Could you please help me with this problem:

Question

Consider an oligopolistic market with two firms. Each of them produces using a cost function given by c(q)=q2.

The aggregate demand in the market is given by 1000−p.

Suppose that, in order to increase production, the government gives the firms a $100 per-unit produced subsidy. The cost of the subsidy is financed with an identical lump-sum tax on consumers.

Suppose that firms are NOT owned by consumers.

Let s denote the size of the per-unit subsidy/tax given to the firms. Let positive values of s denote subsidies, and negative values of s denote taxes.

QUESTION: What is the value of s that maximizes total consumer well-being?