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Quality Competition with Stochastic Demand and Costly Search

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. Characteristics of Video Rental Market. Uncertain demand for product

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Quality Competition with Stochastic Demand and Costly Search

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  1. 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

  2. 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.

  3. 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

  4. The Model • Two firms / regions: i, j • Potential customers: qi, qj • Percentage of customers who are active: αi , αj • Pdf from which α’s 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

  5. 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:

  6. Finding the optimal search rate • Consumers balance the cost and benefits of searching the other store • Rearrange to solve for probability of search:

  7. Characteristics of Consumer Search • increasing in valuation gap, v • increasing in rival’s capacity • decreasing in search cost • decreasing in size of rival’s region • decreasing in size of local region • increasing in firm’s own capacity

  8. Probability of search as a function of capacities when v=1, d=0.75, and α is uniformly distributed:

  9. Firm Behavior • Total Rentals From Regional Consumers • If they don’t stock out: • If they stock out: • Or

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

  11. Total Rentals as a function of capacities for given parameters:

  12. Profit Maximization • Firm’s Profit: • First Order Condition: • Where

  13. Conflicting Marginal Effects of Capacity on Rentals One Regional Consumer Doesn’t Search Anymore Other Regional Consumers are More Likely To Search Non-Regional Customers Search More

  14. 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.

  15. Profit as a function of capacities for given parameters

  16. Nash Equilibrium exists at ki=kj=333

  17. 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.

  18. The Data Source • Of 21 video stores listed in Savannah yellow pages: • 8 no longer in business • 2 don’t offer new releases • 11 stores offer new release rentals • 4 Blockbuster • 2 Hollywood Video • 2 Movie Gallery • 3 Independent (Videorama, Video Heat, Video Bob)

  19. 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

  20. 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.

  21. 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 Availability by Movie

  22. Firm Blockbuster Hollywood Video Movie Gallery Video Bob’s 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 Availability by Firm

  23. 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.

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