2 Product proliferation Bank-matic is planning to enter the ATM business in a pa
ID: 363578 • Letter: 2
Question
2 Product proliferation Bank-matic is planning to enter the ATM business in a particulartown Suppose that the town has one main street and Bank-matic must decide how many ATMs to locate along this street. Let's represent the street by the 0,1] interval. Customers are uniformly distributed along the interval, and they are willing to travel at most 0.25 in order to use an ATM. Suppose that any firm that serves a proportion p of the customers gets a profit of p. In addition, placing an ATM at any location along the 10.11 line costs 0.20. For example, if Bank-matic decides to place two ATMs, one at= 0 and another at x = 1, then it serves a proportion 0.25 0.25 0.50 of customers, making a profit of 0.50 but paying an entry cost of 2x 0.20 0.40. Net profits are then 0.10 (a) Where will Bank-matic decide to place its ATMs? How many ATMs will be placed, and what are the net profits? Things get a little bit more difficult now that a close competitor, ReadyCash, comes to town. ReadyCash has the same cost of 0.20 per cach ATM it decides to locate, and customers don't really care which ATM they use: they always choose to go to the ATM that is nearest to them (and, as before, decide not to use an ATM if there is no ATM witin 0.25 of where they live). Bank-matic has been studying the market for a longer time, and is therefore in a position to choose the location(s) of its ATMs before ReadyCash gets to make this choice (b) Suppose that Bank-matic made the decision you suggested in (a). Where would ReadyCash decide to locate, after seeing Bank-matic's decision? What are the net profits for each firm? (c) If Bank-matic can anticipate that ReadyCash will come to town after its location decision, it is likely that Bank-matic will want to do something different than (). Where do you recommend Bank-matic to locate in this case? What will happen when ReadyCash comes to town? What will be the profits of both firms?Explanation / Answer
a) ATM can be place in an interval of [0,1] which is uniformly distributed its means probability of choosing would be same at every point. Customer is ready to move for 0.25 and can move left or right, in this way, customer movable area would increase to 0.5.
For maximum profit, Bank-matic would place 2 ATMs, one at 0.25 and other at 0.75 to cover the whole area.
Net Profit = 1 -.40 = 0.60
2) After installation of Bank-matic ATM, the only places left for is at 0, 0.5 and 1. But, at 0 and 1 Readycash would be making loss of 0.075 as on these places it would only able to cover the proportion of 0.125. Now, the only left for Readycash is at 0.5 where it can cover the total proportion of 0.25. Hence, Readycash would install only one ATM at 0.5.
Net Profit for Readycash = 0.25 - 0.2 = 0.05
Net profit for Bank-matic = 0.75 - 0.4 = 0.35
c) In this case, Bank-matic should install its ATMs at 0, 0.5, and 1. In this way bank can cover the entire Interval and there will be no place for Readycash.
In this situation, Readycash won't be installing its ATMs.
Net profit of Readycash = 0
Net profit of Bank-matic = 1 - 0.6 = 0.4
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