In “Women on the Market”, written in 1978, Irigaray attempts to meld ideas from Karl Marx with feminism. The result is not good. In fact, it's terrible. She gets some of Marx's critique correct, but a lot of it is completely wrong. The connection between her interpretation and how it relates to women is almost entirely nonsensical. Her essay is almost devoid of substance, with an utterly conservative, pro-capitalist conclusion.
Irigaray's first sentence is:
The society we know, our own culture, is based upon the exchange of women.A contemporary capitalist society is generally not based on the exchange of women. Slavery, especially sex slavery of women and girls, is a very important component of modern capitalist society. These women, millions around the world, are living as slaves. They are exchanged in the market. However, billions of women aren't slaves - they aren't exchanged as commodities.
It's true that women exchange their ability to work (labour-power) for money. They are generally paid atrociously for their time. Their wage is frequently below its value (meaning they must rely on other sources of income to survive). It's true that women have to do large amounts of unpaid work in a house. This is a horrible, never ending grind that destroys women's physical and mental health. But neither of those situations mean that women themselves are being exchanged. Sure, there is bride price for marriage, but this is not enough to go on.
Therefore, Irigaray's first sentence is false. Not a great start.
Later, she says:
 In this new matrix of History, in which man begets man as his own likeness,  wives, daughters, and sisters have value only in that they serve as the possibility of, and potential benefit in, relations among men.I broke this sentence into two parts.  I entirely do not understand this. What could "man begets man as his own likeness" possibly mean? Irigaray gives no explanation.  This part of the sentence is correct. Women are forced, by men, into roles of subservience. They are forced to find a life as sex worker or unpaid house-worker. If they go off by themselves they're attacked as being too masculine, or worse, lesbian. Women have been, and still are, persecuted for not filling their gender role - they are violently forced to do so.
In other words, all the social regimes of “History” are based upon the exploitation of one “class” of producers, namely, women. Whose reproductive use value (reproductive of children and of the labor force) and whose constitution as exchange value underwrite the symbolic order as such, without any compensation in kind going to them for that “work.”The first sentence is correct. Since the beginning of class society, women have had the worst of it. The second sentence throws in some Marxist terms, use-value and exchange-value. It's ambiguous, but it appears that Irigaray is suggesting that exchange-value exists in all class societies. It doesn't. Exchange-value only exists in commodity economies. Furthermore, exchange-value is compensation for work! In a capitalist economy, if you don't receive your exchange-value for your labour-power, you die.
Commodities among themselves are thus not equal, nor alike, nor different. They only become so when they are compared by and for man.If a tree fell in forest and no-one was around, would it make a sound? If there are no humans around to turn things and actions into commodities, they aren't commodities. Commodities can't be "among themselves." Things and actions (products and services), regardless of whether they are commodities or not, are never equal nor alike.
the commodity obviously cannot exist alone, but there is no such thing as a commodity, either, so long as there are not at least two men to make an exchange. In order for a product - a woman? - to have value, two men, at least, have to invest (in her.)This appears to contradict the above, though at least Irigaray is correct this time. But she's really not saying anything new. Yes, you need (at least) two men (or women) for an exchange of commodities.
Why does Irigaray keep trying to reduce women to mere commodities?! Commodities are empty vessels with no power to change the world. Irigaray is espousing an anti-feminism. Women can, and have always, resisted; as commodities (slaves), as serfs, as waged workers, as unpaid servants of fathers and husbands. Admittedly, women's role over the past hundred years has often come extremely close to slavery, in practical terms it was/is, but women don't generally take the form of commodities on the market - except when they literally are slaves like in the illegal sex industry and mail order brides, etc. If Irigaray was making an analogous argument, I wouldn't mind. But she isn't. She is literally saying that women are exchanged as commodities. That's just not true.
The price of the articles, in fact, no longer comes from their natural form, from their bodies, their language, but from the fact that they mirror the need/desire for exchanges among men.The price of articles have never come from their natural form, they have always come from their value form.
The general equivalent of a commodity no longer functions as a commodity itself.Irigaray throws in some Marxist jargon with no definition of her terms. That's fine for Marxists, no good for everyone else. The general equivalent is (basically) money. She's also completely wrong in her conclusion. The general equivalent is a commodity and it always will be. If it weren't a commodity, it couldn't be used in exchange. If it ever ceased to be a commodity, the entire capitalist economy would immediately collapse because there would be no equivalent to exchange for the relative.
We must emphasize also that the general equivalent, since it is no longer a commodity, is no longer useful. The standard as such is exempt from use.Therefore, money is no longer useful? Okay...
This means that mothers, reproductive instruments marked with the name of the father and enclosed in his house, must be private property, excluded from exchange.
Once deflowered, woman is relegated to the status of use value, to her entrapment in private property; she is removed from exchange among men.Is Irigaray suggesting that private property is excluded from exchange? It appears so. Either way, these sentences are nonsensical.
Mother, virgin, prostitute: these are the social roles imposed on women.Agreed. But what about violence against women? What about the culture of rape, domestic abuse, honor killings and slut shaming? What about old women being ignored in society? Irigaray only scrapes the surface of women's oppression and exploitation.
For, without the exploitation of women, what would become of the social order? What modifications would it undergo if women left behind their condition as commodities - subject to being produced, consumed, valorized, circulated, and so on, by men alone - and took part in elaborating and carrying out exchanges?This paragraph, right at the end of the essay, is where Irigaray reveals her true colours. It's only here that her utterly conservative approach to political economy is exposed. What would happen if women "took part in elaborating and carrying out exchanges?" Exactly what was already happening in 1978 and what is still happening today (2013). Women were and are an integral part of the economy. Women are slaves, unpaid labourers and wage slaves in capitalist society. They are not and never were mere commodities exchanged among men. They have no need to become full citizens of exploitation because they are that already.
Instead of joining the market (that they've already joined), women need to: 1) refuse their gender role to end their oppression and 2) refuse to be workers to end their exploitation. Both refusals are interconnected. To fight against one is to threaten the other. But they're not the same thing and women need to deal with both issues. Men, on the other hand, only really need to deal with their exploitation as workers. Men clearly materially benefit from women's gender role. If men want all humans to be free, they will have to completely change their relationship with women and in doing so, give up a substantial component of what it is to be a man. In effect, they'll have to stop being men. They're not going to do this willingly.
By horribly mangling Marxism and feminism, Irigaray's essay, if it reflects the rest of her work, suggests that she is a poor critic of patriarchal society and doesn't understand the critique of capitalism, let alone have any sort of anti-capitalist politics.