The price of ethereum should increase for two main reasons. One, the lock up mechanism of staking ether will decrease the functional supply available on the market. With less sellers on the market, there will be upward pressure on price. Two, there will be a built in appreciation mechanism. What would you pay more for, pure gold or a special form of gold that literally grows while it's sitting in the vault?
One potential factor that could decrease the price of ether under Casper is mining costs. Currently, mining costs are accounted for in the price of ether because they are part of the cost of production. A move away from mining means a move away from suppliers with significant electricity costs, effectively making ether “cheaper to produce.”
My opinion is that the latter is a relatively minor factor in price compared to the first two. In the same way that additional copies of computer software and digital media and trading cards are cheap to produce, asset prices in the modern age are less and less dependent on the cost of production.