Quality Competition with Stochastic Demand and Costly Search

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Quality Competition with Stochastic Demand and
Costly Search

• Theory and Evidence from the Video Rental Market

Amanda King John King School of Economic
Development Georgia Southern University
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Characteristics of Video Rental Market

• Uncertain demand for product
• Consumers may search alternate stores
• Imperfect substitutes are available
• Consumers tend to shop near home
• Prices are rigid and vary little between stores
• Similar to produce markets, clothing markets,
  furniture, etc.

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How do firms compete in this environment?

• Firms compete in quality or service rates
• Carlton (1978) showed that firms will balance the
  risk of not being able to serve a customer
  against the cost of holding excess inventory
• Price will exceed marginal cost and customers
  face a positive probability of being rationed

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The Model

• Two firms / regions i, j
• Potential customers qi, qj
• Percentage of customers who are active ai , aj
• Pdf from which as are drawn f(x) with support
  0,1
• Firm capacities of preferred good ki , kj
• Marginal cost of capacity c
• Firm capacities of imperfect substitute are
  unlimited and costless
• Fixed price for all output p
• Customer premium for preferred good v
• Probability of search in case of stock-out µi ,
  µj
• Customer search cost d

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How likely is customer to find the new release
upon searching?

• Probability of successful search equals the
  expected number of videos left at store to be
  searched (positive as a condition for our
  equilibrium) divided by the expected number of
  searchers

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Finding the optimal search rate

• Consumers balance the cost and benefits of
  searching the other store
• Rearrange to solve for probability of search

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Characteristics of Consumer Search

• increasing in valuation gap, v
• increasing in rivals capacity
• decreasing in search cost
• decreasing in size of rivals region
• decreasing in size of local region
• increasing in firms own capacity

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Probability of search as a function of capacities
when v1, d0.75, and a is uniformly distributed
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Firm Behavior

• Total Rentals From Regional Consumers
• If they dont stock out
• If they stock out
• Or

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Firm Behavior

• Rentals to Non-Regional Consumers if the Rival
  Firm Stocks Out
• Total Rentals are thus

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Total Rentals as a function of capacities for
given parameters
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Profit Maximization

• Firms Profit
• First Order Condition
• Where

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Conflicting Marginal Effects of Capacity on
Rentals

• One Regional Consumer Doesnt Search Anymore
• Other Regional Consumers are More Likely To
  Search
• Non-Regional Customers Search More

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Conflicting Marginal Effects of Capacity on
Rentals

• The overall effect can be shown to be positive at
  least for the uniform distribution and is likely
  to be so for others.

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Profit as a function of capacities for given
parameters
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Nash Equilibrium exists at kikj333
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Result to be Tested

• Assuming concavity of profits, this implies that
  capacity will decrease with search costs.
• We test this result for video stores using
  distance between stores as a measure of search
  costs.

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The Data Source

• Of 21 video stores listed in Savannah yellow
  pages
• 8 no longer in business
• 2 dont offer new releases
• 11 stores offer new release rentals
• 4 Blockbuster
• 2 Hollywood Video
• 2 Movie Gallery
• 3 Independent (Videorama, Video Heat, Video Bob)

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The Data

• Collected seven times over four weeks
• Availability of four top new releases
• 12 titles used in all
• Time dimension irrelevant since we always
  considered the then-current top movies
• Distance between stores measured in time and
  distance
• Dollar amount of nation-wide rentals for week of
  observation
• Time of day and location of observation

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Title-Specific Availability Effects

• One outlet had 97 copies of The Last Samurai,
  while the highest observed for Miracle was 9.
• Rather than using absolute availability, we used
  the difference between observed availability and
  the average availability for that particular
  title.

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Availability by Movie

• Movie
• Big Fish
• Calendar Girls
• Kill Bill
• Last Samurai
• Lord of the Rings Return of the King
• Love Actually
• Master and Commander
• Miracle
• Paycheck
• Scary Movie 3
• Stuck on You
• Welcome to Mooseport

• Mean Standard Deviation
• 8.45 7.12
• 3.33 4.55
• 12.09 13.89
• 18.55 23.09
• 11.36 11.35
• 10.00 9.52
• 9.18 10.68
• 2.27 2.97
• 14.09 28.01
• 7.45 13.36
• 13.68 19.72
• 22.52 26.09

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Availability by Firm

• Firm
• Blockbuster
• Hollywood Video
• Movie Gallery
• Video Bobs
• Video Heat
• Videorama

• Mean Standard Deviation
• 10.24 11.30
• 22.52 26.09
• 7.48 10.82
• 1.11 0.99
• 1.29 1.30
• 7.39 4.43

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Conclusions

• The video rental industry competes in
  availability on the local level.
• Consumer search is less likely when imperfect
  substitutes exist (search is increasing in the
  valuation gap)
• Higher capacities increase the likelihood that a
  customer searches upon a stock-out.
• Weak assumptions ensure that rentals increase in
  capacity.
• Search becomes less likely as the cost of
  searching increases.