The Imrei Noam wrote that the question is not about the value of the אתרוג to the woman because woman are exempt from מצוות עשה שהזמן גרמא. What he meant was that if she was personally obligated she would be מקודשת with the value of the אתרוג to her as a mitzva object and we wouldn't need to measure its value on the free market.
The problem is that the Raavad [commentary to Toras Kohanim] says that women have every right to perform מצוות עשה שהזמן גרמא if they so desire and the Torah was given to women as it was to men. Men are OBLIGATED in all the mitzvos and women have the option of keeping all the mitzvos that are time bound to the extent that even if an איסור is involved we would employ the rule of עשה דוחה לא תעשה and thus allow her to wear כלאיים בציצית. If so, the psak of the זקן ממרא DOES relate to a חיוב כרת if he was מקדש her with an אתרוג that she wanted to use in order to fulfill a mitzva.
What the Imrei Noam must have meant was that there is no הנאת מצוה because she is not obligated but rather he is referring to "משתרשי" - since she wants to fulfill the mitzva of אתרוג and doing so would have cost her money, now she benefits because she doesn't have to buy an אתרוג [as the Rashba writes in Kiddushin 8b that a woman can be married with הנאת משתרשי]. Now, just like Tosfos [חולין קל"א. ד"ה שאני] says that someone who eats מתנות כהונה can't be obligated because of משתרשי as he can claim that he could have fasted, so too the woman could have said that she could have decided not to fulfill the mitzva and thereby not have to spend the money. So it is not considered הנאה.
The problem is that since women took upon themselves this mitzva as an obligation, she can't make such a claim.
Also, the Imrei Noam added a reason that she is not married with the value of this אתרוג to her - namely מצוות לאו ליהנות ניתנו [from now on "מלל"נ"], so the fact that she has the benefit of being able to fulfill a mitzva with this אתרוג is not considered הנאה and she is thus not מקודשת.
However that is not so simple. Said the Ateres Yeshua [son of the Imrei Noam סי' ד]: The rule of מלל"נ was only said about a מצוה חיובית - an obligatory mitzva that is incumbent אקרקפתא דגברא - literally "on the skull of a person". But about a מצוה קיומית, non-obligatory mitzva, we can't say מלל"נ. He derives this from Rashi [ר"ה כ"ח. ד"ה לאו] who says that the סברא of מלל"נ is that mitzvos were given as a YOKE on their necks and not for pleasure. Said the Ateres Yeshua that this doesn't apply to non-obligatory mitzvos. They are not yokes on their necks and ARE for pleasure.
So we can extend this idea further and say that מלל"נ doesn't apply to מצוות עשה שהזמן גרמא since women aren't obligated.
So now we are, like, TOTALLY stuck. Both reasons given by the Imrei Noam to explain why a woman can't be married with an אתרוג worth less than a פרוטה since it doesn't have "mitzva value" to her [and only if it has market value] wouldn't apply. You can't say that she is not obligated because women took upon themselves the obligation. You also can't say מלל"נ because that rule only applies to obligatory mitzvos but when it comes to non-obligatory mitzvos we say מצוות ליהנות ניתנו and this mitzva has הנאה value for her.
So we need a GOOD LAWYER for the Imrei Noam....
[מתורת מו"ר שליט"א]
The problem is that since women took upon themselves this mitzva as an obligation, she can't make such a claim.
Also, the Imrei Noam added a reason that she is not married with the value of this אתרוג to her - namely מצוות לאו ליהנות ניתנו [from now on "מלל"נ"], so the fact that she has the benefit of being able to fulfill a mitzva with this אתרוג is not considered הנאה and she is thus not מקודשת.
However that is not so simple. Said the Ateres Yeshua [son of the Imrei Noam סי' ד]: The rule of מלל"נ was only said about a מצוה חיובית - an obligatory mitzva that is incumbent אקרקפתא דגברא - literally "on the skull of a person". But about a מצוה קיומית, non-obligatory mitzva, we can't say מלל"נ. He derives this from Rashi [ר"ה כ"ח. ד"ה לאו] who says that the סברא of מלל"נ is that mitzvos were given as a YOKE on their necks and not for pleasure. Said the Ateres Yeshua that this doesn't apply to non-obligatory mitzvos. They are not yokes on their necks and ARE for pleasure.
So we can extend this idea further and say that מלל"נ doesn't apply to מצוות עשה שהזמן גרמא since women aren't obligated.
So now we are, like, TOTALLY stuck. Both reasons given by the Imrei Noam to explain why a woman can't be married with an אתרוג worth less than a פרוטה since it doesn't have "mitzva value" to her [and only if it has market value] wouldn't apply. You can't say that she is not obligated because women took upon themselves the obligation. You also can't say מלל"נ because that rule only applies to obligatory mitzvos but when it comes to non-obligatory mitzvos we say מצוות ליהנות ניתנו and this mitzva has הנאה value for her.
So we need a GOOD LAWYER for the Imrei Noam....
[מתורת מו"ר שליט"א]
