Can someone please help me with a hint to solve this problem?? I'm struggling really hard with this.

Question

"Consider an oligopolistic market with two firms. Each of them produces using a cost function given by c(q)=q^2.

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.

What is the total level of production and the equilibrium price in the market?"

I think that first of all you need to calculate the oligopoly equilibrium (without the tax), and you'll get Q=400 and P=600 right???

But the subsidy (for producers)reduces the cost; so the answer for the new Q should be Q=440.

My question is about the Price; because a lum-sum tax does not affect the inverse demand function, then:

P = 1000 - Q = 1000-440 = 560.

It's that correct??

Answer 1

Yes
how about this one?
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? (Note: Don't forget to add the sign in entering your answer, if necessary).
?

Answer 2

I think that is 250

Answer 3

Wrong values: 250,-250,-300,-500

Answer 4

Aldo 125. Answer should be positive

Answer 5

Also sorry. 125 is wrong