Hotelling's law

Hotelling's law is a theorem in microeconomics. It states that acting rationally producers are trying to make their products as similar as possible in comparison to their competitors. Hotelling's law is also referred to as the " principle of minimum differentiation " '. It was mentioned as the first of Harold Hotelling in 1929 in his essay in the Economic Journal "Stability in Competition".

The opposite phenomenon is called (vertical ) product differentiation.

Example

The ice cream man - on - beach - problem describes Hotelling's law based on the location factor and illustrates possible strategies of two suppliers in the search for the optimum location. In a market economy with competition, it turns out that the end result would be that both ice cream vendors closer together as close as possible.

A beach of 10 m width and 100 m length is bounded on the east and west by rocks, on the north by the sea and in the south by a promenade. On this beach there are exactly two ice cream vendors, each with a mobile Eisverkaufsstand, but only along the waterfront can be moved, not in the sand. The beach is uniformly filled with bathers. Both ice cream vendors offer the same ice at the same price. Wanted is the optimum position of both ice cream vendor.

Solution in antitrust / vote

The two ice cream vendors would be well positioned if they had large catchment areas equal as possible and so served each guest beach. There are exactly the following solution:

Iceman E1 positioned x meters from the western edge away, Iceman E2 positioned to (100 -x) meters. Both have a 50 m beach as their catchment area. The reason is that all bathers from the catchment area for E1 to E1 have it closer than E2. All bathers from the catchment area for E2 it closer to E2 instead of E1. This works but only if both ice-cream man deny himself and comply with their agreement.

One example is x = 25 taken: E1 is set to 25 m, E2 at 75 m. ( Then the beach guests have seen a total of the shortest paths, but that is irrelevant to the problem. )

Solution in competition

If one assumes that both ice cream vendor who E1 and E2 in collusion and initially located at its optimum position, possibly because they actually relate to each other, competing to play in Iceman E1 following train of thought: " If I do a bit more in direction E2 move, then my catchment area is greater. For then is the way to me for more bathers than before shorter. He will not even remember. ". The next day, E1 is no longer at 25 m, but at 29 m:

On this day, on which E1 is located at 29 m and E2 at 75 m, the center line between them is no longer at 50 m, but at 52 m. This means that the catchment area of E1 no longer 50 m, but 52 m long. The catchment area of E2 is not more than 50 m, but only 48 m long. Accordingly, fewer customers will receive E2.

At least now remembers E2 that it is likely to be important, even a bit to move more in the direction of E1 to its own catchment area (again) to enlarge. So E2 moves the next day in the direction of E1:

On the third day, the center line between E1 and E2 has accordingly moved toward E1. E2 makes more sales than E1. E1 noticed that this is obviously because of the fact that E2 has expanded its stretch of beach. So E1 repositioned to the next day to increase its stretch of beach:

This game works for a few days until the two meet ice cream vendor in the middle. They can not come closer together as very close. So the turf wars cease in this way. The catchment area of the ice cream man is again the same as in the beginning, no one is favored, and there's again a " tie ", this time, however, the Nash equilibrium is reached.

Under the assumption that there is a maximum path length, which are the bathers prepared to travel for their ice cream, however this is so great and the guests are distributed so that, at the assumed above advantages of the decision to move to the center nothing changes, the following consequences:

• For the visitors who all are on the edge of the beach, the road to the selling ice cream is now too far. Although they want to buy an ice cream, they will not buy one if they so much need to walk through the hot sand.
• Both Iceman make any less revenue than before.

Clearly, the situation would be as they had been at the beginning, optimally, both for the ice cream man and for the bathers. But the strategy described the Iceman has all parties except the customer in the middle of the beach, only harm. A similar process describes the Braess paradox.

A similar situation also occurs in the prisoner's dilemma, the main difference is that there are no intermediate values.

Significance of the model and criticism

The model serves to illustrate the question of the optimal location search under market economy conditions. It is often claimed, the ice cream man would in the drift to the right customers lose more on the left than he can win on the right side. Depending on customer behavior, this is not necessarily the case. The New Institutional Economics deals with problems such as this and offers solutions on the introduction of institutions.

Supplement: All down | all up

With reference to the economic welfare, there is the consideration of events in case of changes of relevant factors in the model. Assumption: If descends from multiple suppliers with a provider the price, this can increase his market. As a result, this makes them intrinsically a part of the sales market, which he has shared before the price change to a different provider.

• The supplier with the constant higher price has now recorded a loss of consumer surplus, producer surplus and total welfare - All down.
• The provider with the new price, which is now under the old, can increase its producer surplus, his consumer surplus and the total welfare - All up