An Etymological Dictionary of the German Language/Kost
Kost (1.), f., ‘cost,’ from MidHG. koste kost, f. and m., ‘value, price, expense,’ even in OHG. kosta, f.; borrowed in the OHG. period from MidLat. costus, m., costa, f. (comp. Ital. costo, m., Fr. coût, m., Span. costa, f.; ultimate source Lat. constare, ‘to come to, cost’). From Rom. are derived MidE. costen, E. to cost, whence Scand. kosta, ‘to cost.’
Kost (2.), f. (in the 16th cent. also m.), ‘board,’ from MidHG. koste, kost, f., ‘living, food, victuals’; comp. Scand. kostr, m., ‘victuals, provisions.’ In Scand. as in the G. word, the meanings of (1) and (2) overlap; at all events (2) is a later development of (1). We must certainly assume that the Scand. loan-word kostr, ‘expense, victuals,’ was confused with an OTeut. word which would be most closely connected with Goth. kustus, m., ‘trial, proof,’ and gakusts, ‘test’; OIc. kostr, m., ‘choice, condition, circumstances.’ With regard to these nouns see kiesen.