The Drunken Lizard Pub

It seems that arrows cost 2 gp each, and they are consumed with every shot.

Am i missing something or does this make archery economically impossible for a beginning character?

Archery is expensive at the start. Try to avoid attacking things until you can get the focus shot feat. Concentrate on abilities like dexterity and concentration that improve your chance of hitting.

The other thing is get some mercantile to reduce your purchase cost.

Depending how you set up your character*, no, it's not impossible. But it is expensive.

*Mercantile skill investment will help lower prices of other items you need, thus freeing up more cash for arrows. As well, you'll get better prices for items you sell, thus gaining more cash for arrows. Also, you can invest in Foraging and sell the reagents you gather after resting to get yourself a steady flow of income. Just a couple ideas to make it easier for an archer.

One point in mercantile skill brings the price of plain arrows down to one gold each, which is a little more bearable. If you buy some levels in foraging, money is not a real problem anymore.