The Shulhan Aruch (siman 246) discusses renting utensils and tools used for melacha to a non-Jew. For example, a non-Jew wants to rent a lawn mower or a car from a Jew over Shabbat. Would such a rental constitute a violation of the Ten Commandments, which expressly prohibit work being performed on Shabbat by servants or animals belonging to a Jew. Even though the utensils are rented to the non-Jew, the Jew retains ownership.
The Halacha permits such a rental, because as the Gemara in Shabbat clearly says, according to the opinion of Beit Hillel "Ain anu metzuvim al shevitat kelim," we are not commanded that our utensils desist from working on Shabbat. The Torah prohibited only a Jew along with his servants, household and animals.
Once it has been established that fundamentally, one can rent his utensils to a non-Jew, the question is when they can be rented. Can the rental begin even on Friday, immediately preceding Shabbat or must the rental begin on Wednesday or Thursday. There is a dispute between the Poskim on this issue. Ashkenazim hold like the opinion of the Ran that the rental must begin before Friday. However, Maran holds like the Rambam and the Rif who say that it is even permissible to rent out utensils on a Friday. Although Maran does bring a "Yesh Omrim" (supplementary citation) like the Ran, nevertheless the Halacha is in accordance with the "Stam" (unattributed) opinion.
After citing the "Yesh Omrim", Maran adds a caveat that the rental can only be "B’Havlaa"-(swallowed). That is, the period of the rental must be longer than just the day of Shabbat; the Shabbat should be incorporated and "swallowed" in a longer term. However, many of the poskim, including the Mateh Yehuda, understand that this caveat is only according to the opinion of the "Yesh Omrim" which prohibits renting on Friday. Maran added this restriction at the end of the ruling to indicate that it is only in accordance with this stricter opinion. According to Maran himself, who permits renting on Friday, it is also permitted to rent exclusively for the day of Shabbat. The basis for both lenient rulings is an understanding that rental is Halachically deemed a temporary transfer of ownership. Therefore, the utensil does not technically belong to the Jew on Shabbat, and there is no problem of profiting from Shabbat.
Hacham David rules in accordance with this understanding that Maran permits both leniencies- to rent on Friday and to rent for Shabbat alone. Of course, if it is easy to make a two day contract, all the better.
SUMMARY
It is permitted to rent to a non-Jew on Friday implements for performing Melacha, even for just the day of Shabbat.
