If the government intervenes to correct a market failure caused by negative externalities, what is the likely effect on socially optimal output compared to the competitive output?

When the government steps in to address a market failure caused by negative externalities, it aims to reduce the harmful effects that certain activities have on society, like pollution. In a competitive market, businesses may produce more than what is socially optimal because they do not consider the costs their actions impose on others, such as health issues from smoke or waste. By intervening, the government can implement regulations or taxes that encourage companies to reduce their negative impact, leading to a decrease in production to a level that is better for society as a whole. For example, if a factory is polluting a river, the government might impose a tax on the pollution, which encourages the factory to either clean up its operations or reduce production. As a result, the socially optimal output, which considers the well-being of all affected, will be less than the output produced in a competitive market without government intervention.