It might be more economical to ride a motorcycle (cheaper vehicle, cheaper gas, cheaper tolls, cheaper insurance). If all maintenance is done yourself, it can definitely be a somewhat cheaper option for commute.
However, motorcycle doesn't replace a car, and car doesn't provide the same experience as riding a motorcycle.
I'm not convinced on that. The vehicle may be cheaper, but there are plenty of cars that get motorcycle level fuel economy these days, so I think the fuel savings aren't nearly as much as people think they are. Cheaper tolls might apply, that just depends on where you live. We've got a number of toll roads around here, and some of them are free for motorcycles to use, but there are some that charge for motorcycles.
As for maintenance, I'm not convinced on that one either. First, in my experience the cost of taking the vehicle somewhere to have maintenance done if you can't do it yourself is significantly higher for motorcycles. There is far less competition in that market, so the labor rate is much higher. I get oil changes on my car for $35 at the dealership and could probably get that down to $25 if I searched around. I got stupid and took a motorcycle into a shop for an oil change one time and it cost me nearly $200 for that lesson.
Second, from a parts standpoint, although the bike has less oil in it, resulting in cheaper oil changes, I find the biggest maintenance cost to be keeping tires on a vehicle. I can get tires for my car at around $100 each, including mounting and balancing; I just roll into the dealership and roll back out an hour or so later with new tires. By contrast, motorcycle tires seem to run around $100 each for the cheaper tires, and that's just the tire. If I want to save money, I have to take the tire off and take it to the shop to have them swap the rubber, which will cost me around $25 per tire. I'm now at around $250 for motorcycle tires vs $400 for car tires. Seems like I saved a lot of money, right? Wait just a minute. Motorcycle tires seem to get maybe about 5-6k miles. If you drive really conservatively and get hard tires that will corner like crud, you might get 10k out of them. By contrast, I can get 30k miles out of a set of car tires while driving like Dale Jr and I know people who regularly get 60k miles out of a set of tires. Let's do the math on the tires and equal them out:
Motorcycle - 10,000 miles for $250
Car - 60,000 miles for $400
Motorcycle - 60,000 miles for $1,500
That's just tires. I haven't gotten into the cost or replacing clutches on the motorcycle vs the fact that my car's CVT has 160k on it and hasn't even needed any maintenance done to it.
Oh yeah, one more thing is insurance. Yes, motorcycles are cheaper, but usually, people aren't getting what they need. One reason they're far cheaper is that insurance companies list them as recreational vehicles and expect that they will only be operated on the weekends for a few months out of the year. If you're going to use your motorcycle for regular transportation, you should tell your insurance company that and expect that your rate will immediately double. If you don't, you'll most likely be fine, but if an adjuster figures out that you've been using it for primary transportation and not as a recreational vehicle, they could nullify your policy and refuse a claim when you need it most. Granted, even at double the cost, my motorcycle insurance would still be hundreds less than my car, but that is something to consider.
Sorry but from the numbers I've run, cars are far more economical than people think they are and motorcycles cost a lot more than people seem to believe. Your mileage may vary, of course, but I wouldn't encourage anyone to go for a motorcycle just to save money. They are cool though, and that is worth something.