pair as

• – budget constraint

• – Classical Marshallian demand

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Why this model cannot be used?Because of the non-rational preferences! There are:

1. Problems with equvivalence (lack of knowledge about the alternatives);

2. Problems with transitiveness (cup of tea with 1 mg of sugar cup of tea

with 2 mg of sugar … cup of tea with 20 g of sugar, but not cup of tea

with 1 mg of sugar cup of tea with 20 g of sugar);

3. Dependence of the preferences on context (fashion, external

conditions);

4. Dependence on the question preposition [Canheman, Tversky, 1979];

5. Dependence of the preferences on the time.

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Particular models(2) Using of the generalized utility function [Shafer, 1974];

(5) Using of the discounted utility in the problem of intertemporal choice (Exponential,

hyperbolical discounting) [Shane, Loewenstein, O'Donoghue, 2002];

(3) Models of price setting for new product (innovators - followers) [Bass, 1989];

(3) MAUT (multiattributive utility theory) - dividing the utility of product on attributes [Dyer,

2005];

(3) Using of the preference which is depended on context [Ozhegov, 2010]:

– external factors and if

that and then

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Multicriteria consumer choice problem (*)

• – product set

• – utility criteria

•

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Solution concept using the method of criteria weighting

If than the k-th criterion is more important than the l-th.

Then the problem (*) will be:

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How to use that model?

• Why in different context we see different behavior (except

for different <p,I>)?

• Because of the different weights of the criteria during the

time!

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Dynamical case (**)

• – product set, – i-th product consumption density in the t

time moment;

• – utility criteria;

• ;

• – weight of j-th criterion importance depending on the

context );

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Dynamical case (**)

• I – consumer expenditure for the period;

• [0..T] – time interval;

• – weighted utility criterion;

• ;

• – budget constraint.

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Fixing the consumtion effects

• Consumption effect is constantly observed dependence of the

utility of some product on the external factors.

• How can we fix the existence of that effect and its functional

form?

• Denote that product as and will be all other goods (a quantity

that characterizes the change in amount of the consumer

basket, with the exception of the investigated product).

• - j-th criterion parameters vector

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Fixing the consumption effects

• for each t

• Denote as the value of relative importance of the criteria

which describes the investigated effect

• will be the fixed relative importance of other criteria

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Empirical issue: Giffen effect to buckwheat

• The prices for the buckwheat rose from 45 rubles per kg to 140

in summer 2010;

• There was unreasonably high demand for the buckwheat under

the Giffen effect;

• The sample contained 888 observations of the consumers from

25.04.2010 to 13.08.2010 (111 days, 8 random consumers in

each day) in big retail store;

• Known the amount of buckwheat bought, the price for 1 kg,

expenditure and the weighted price level for each product set.

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Empirical issue: Giffen effect to buckwheat

• At each time t each consumer performs a consumption of

product set which is close to optimal

• Where m is the amount of criteria which he takes in

account

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Empirical issue: Giffen effect to buckwheat

• ;

• Number of estimated params for each m is 6m+2;

• Estimated by the method of maximum likelihood;

• The best model with the minimum AIK compared with best

model without criterion with

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The best model: 2 criteria

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25.04.2010 05.05.2010 15.05.2010 25.05.2010 04.06.2010 14.06.2010 24.06.2010 04.07.2010 14.07.2010 24.07.2010 03.08.2010 13.08.20100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

20

40

60

80

100

120

140

160

Importance of (𝑡) Price for buckwheatImportance of

The best model: predicting power

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25.04.2010 05.05.2010 15.05.2010 25.05.2010 04.06.2010 14.06.2010 24.06.2010 04.07.2010 14.07.2010 24.07.2010 03.08.2010 13.08.2010

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

0

20

40

60

80

100

120

140

160

(𝑡)Predicted (𝑡) Price for buckwheat

THANK YOU FOR THE ATTENTION!Your questions

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References1. Бусыгин В.П., Желободько Е.В., Цыплаков А.А. Микроэкономика – третий уровень.

Новосибирск: Новосибирский государственный университет, 2003.

2. Ожегов Е.М.. Моделирование потребительского выбора нетранзитивными предпочтениями, Сборник материалов XIII Международной научно-практической конференции «Актуальные вопросы экономических наук», Новосибирск, 2010, c. 36-40.

3. Подиновский В.В. Анализ и поддержка решений. Введение в теорию важности критериев в многокритериальных задачах принятия решений, Москва, Физматлит, 2007.

4. В. В. Подиновский, В. Д. Ногин. Парето-оптимальные решения многокритериальных задач, Москва, ФИЗМАТЛИТ, 2007.

5. Ariel Rubinstein: Lecture Notes in Microeconomic Theory, Princeton University Press, 2006

6. Frederick Shane, George Loewenstein and Ted O'Donoghue. Time Discounting and Time Preference: A Critical Review. Journal of Economic Literature. Vol. 40, No. 2, 2002, pp. 351-401.

7. Frank M. Bass, A New Product Growth for Model Consumer Durables, Management Science, Vol. 15, No. 5, 1989, pp. 215-227.

8. James Dyer. Multiple Criteria Decision Analysis: State of the Art Surveys, International Series in Operations Research & Management Science, 2005, Volume 78, IV, 265-292.

9. W. J. Shafer. The Nontransitive Consumer, Econometrica 42, 1974: 913–919.

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