Yes, the moon is closer. On average it is 1,000 times closer than mars but you only need about 2.3X the rocket power (DeltaV: Moon: 2,635m/s vs Mars: 6,268m/s ) to get there compared to the moon.
But they are both far enough away that is doesn't really matter.
A colony in either place cannot rely on outside assistance to come and help them.
Right. So the trip to set up shop on the moon would be a little less than half as expensive as the one to set up shop on Mars. Since they're both far enough away to be necessarily independent, I just assumed the closer cheaper one.
Not really. The extra thrust involved would be a rounding error in the total costs.
If I need a buy car to drive to the shops to get food, the extra added cost in fuel if the shop is 10 km away vs 30 km away is nothing compared to the cost of the car.
It's nothing at all like that. The moon is 384 megameters away. Mars is 54000 to 150000 megameters away, depending on orbits.
So it would be like 384 meters vs 54-150 kilometers.
Escaping the gravity well on the moon is also much cheaper.
[In terms of infrastructure and accessibility, it’s really no contest. The Moon is closer, always has a view of Earth, can exchange signals and deliverables hundreds of times more quickly than can be exchanged between Earth and Mars, and is easier to land on and take off from. Certain infrastructure could be easily shared between the Earth and the Moon, such as the internet, whereas Mars would likely, due to its remote nature, need its own standalone infrastructure.]