A factory located on a river releases pollutants as a byproduct of its production process. These pollutants harm a downstream community that relies on the river for fishing and recreation. Analyze how each of the following two distinct proposals would compel the factory's decision-makers to account for the costs its pollution imposes on the community:

1. The government imposes a tax on the factory for each unit of pollution it releases.
2. The downstream community pools its resources and buys ownership of the factory.

In your analysis, explain the specific mechanism through which the external cost is made internal to the firm's operational and financial decisions in each case.