A competitive market has a demand function given as

A competitive market has a demand function given as BUD) = 90 p. The supply comes from 16 identical sellers each with the cost function 60;) = 4-q2 + 16. (3) Use this information to construct the profit function of an individual seller as a function of the quantity :3; of output that seller produces and sells at the competitive price p. {2 marks) Is the profit function strictly concave in the quantity q of a seller? {2 marks) Find the supply function of an individual seller as a function of the output price p. {3 marks) Find the market supply function as a function of the output price. {2 marks) Find the competitive equilibrium price and overall market quantity in this market. {5 marks) Find the competitive equilibrium profit and quantity of each seller. {3 marks) If we go to a long run equilibrium where entry and exit is allowed, what does your answer to part (f) suggest about whether sellers will enter or exit the market? {3 marks) Find the long run competitive equilibrium number of sellers, quantity of each seller. total market quantity and market price. {10 marks)