As you know, the fee is ridiculously low. I understand giving a discount when you are new and unproven on the site. It doesn't matter what you bring, clients want to see Upwork jobs. Most people will lower their fee initially until they have a few jobs. However, there is an enormous difference between a discount, and dirt cheap.
I'm well aware that everything is relevant, including money. What $60 means in the U.S. is different in all other countries. Upwork is a worldwide platform, using the U.S. dollar. Freelancers need to charge for their skills and capabilities, regardless of their location.
No one should ever give away work, even if they are desperate. It never pays, literally or figuratively. If a client asks for free work, it is against the Terms of Service and should be reported to Upwork.
There aren't any figures on averages. There are jobs for less than a penny to twenty cents per word. The latter is extremely rare. Also, it depends on the type of writing. Academic writing is more expensive than copywriting. You need to set a fee that will not just give you some immediate money, but pay for all of your expenses. Most people have multiple bills for access, subscriptions, connects, etc. and it's important to look at all costs.
Prashant phrased it well. If you start with extremely low fees, you will end up locked into that range. Sometimes, people will receive such little money, they would be better off working locally. Also, charging less than average, says you are desperate. While you may indeed be desperate, you never want the client to know, because they tend to run away.
The client is offering far too little, and they know it. Another issue with dirt cheap clients is problems. The ones who are happy to pay dirt, are not going to turn into good clients after the contract. There are all sorts of variations on scammers, but they target the new and inexperienced. I believe you should not accept the job. By the way, was this an invitation? If so, then I definitely would not do it. It smells of scam.
Only you can decide what to do. People have posted great comments, and are trying to help, but it is your decision. Consider this: if you are desperate to the point of having to take any job available, freelancing is not going to work. You might make a little money, but if you want to support your family into the future, you must present a professional image from the beginning. The truth is, most people never make any money here - but they never make an effort. The ones who earn, usually make some extra money. There are freelancers who make their living here, but they are few and far between. I suggest thinking of typical discounts. 10% or 20% is a discount. If it's 50% or more, it's a definite desperate act, or such an untalented person they know they have to accept dirt cheap jobs.
Read this excellent post by Wes on the Red Flags on Scams. It will help you navigate through the scams on the platform. Good for you to bring your concerns to the community. If you have concerns or questions, please post again.
