Both of my elderly in laws just moved in with us. Now that they don't have expenses of a home what is a fair rent to offset expenses?

How many people now live in the house?
If it is you, your husband and both in laws I would say 1/2 of the total expenses. This includes mortgage, gas, electric, garbage service, water, food, cable.....

And make sure you get t documented, legally. A renter or caregiver agreement so that Medicaid benefits are not at risk.

Make an appointment with an elder law attorney. Do you have their POA's and other documents.

It would have been a good idea to take care of all this before they moved in.

And keep receipts/statements/invoices for any expenses you share.

IMHO, there are two ways to go.

1.  Per person share of all expenses.   This is more akin to a roommate agreement, not a rental.  You do not have to include amounts in taxable income.   

2.   Estimate of Fair Market Value.  If you do not have a mortgage anymore, this may be more fair.   You do  have to include amounts in taxable income, but get to depreciate a portion of the house.

Agree with pp, this should have been discussed ahead of time, but you should get a written agreement, signed by all parties ASAP.

You are so wise to ask your in-laws to contribute their fair share of living expenses. Not doing so could jeopardize their current social security benefits.
 
The Social Security Administration places recipients into one of four Living Arrangement Categories—A, B, C, or D. While your in-laws are effectively in Category B, it is important for them to pay a pro-rata share of the household food and shelter. Their benefits could be reduced if they don't.

Here is nice article for you: https://www.ssa.gov/ssi/text-living-ussi.htm
 
Failing to charge fair value room and board can also jeopardize their potential for future Medicaid benefits should the need ever arise—heaven forbid. An Elder Law attorney in your state can best help you with this.
 
So, what is a “fair share”?
 
·      Determine the fair-market value of room and board. Research what tenants are paying for rent in your demographic area for similar homes as yours. Charge them a reasonable amount after taking into consideration the percentage of square footage they occupy exclusively. Then consider a fair amount for any shared space such as the kitchen and living room. Also, include their fair share of utilities, food, and transportation.
 
·      Afterwards, talk it over with your parents and agree upon a comfortable compromise. Resist any temptation or pressure to either under-charge or over-charge. To protect them, put your agreement in writing.
 
·      Finally, talk with your tax preparer about how the transaction will impact your federal and state tax returns. You may be required to declare the rent as income but may also have deductible expenses in the mix. Keeping good financial records is imperative.
  
Enjoy each others company!