mysql group by para devolver el valor mínimo y obtener los datos de fila correspondientes

SELECT Merchant.Product, Merchant.Name, Merchant.Price
FROM a_table AS Merchant
JOIN
(
SELECT Product, MIN(Price) AS MinPrice
FROM a_table
GROUP BY Product
) AS Price
ON Merchant.Product = Price.Product
AND Merchant.Price = Price.MinPrice

Devolverá dos filas si dos comerciantes tienen el mismo precio muy bajo.