Question

Two street vendors (Vendor 1 and Vendor 2) with mobile carts produce the same good which they sell at the same price. 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 below 18 So, there are X customers in location A, 4 in B, 6 in C, 2 in D, 8 in E and 18 in F. There are 38 X customers total. Customers will make a purchase from whichever vendor is closest to them, and equally close customers will be split evenly between Vendor 1 and Vendor 2. The vendors CAN locate in the same location (so, both could locate in location A) 22. If X- 12, where will Vendor 1 locate in equilibrium? a. A b. B d. D 23. lfX = 12, where will Vendor 2 locate in equilibrium? a. A b. B d. D 24. What is the smallest value of X that would make (A, A) an equilibrium?

Answer 1

22. E

23. E

24. 38

Explanations

Every vendor will want to locate themselves in the middle with equal customers on both sides. This is because if there are more customers on one side, the competitor will set up stall on that side and get more customers.

For example, in this case, if vendor 1 sets up stall in Location A, vendor 2 will set up store in Location B. This will result in vendor 1 getting only 12 customers while Vendor 2 gets 38 customers.

Thus, vendor 1 will set up shop in Location E. This way, he will not be exploited by vendor 2. If vendor 2 sets up shop in location D, vendor 1 will get 26 customers. If vendor 2 sets up location in F, vendor 1 will get 32 customers. And if Vendor 2 also sets up shop in Location E, both vendors will get 25 customers each.

Thus Vendor 1 will set up shop in Location E. By the same logic, Vendor 2 will also set up shop in Location E.

Suppose (A,A) is the equilibrium. Then there should be no incentive for any vendor to move to a different location. If a vendor moves to Location B, he will acquire all customers from Location B to Location F, i.e, he will have 38 customers. For the vendor not to move to B, the current number of customers should atleast be equal to 38. But the current number of customers for each vendor is equal to half of total customers (38+X)

Then,

0.5 * (38+X) >= 38

=> 0.5X >= 19

=>X >= 38

That is, minimum value of X to ensure (A,A) as equilibrium is 38.