There are so many variables to the question, as to how much it would cost to install a pool. It really depends on the type, the size, etc. I would thik that as a generalization, somewhere starting around 35,000. The issue of the tax increase is also interesting. From a real estate perspective, having a pool does not really add value to a property. As such, the pool should have no impact on the taxes you pay. From a practical standpoint, your taxes will be increased, once they re-assess following the pool installation. My guess would be that your taxes would go up by 5%, but that is just a guess, and an appraiser might have a better idea.
I can also suggest, that depending on what your taxes are, and how old your house is, you may be able to appeal your taxes, if you have not already done so. I have an active blog that I maintain, at www.BucksCountyPaToday.com, and I have written a number of posts about the process of filing an appeal, and basically how easy it is. You are welcome to refer to my blog, for additional information on the appeal process. You can also contact me, for additional information.
You may already be aware of this, but from a real estate standpoint, a pool is not a very good investment. It's great to do, for your family's enjoyment, but the overwhelming probabililty is, that if you go to sell your house, you will not get more money becuase the house has a pool.