The government will offer a $20 as tax to achieve market equilibrium.
Step-by-step explanation:
Socially optimum point occurs at that level of production which is the best point of production. There is optimum utilization of resources at that this point of production.
At the situation, when Private marginal cost is equal to the private marginal benefit, it occurs at a point which is above the socially optimum point. This means that at this level there is exploitation of resources. So the government should encourage the reduction in the level of production. For this it should impose tax on the production equal to the amount of $70-$50 = $20.