We'll cover 0-3* because after that, it's not hard to see that buying unbound gear is way more expensive than crafting.
Auction house and energy prices as of October 4, 2011
Assumptions:
1. Time is ignored. Assume player has unlimited time.
1a. To make #1 not very complicated, the cost savings of using Mist Energy instead of CE is ignored. All costs listed will be assumed as CE.
2. Boss token items are ignored... for now. Which means no freebies, and ALSO no buying of Pulsars or Sealed Swords.
3. Cost of 100 CE is pegged at 6,000cr. (60cr/CE)
4. Cost of materials is ignored.
5. 2-star gear: trying to go as fast to Tier 2 as possible, so only 1 weapon will be upgraded.
6. 3-star gear: 2 weapons, armor set and shield will be upgraded.
Using the auction house: 2* (skipping 1*)
Brandish or Calibur (1,800 cr)
Cheapest 2* armors and shields available (average of 2,000cr each)
Total: 7,800 cr (without upgrading second weapon)
...About 4 Snarbo runs. Meaning posible to use tokens for a shield or sword to save even more money! Tier 2 in 2 days or less... it's possible.
Through crafting 2* (again, skipping 1*)
Recipes: 1000cr x4
Energy used in crafting: 50CE x4
Crowns used in crafting: 400cr x4
Total: 5600 cr + 200 CE = 17,600 cr (!)
Note 1: Mist Energy can be used for crafting. Save up to 200CE or 12,000cr this way, making total cost only 5,600cr and 2,200cr less than buying.
Note 2: You'd rather run the clockworks with your Mist Energy right?
Verdict: Don't end up on the streets begging, buy !@#$ from the Auction House.
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Using the auction house: 3*
Average weapons, armor and shield: 16,000 x 5
Total: 80,000cr
Note: Some 3* items sell for less than 16k sometimes. Shop around to find a better deal.
Through crafting: 2* to 3*
Recipes: 4000cr x5
Energy used in crafting: 200 CE x5
Crowns used in crafting: 1000cr x5
Total: 25,000cr + 1000 CE... convert that CE to cr, that's 60,000. = 85,000cr
Note 1: Mist Energy can be used for crafting. Save up to 500CE or 30,000cr this way, making total cost only 55,000cr.
Note 2: A daily player can't afford to wait like this, however. People starting out would most likely play using their Mist over waiting.
Verdict: Buying can be better by at least 5,000cr.
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EDIT:
(October 7, 2011) Added the non-trivial alchemy crown costs which I have mistakenly omitted. Changed layout.
You should reall y factor in the material cost, because you'll need a lot more runs to obtain them or make the money to buy them.
Therefore, up to 3* it's cheaper to buy from the AH. Period.
And, by the way, since I've been crafting Brandishes for about a week now looking for a specific UV, I can assure you that the price is most of the times closer to, or lower then 1500cr, not 1800. The same with the Wolver Coat, thus reducing significantly the buy-out cost.