Hotelling's Law

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Hotelling's law is a theorem in microeconomics . It states that rationally acting producers try to make their products as similar as possible to their competitors. Hotelling's law is also known as the "principle of minimal distinction". It was first mentioned by Harold Hotelling in his 1929 article in the Economic Journal "Stability in Competition".

The opposite phenomenon is called (vertical) product differentiation .

example

The ice cream seller on the beach problem describes Hotelling's law based on the location factor and illustrates possible strategies of two providers when searching for the optimal location. In a market economy with competition turns out is that the end result would be that both ice-cream sellers closer together as closely as possible.

Initial situation: Both ice cream vendors are each in the middle of their halves
Action: The left ice cream seller moves to the right
Response: The ice cream seller on the right moves to the left
Final result with competition: Both ice cream vendors sell in the middle of the beach

A beach 10 m wide and 100 m long is bordered by rocks to the east and west, the sea to the north and a promenade to the south. There are exactly two ice cream vendors on this beach, each with a mobile ice cream stand, which can only be moved along the promenade, not in the sand. The beach is evenly filled with bathers. Both ice cream sellers offer the same ice cream for the same price. We are looking for the optimal position for both ice cream vendors.

Solution in case of cartel / vote

The two ice cream vendors would be optimally positioned if they had the same large catchment areas and thus served every beach guest as far as possible. There is exactly the following solution for this:

Ice cream vendor is positioned meters from the western edge, ice cream vendor is positioned meters away . Both have 50 m of beach as their catchment area. That is because all bathers from the catchment area have to be closer to it than to . All bathers from the catchment area have it closer to than to . The whole thing only works if both ice cream sellers agree and keep their agreement.

Take as an example : stands at 25 m, at 75 m. (Then the beach guests have the shortest routes overall, but that does not matter for the problem.)

Solution for competition

Assuming that both ice cream vendors and have agreed and are initially in their optimal position, the ice cream vendors may have the following train of thought , because they are actually in competition with each other : "If I move a little more in the direction of then my catchment area will be larger. Because then the way to me is shorter for more bathers than before. He won't even notice. ” The next day, E1 is no longer at 25 m, but at 29 m:

On this day, when you are at 29 m and at 75 m, the center line between them is no longer 50 m, but 52 m. This means that the catchment area is no longer 50 m, but 52 m long. The catchment area of is no longer 50 m, but only 48 m long. Receives correspondingly fewer customers .

At least now you realize that it is probably important to move a little more in the direction of your own in order to (again) enlarge your own catchment area. So the next day moves towards :

On this third day the center line has moved between and accordingly in the direction . makes more sales than . notes that this is obviously due to the fact that his stretch of beach has increased. So he repositioned himself to enlarge his stretch of beach the following day:

This game runs for a few days until the two ice cream vendors meet in the middle. They can't get any closer than very close together. So the turf wars stop in this way. The catchment area of ​​the two ice cream vendors is again the same as at the beginning, neither has an advantage, there is again a "tie", but this time the Nash equilibrium has been reached.

Provided that there is a maximum distance that the bathers are willing to cover for their ice cream, but that this is so large and the guests are distributed in such a way that the decision to move to the center is based on the above-mentioned advantageousness, If nothing changes, the following consequences arise:

  • For the bathers, who are right at the edge of the beach, the way to the ice cream vendors is now too far. Although they want to buy ice cream, they won't buy one if they have to walk that far through the hot sand to get it.
  • As a result, both ice cream sellers make less sales than before.

Clearly, the situation as it was at the beginning would be Pareto-optimal , both for the ice cream sellers and for the bathers. But the described strategy of the ice cream vendors only harmed everyone except the customers in the middle of the beach. The Braess paradox describes a similar process .

Under the (additional) assumption that the total sales of the salespeople decrease because the customers would have to walk too far at the edge and would rather forego ice cream, a situation similar to the prisoner's dilemma arises from the salesperson's point of view . However, it differs from this model in that the decision variable (location) is continuous and not discrete ("cheat" vs. "cooperate"). If one assumes that the total turnover remains constant, there is no parallel to the prisoner's dilemma, but only a deterioration in the access conditions for customers.

Importance of the model and criticism

The model serves to illustrate the question of the optimal location search under market economy conditions. The objection is often made that if the ice cream seller wandered to the right, he would lose more customers on the left than he can gain on the right. However, depending on customer behavior, this may not necessarily be the case. The New Institutional Economics deals with problems like this and offers solutions on the introduction of institutions .

Addition: All down | All up

With regard to economic welfare, there is also the consideration of events in the event of changes in relevant factors in the model. Assumption: If the price drops with several providers, one provider can enlarge its sales market. The result is that he owns part of the sales market that he shared with another provider before the price change.

  • The provider with the consistently higher price now has a loss of consumer surplus, producer surplus and total welfare - all down.
  • The provider with the new price, which is now below the old one, can increase his producer surplus, his consumer surplus and the overall welfare - all up.

literature

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