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In competition economics, authorities evaluate retail mergers by analyzing specific geographic catchments. If a merger creates a local monopoly, it harms consumers in that specific town.
We define a local market by a Maximum Distance (Dmax), representing how far a consumer is willing to travel.
Competitors located right next door exert massive pressure, while competitors on the edge of the catchment exert very little. We weight each store's volume by its distance ($d$):
To find a specific site's local market share, we take its volume, add the weighted volume of all allied stores in range, and divide it by the total weighted volume of ALL stores in range.
If this share exceeds the regulatory "Safe Harbor" threshold (e.g., 35%), the authorities will likely demand a divestiture remedy.