In this paper, an estimation of a Spatial Covariance Function was proposed for determining the relevant geographic market for a merger. This methodology was applied to a proposed merger between two competing Brazilian supermarket chains. During this application, the shortcomings of the analysis carried out by the Brazilian Antitrust System were initially pointed out, including the geographic dimension of the relevant market, which was found to be separated in each municipality located on the shore of Sao Paulo state. The results, based on the estimated spatial covariance function using price data on 22 products in 43 supermarkets, indicate a single geographic market for all municipalitiesIn this paper, an estimation of a Spatial Covariance Function was proposed for determining the relevant geographic market for a merger. This methodology was applied to a proposed merger between two competing Brazilian supermarket chains. During this application, the shortcomings of the analysis carried out by the Brazilian Antitrust System were initially pointed out, including the geographic dimension of the relevant market, which was found to be separated in each municipality located on the shore of Sao Paulo state. The results, based on the estimated spatial covariance function using price data on 22 products in 43 supermarkets, indicate a single geographic market for all municipalities