Well, the cost stays the same, but the reward is halved -- so yes the effect is similar to each costing double, but that's not really precise.

It's better to consider it as miners subscribe to a lottery (for the cost of their electricity). Roughly every 10 minutes someone wins that "block". Yesterday the reward for winning was 12.5 BTC per block, and now it's 6.25... the cost of entering hasn't changed.

There's more to it of course, e.g. as the difficulty adjusts as in line with the hashrate on the network, but lagged by roughly a couple of weeks worth of blocks being mined. Fees in any given block vary, which are added to the block reward. Many miners pool rosources and each share a fraction of the reward. Etc.