Establishing the presence of market power in food chains has become an increasingly pertinent line of enquiry given the trend towards increasing concentration that has been observed in many parts of the world. This paper presents a theoretical model of price transmission in vertically related markets under imperfect competition. The model delivers a quasi-reduced form representation that is empirically tractable using readily available market data to test for the presence of market power. In particular, we show that the hypothesis of perfect competition can be rejected if shocks to the demand and supply function are significant and correctly signed in price transmission equations. Using a cointegrated vector autoregression, we find empirical results that are consistent with downstream market power in six out of seven food products investigated, supporting both the findings of the UK competition authority's recent investigation in to supermarkets and renewed calls for further scrutiny of supermarket behaviour by the UK's Office of Trading.