Answer
a) It does matter whether the government distributes or auctions the permits.
b) The allocation does matter for efficiency.
Work Step by Step
a) If the government distributes the permits, there will be some surplus remaining (within the firms). If the government auctions the permits, the prices will be closer to what the market would allow, and the permits would go to the firms who can best pay those prices.
b) The firms that value the permits the most should be given the permits (to minimize the amount of surplus). Since the permits are tradable, the eventual benefit should be the same (since the firms should trade among themselves and get the permits to the firms that would value the permits the most).
