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Habit Formation, Information Exchange and Geography of Demand

Zakaria Babutsidze† & Robin Cowan†‡

† UNU-MERIT

Maastricht University & United Nations University

‡ BETA

Louis Pasteur University

DIMETIC, October 2007, Maastricht

agenda

• 1. motivation
• 2. literature
• 3. model
• 4. results
• 5. simulations
• 6. conclusions

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motivation

• consumer behavior

– heterogeneity – interactions – propagation of knowledge/information

• implications for the geography of demand

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main components

• modeling dynamics of the utilities of a single good for a single consumer
• main components: (i) interdependency among consumers & (ii) inertia
• two interpretations

– 1st: (i) information exchange & (ii) tendency to consume the familiar good – 2nd: (i) network effects & (ii) habit formation

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literature

• geography of demand (on services): Wang & Graham (98), Hudman &

Jackson (02)

• imperfect information: Nelson (70), Samuelson (04)
• local (non-market) interactions: Eshel et al. (98), Glaiser & Scheinkman (00)
• network effects: Cowan et al. (97), Cowan et al. (04)
• habit formation: Deusenberry (49), Abel (90)

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model i: full specification

• many consumers (on the line/circle)
• many substitute goods (with equal prices)
• social network: fixed neighborhood (on the line/circle)
• discrete choice: consumer s buys one unit of one good n every period t and

derives utility us

n;t

• utility: us

n;t = is n;t + es n;t

• dynamics:

– inherent (habit formation):

dis

n

dt =

8 < : ζ ifn = ¯ n

• therwise

– network (information exchange):

des

n

dt = P j

µ(uj

n − us n)

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model ii: modified

• only two goods
• only two neighbors
• problem: habit formation
• solution: probabilistic choice P s

n = us

n

P

j∈N

us

j ⇒

dis

n

dt = αus n

• result:

dus

1

dt = αus

1 + µ(us+1 1

+ us−1

1

− 2us

1)

dus

2

dt = αus

2 + µ(us+1 2

+ us−1

2

− 2us

2)

• or

dys dt = αys + µ ` ys+1 + ys−1 − 2ys´ where ys = us

1 − us 2.

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model iii: analytic solution

• using Turing (52) and Childress (05)
• Taylor expansions around agent s
• continuous time and space
• partial differential equation:

∂y ∂t = αy + ˜ µ∂2y ∂s2

• solution:

y = eσt cos „ k 2π S s « y0 where σ = α − µk2 4π2

S2 and k is a positive integer.

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results

Remember: σ = α − µk2 4π2

S2

comparative statics

• current parameters

– habit formation rate:

∂σ ∂α > 0

– information exchange rate:

∂σ ∂µ < 0

– number of agents:

∂σ ∂S > 0

• putting back neighborhood size and number of goods

– neighborhood size:

∂σ ∂H < 0

– number of goods:

∂σ ∂N = 0

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simulations i: modified model

100 80 60 40 20 Agent 500 400 300 200 100 Time 8 6 4 2

Figure 1: Good purchases in the simulation of modified model

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simulations ii: full model

100 80 60 40 20 Agent 500 400 300 200 100 Time 8 6 4 2

Figure 2: Good purchases in the simulation of full model

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conclusions

• information spillovers from geographically fixed social networks do affect the

geography of demand

• interplay of social (information exchange) and individual (inertia) forces

generate rich dynamics for the single goods on the market

• this kind off behavior generates the clustering in demand: some geographic

neighborhoods collectively prefer one good over another, while other neighborhoods do exactly the opposite.

• depending on the characteristics of the society, the clustering pattern can be

short-run or long-run.

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