I think AuntieFlo is right. It also depends on where you want to live. If you plan to live in Panama City or in one of the other popular expat haunts, like Boquete, you can expect to pay quite a bit. If you're willing to go a little more local and live in an area like Las Tablas or Aguadulce, both of which are nice towns (they're just a little more third-world and a lot more boring) you can find a house for rent for somewhere in the $300 per month range.
Electricity is another part of your budget that can be very low if you live like a local. I live in the city and have a large air conditioner that runs close to 24-hours per day. I have a small deep freeze, a ceiling fan in each bedroom, a washer and dryer (dryer is mostly gas) and I pay $300 or so per month. That's a lot. And I hate it. I know a lot of people who pay less than $100. If you're in a one-bedroom apartment/condo or a small house and you plan to use fans most of the time, you should be able to stay below $100 per month. Most Panamanians use gas for cooking and drying their clothes (unless you plan to hang dry your clothes like AuntieFlo). I tried the hang drying, but I found that my clothes always had a funky smell to them after. The dryers and stove can operate on the typical small propane tank you'd use for a gas grill in the U.S. You can swap those gas tanks out for less than $5 and each one will probably last about a month. You can buy larger gas tanks that last about 3 months for like $40.
Like AuntiFlo said, if you plan to eat out a lot, you have to know your budget will increase significantly. Unless you're in one of the small towns like I mentioned before. My wife and I had lunch in Las Tablas for $5.50 total for the two of us. So for about $2.25 each we got a main dish (meat or chicken), a side salad, rice with beans, a small soup, and a juice. You're not going to find lunch for that price in the banking district of Panama City's Marbella. But you will find it in Las Tablas. I had a full pound of shrimp with fried plantains near the beach in Aguadulce for less than $10. If you like pastries and cheap snacks like the meat filled empanadas, you can grab a bite to eat at many of the fondas or streetside vendors for about fifty cents a pop. So eating can be very cheap if you don't mind eating like a local. Also, like AuntieFlo said, most expats love to drink. If you drink local beer you'll only pay like 49 cents per can. That's a 12-pack of beer for $6. Panama's Ron Abuelo is much cheaper than paying for Captain Morgan.
In most places you'll save a lot of money not owning a car. In fact, in many of the towns in the interior, I'd recommend you ditch your high-maintenance vehicle. You can catch a bus from places like Las Tablas to Panama City's Albrook Mall (which has a supermarket, restaurants, major department stores, a huge movie theater, and even a bowling alley) for less than $10 each way. It would cost a heck of a lot more than that in gas to drive back and forth. You can take a taxi from one place to any other place in town (in most of Panama's interior towns) for about $2. I have 4 kids so I'd definitely need a car (for the amount of groceries I buy alone) but if I lived outside of Panama City, and didn't have kids, there's no way I'd own a car. Inside the city you're better off having one, unless you can afford to live in the high-rent district of Marbella/Bella Vista, where you can walk to most places.
Hmm, what else...groceries are quite affordable here if you can learn to buy Panamanian brands. The Americanized supermarkets like Riba Smith will have most imported brands that you're used to, but you're going to pay a lot more for them here than you would in the States. A 12-pack of Mountain Dew, for example, will cost about $8. You'd pay half that in the states. Milk is not cheap here though, even the Panamanian brands. A gallon of Panamanian brand milk is $4.49. I just bought one tonight.
I hope I've helped a little bit. I guess what I'm trying to say in all this is you can still live here on a shoestring budget, if you're willing to go a lot more local than most expats want to go. Just to give you an idea of rents, you can expect to pay at least $1,500 in rent in Panama's hip and trendy old town of Casco Viejo, close to $1,700/$1,800 in the Marbella (Panama City), $500 in the beach town of Pedasi, $300 in Las Tablas, probably close to $1,000 in the mountain town of El Valle de Anton, probably close to $800 (read AuntieFlo's post) for Boquete. You can always find cheaper or a lot more expensive though depending on what amenities you need.
I blog about a lot of the nuts & bolts of living in Panama in my blog at www.thestayathomegringo.blogspot.com. Check it out. Maybe you'll find some info there that can help. I just wrote about how affordable a trip to the movies can be here.
Chris