Question

I need this question solution: please

1. Consider the variant of the Hotelling ‘location-then-price’ duopoly model (studied in lectures) in which consumers must travel to the location of the firm they choose to purchase from. The cost incurred by a consumer located at x ∈ [0,1] of travelling to location xi of firm i is given by t|x − xi | (t > 0 is the disutility or transport cost per unit of distance). Assume that firms are situated away from each other at x1 = 0 and x2 = 1.
(a) Explain how the formula expressing the firms’ demand as a function of prices is derived. Using a graph, explain how the value of t influences the firms’ incentives to compete on prices.
(b) Justify the following statement: ‘The higher the value of t, the more the firms benefit from having located away from each other’.
(c) Explain how and why the gains of both firms’ from locating away from each other (and their motivation to do so) are different from what we see in the vertical differentiation model.

Answer 1

A duopoly is a form of oligopoly, where only two companies dominate the market. in this given problem the competition is between two hotels they are doing business on the basis of location. Here so the situation point is X1=0 and X2=1 and t is transportation cost of the difference between from one hotel location to another. it is a non-collusive oligopoly.

a) if the price of X1 location is high then the transportation cost along with the cost of the hotel then the customer would like to chose X2. but the cost of the X1 is lower than the customer definitely choose the first location. So here the transportation cost plays a significant role to decide the customer stays in any location along with the price quoted by the hotel.

b) The higher the value of t, the more the firms benefit from having located away from each other. To justify this sentence the argument is, if they are located nearby the customer is having a fair choice to choose any of the hotels which may cost them. so if the location is far away the customer will choose the hotel according to its requirement. he doesn't have a choice over the hotel as the distance and the cost is high. so it is better to choose the available or the near hotel over the distance hotel.

c) When they are away from each other they will earn profit due to the high transportation cost and also the time consumption. when we discuss the vertical differentiation model it presents that it is ambiguously different in quality. so here the situation is different as both the hotel are providing almost the same facility the only difference is the location. so if they will do the business staying away from eachother then they cam make more profit independently.