Questions 6-8 rely on the following prompt: Two street vendors (Vendor X and Ven
ID: 1117168 • Letter: Q
Question
Questions 6-8 rely on the following prompt: Two street vendors (Vendor X and Vendor Y) with mobile carts produce a homogenous (identical) good which they sell at identical prices. Customers are located along a linear boardwalk with six locations Location A through Location F), with a different number of customers in each location, as pictured: C D 10 12 So, there are 2 customers in location A, 4 in B, 6 in C, etc. There are 42 customers total. Customers will make a purchase from whichever vendor is closest to them, and equally close customers will be split evenly between Vendor X and Vendor Y. The vendors CAN locate in the same location (so, both could locate in location A).Explanation / Answer
6.) For Vendor's X and Y to be in Equilibrium, both should have the same number of Customers coming to each of them.
Due to the asymmetry in the way customers are distributed, This scenario is only possible when both the vendor's are located at the same location as then the customers would divide themselves equally amongst the vendors
Hence the answer could be both (D,D) and (E,E), in which case both the vendor's would get 21 customers each .i.e. 42/2 = 21
7.) For (D,E) to be an equilibrium both vendor's should get equal customers. Vendor X is at D, Vendor Y is at E
Customers coming to Vendor X = 2 + 4 + 6 + 8 + x (Sum of customers in locations A, B, C, D due to proximity to location D)
Customers coming to Vendor y = 10 + 12 (Sum of customers in locations E, F due to proximity to location E)
These two numbers should be equal
Hence,
20 + x = 22, x = 2
8.) All three Vendor's in this new case cannot be at the same location because of the fact the in order to get equal number of customers the customers at each location should be in multiples of 3 which is clearly not the case in the above mentioned scenario, option (c) and (d) eliminated on this basis
if the 3 vendors locate themselves at C, D, E respectively, Vendor at E would have an undue advantage as he would be able to cater to 38 customers (location D and E) out of the total 54, which is clearly not an equilibrium, hence option (b) eliminated
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