Hi there, please explain the answers to these questions in full detail with working out.

Thanks

Q1) A market has an inverse demand curve p = 100 - 2 Q and four firms, each of which has a constant marginal cost of MC = 20. If the firms form a profit-maximizing cartel and agree to operate subject to the constraint that each firm will produce the same output level, how much does each firm produce?

Q2) Duopoly quantity-setting firms face the market p = 150 - q 1 - q 2 . Each firm has a marginal cost of $60 per unit. What is the Nash-Cournot equilibrium?

Q3) Suppose that a market for toothpaste has two sellers, each of which says its product has the best combination of ingredients to protect against tooth decay and to control plaque, tartar, and gum disease. Each of the profit- maximising oligopolists faces the same constant marginal cost, MC = 1. The demand function for Firm 1 is q₁ = 10 - 2p₁ + p₂ and for Firm 2 is q₂ = 21 - 3p₂ + 2p₁ , where p₁ is Firm 1's price and p₂ is Firm 2's price. What are the Nash- Bertrand equilibrium prices and quantities? If an advertising campaign featuring product endorsements by the dental association increases the demand for the first firm's product to q₁ = 14 - 2p₁ + p₂ but does not affect the second firm's demand function, what are the new equilibrium prices and quantities, and how do they compare to the pre-merger prices?