An industry's market demand is given by: Q = 100 - 10P

The market has one dominant firm and a fringe of four smaller firms. The fringe firms act as price takers, producing where their individual marginal costs equal the market price.

Each fringe firm has a total cost given by: TC_i = 20Q_i + 4Q₁²

The market leader has a total cost given by: TC_L = 10Q_L + 1Q_L²

a. What is the market price?

b. What is the quantity produced by the market leader?

c. What is the total profit of the fringe firms?

d. What is the total profit of the market leader