How does government intervention improve society's welfare by changing people's incentives?

Government intervention improves society?s welfare by changing people?s incentive by providing incentive in kind through positive externality.

Government intervenes by providing subsidy for the consumption of the goods that that improves the basic necessities and by improving the social cost of goods and services. Government also enforces laws that protect the consumer from getting harm through negative externality. For Example, when some industry pollutes the environment harming the neighbors and the animals nearby, government enforces law of giving strict punishments to reduce pollution.

When government provides street lights and the benefits are enjoyed by the passerby, it is and incentive to the people by the government.