This is actually a common misunderstanding. The example of ice-cream vendors on a beach or, in this case, gas stations, are toy examples.
The model is not really about location. It is about product differentiation in SOME dimension. By extension, it is also about the number of market participants with differentiated products.
Distance or location stands for this differentiation of products.
This is typical of econ models. They are not trying to be realistic, but show a certain mechanism.
By the way, the model can be extended with different pricing mechanisms and many actors (for example on a circle, not a line, to show that generally too many firms enter a market than can be supported).
As for your points:
1) Pricing depends on demand and maket configuration. Usually, one would work with what is called the "inverse demand", where the company has basically solved price as a function of the the amount of goods it WANTS to sell, given other market participants.
Note how pricing is implicit in this. While these functions are of course usually assumed to be well behaved, you could do what you want here. So it doesn't miss pricing, it just abstracts from it
In particular, that you can jack up prices depending on location is _explicitly_ in this model.
2) Note how the locations depend on the distribution of demand along the "line". Your intuition depends on this as well. If demand is concentrated somewhere in the middle, you will get a different result...
By the way, think about what would happen if you could differentiate in two dimensions? You'd be on a plane or a circle on which a demand distribution exists... etc.
Comments
This is actually a common misunderstanding. The example of ice-cream vendors on a beach or, in this case, gas stations, are toy examples.
The model is not really about location. It is about product differentiation in SOME dimension. By extension, it is also about the number of market participants with differentiated products. Distance or location stands for this differentiation of products.
This is typical of econ models. They are not trying to be realistic, but show a certain mechanism.
By the way, the model can be extended with different pricing mechanisms and many actors (for example on a circle, not a line, to show that generally too many firms enter a market than can be supported).
As for your points:
1) Pricing depends on demand and maket configuration. Usually, one would work with what is called the "inverse demand", where the company has basically solved price as a function of the the amount of goods it WANTS to sell, given other market participants. Note how pricing is implicit in this. While these functions are of course usually assumed to be well behaved, you could do what you want here. So it doesn't miss pricing, it just abstracts from it
In particular, that you can jack up prices depending on location is _explicitly_ in this model.
2) Note how the locations depend on the distribution of demand along the "line". Your intuition depends on this as well. If demand is concentrated somewhere in the middle, you will get a different result...
By the way, think about what would happen if you could differentiate in two dimensions? You'd be on a plane or a circle on which a demand distribution exists... etc.
That's the idea.