C W E m n P r s Trade would be profitable only if the price ratios are not equal; that is, using the SNDG ratios, only if m/n > r/s, or if m/n < r/s; or using the DNSG ratios, only if m/r > n/s, or if m/r < n/s.
If the SNDG method is chosen, trading profits occur irrespective of productive efficiency and, as will be argued below, irrespective of whether the trade is free or is protected by tariffs.
A possible preference for the SNDG ratios might also be implicit in Ricardo's Note 259 in his Notes on Malthus, as quoted above:
His Note 259 thus seems to have been comparing SNDG ratios rather than DNSG ratios; that is, comparing the labour cost of cloth in England with the labour cost of wine in England (where the labour units for cloth and wine are comparable), and comparing the labour cost of cloth in Portugal with the labour cost of wine in Portugal (where the labour units for cloth and wine are comparable); rather than comparing the labour cost of cloth in England with the labour cost of wine in Portugal (given that the labour units of the two countries are not comparable), and comparing the labour cost of wine in England with the labour cost of wine in Portugal (for the same reason).
If Ricardo did in fact regard the SNDG ratios as preferable to the DNSG ratios, then it will be argued below that the LCA of Ricardo does not provide a justification for a policy of international specialisation in production.
The custom of discussing the LCA in terms of trade between countries--a custom fostered by Ricardo--encourages policy recommendations for territorial specialisation, especially when the argument is based on DNSG ratios instead of SNDG ratios.