mrg = F1.merge(F2, on=['k1', 'k2'])
mrg['r1'] = mrg.filter(like='r1').prod(1)
mrg['r2'] = mrg.filter(like='r2').prod(1)
drops = ['r1_x', 'r1_y', 'r2_x', 'r2_y']
mrg.drop(drops, axis=1)
How to multiply pandas dataframes and preserve row keys