What are subsidies for?

It needs a compensation in the case of negative externality, not subsidies. And based on Coase theorem, the government should intervene only when the cost of negotiating is higher than the compensation. But in the case of positive externality, it is great for the society. The government should support the individual investors to carry out the projects. Such as healthy foods cost more to produce but it will make people healthy. Without subsidies private investors will not be able to bear a loss for so long.