I once read that the main regret in the design of Puerto Rico was over-pricing the University. Anyone have any guesses (or statistical analysis) as to the "correct" price?
I've read many people saying the same thing - the university is overpriced. I read one group who attempted to find the true value of the buildings by playing for two years and varying prices based on whether they were bought, and how well the people who bought them did. The write up contains a downloadable copy of their results and final prices for all the buildings.
In their games, most of the prices have seemed to stay fairly close to the original prices. A rough summary of the exceptions from the base game:
Small Market ~ 2 gold
Small Warehouse ~ 4 gold (with 3 players)
Office ~ 3/4 gold
Large Warehouse ~ 5 gold (with 4 players)
Factory ~ 8 gold
University ~ 7 gold
Harbor ~ 9/10 gold (with 3 players)
There's plenty more that could be drawn from their results too, I'd recommend giving it a read.
The results aren't perfect for a number of reasons. Firstly they changed the rules to allow all buildings from the base game and first expansion to be available to them every game. Secondly (as noted above) the power of some buildings vary with the number of players. There are hardly any games played with two or five players, and not many more with four. Thirdly, the same people play many of the games, and their preferences bias the results.
To go back to your question though. If you're interested from a theoretical point of view then this data suggests the university should be about seven gold. Personally I think that seems about right.
However if you're interested because you want to play with different prices then I suggest trying it! I read somewhere of a variant where before the start of a game a few buildings are increased/decreased in price by players putting red/green counters on them. If your group thinks the university is too expensive then it will get more green counters, and you should end up with more interesting in-game decisions.
Regrading whether the factory should cost eight coins and the university seven, according to the wiki page "The designer Andreas Seyfarth has said that he would make this change if he were creating the game today."
Based on other things I've read, I agree with ths.