Dear professor Wolff, let's suppose that the only household task is cooking. The husband provides the raw material and the tools necessary for cooking and the wife adds her living labor to transform them into the meal. The total value of the meal equals the embodied labor provided by the husband plus the living labor provided by the wife, so the meal is the common property of the husband and wife. It is hard to determine the share of each, but on any ground, not all of the meal is for the wife. Given this, I do not think that any major economic exploitation by any party occurs if they consume the meal together. Moreover, if we were to find the exploiter, it would be very hard to find out which party is consuming more than his/her share. Is there anything wrong with my thought? (For those who may read my question; I do not think that traditional family structure is a good thing, I have other reasons to oppose it)
This is a question of how one understands and uses Marx's value theory. First off, no "value" attaches to the homecooked meal because it is not a commodity since it does not pass from producer to consumer via a market exchange. Value is a category Marx applies to commodities alone. Second, you can, of course, compute labor hours - both those embodied in raw materials and tools used up in producing a homecooked meal and those hours of living labor applied by the housewife in the cooking. The final output, the meal, then has the sum of both types of labor hours. Third, the portion of the meal output consumed by the wife is her necessary labor's product, while the portion consumed by the husband is the surplus: the labor hours performed by the wife but appropriated by her husband. Lastly, only if husband and wife together cooked the meal and together decided what portion of their conjoint output would be a surplus (a quantity of output that neither of them consumed) would there be no exploitation in Marx's strict definition of a surplus produced by one person and appropriated by another. In traditional households of the sort you describe the husband does exploit the wife whether or not either of them is conscious of that aspect of their relationship. Let me urge you to read full explanations of all this in (1) R. Wolff and S. Resnick, Contending Economic Theories (MIT Press 2012) and (2) Class Struggle on the Home Front, edited by Graham Cassano (Palgrave 2009).