See the above figure. E is the equilibrium when people only take into consideration private costs, with output Q1 and price P1. When external costs (EC) are added to private costs, the optimal point is E*, with output Q* and price P*. That is, the social optimum with externalities is to produce less and charge a higher price than private costs alone indicates. If a tax is imposed that caused price to increase to P*, or output were restricted to Q*, the optimum could be achieved.