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Markets and auctions
Hotelling linear city
Two shops stand at either end of a high street, and buyers live evenly all along it. Both shops sell the same thing, but walking costs a buyer 1 for the whole length of the street.
Each shop sets a price. Every buyer goes to whichever shop is cheaper once the walk is counted. Stock costs the shops nothing.
You are Shop 1
Set its price for each side, or press a button to make that side play its best reply to the other.
What it teaches
The margin a firm can hold is precisely what it costs its marginal buyer to switch, so differentiation is not a by-product of competition but the thing that makes any profit possible at all.
The usual mistakeRemembering only the ice cream sellers converging on the middle of the beach, and concluding the model predicts
minimum differentiation generally, when that result comes from the version where prices are fixed and only location is chosen.
The checkAsk which variable is being chosen. With positions fixed and prices chosen, firms want to be apart. With prices fixed and positions chosen, they pile into the centre. The two halves pull opposite ways.
In the real world
Real world
What a petrol station can charge depends on the next one
The Competition and Markets Authority's road fuel market study found prices higher in local areas with no supermarket site, or where the one supermarket site faces no supermarket competitor, and found local price variation widening as national competition weakened. Motorway services are the limiting case, since leaving the motorway to find a cheaper pump costs most drivers more than the saving. The retailers' inferred objective is to price up to the point where the marginal driver would rather drive on, which is a margin set by geography and not by cost.
Locations are already fixed and what is being chosen is price, with the sustainable margin equal to the marginal driver's switching cost; deciding where to put the forecourt in the first place is the location game, which is a different object.
Fiction: You've Got Mail
The bookshop round the corner
A discount chain opens round the corner from a small children's bookshop selling the same titles to customers spread along the same few streets. Because walking from one to the other costs almost nothing, there is no margin left to defend, and the small shop closes while the chain keeps the trade. The film gives Kathleen expertise and affection instead of a price advantage, which is the one thing that might have stood in for distance.
Both locations are given and only prices are chosen, and the small shop's problem is that the transport cost between the two is tiny, so the markup the model says it could hold is tiny as well.
Next door on the wall
Bertrand competition with differentiated productsDeriving the degree of substitutability from buyers' positions, so the equilibrium markup has a physical meaning rather than being a demand coefficient. Not on the wall yet.
Median voter gamePositions are chosen and prices are absent, which is the exact complement of that object, where prices are chosen and positions are fixed at the two ends; the two halves of Hotelling's model pull opposite ways, one to the centre and one apart. Not on the wall yet.
Sources
- Hotelling, H. (1929). Economic Journal 39(153), 41-57.
- d'Aspremont, C., Gabszewicz, J. J. & Thisse, J.-F. (1979). Econometrica 47(5), 1145-1150.
- Tirole, J. (1988). MIT Press.