Suppose that there are two firms in a duopoly market: Firm A and Firm B. The market demand for the product produced by these firms is given by the following inverse demand curve:

P = $100 - (Q_A + Q_B)$

where P is the market price, Q_A is the quantity of the product produced by Firm A, and Q_B is the quantity of the product produced by Firm B.

The firms have the following cost structures:

Firm A:

Total cost = $10,000 + $50Q_A + $100Q_AQ_B

Firm B:

Total cost = $5,000 + $30Q_B + $100Q_AQ_B

1. Find the Cournot-Nash equilibrium quantity for each firm.

2. Calculate the market price at the Cournot-Nash equilibrium.

3. Calculate the profit for each firm at the Cournot-Nash equilibrium.

4. Calculate the consumer surplus at the Cournot-Nash equilibrium.

5. Calculate the total surplus (consumer surplus + producer surplus) at the Cournot-Nash equilibrium.