PLEASE HELP ME EXPLAIN STEP BY STEP WHY THESE QUESITON HAVE ANSWERS LIKE THAT

PLEASE HELP ME EXPLAIN WHY THESE QUESTIONS COME TO THOSE ANSWERS. PLEASE EXPLAIN.

Scenario 1: Suppose the city of Springfield has only one gas station, which is owned by a single firm. The demand for gasoline in Springfield is given by the inverse demand function:

p=400 - 2.5Q

where Q is gallons of gas demanded and p is the price charged per gallon of gas. The wholesale price of gas is $10/gallon and there is a fixed cost of $200 of running the gas station. Therefore, the firm's cost function is:

C(Q)=10Q + 200

1. As a monopoly, what price and quantity would the firm set?

p = ____205_____ Q = ______78________

1. How much profit does the monopolist make?

= ____15,010______

1. What is the deadweight loss resulting from having the monopoly?

DWL = ___7605___

To lower food prices on campus, the university decides to allow two separate firms to compete. Assume the two firms each have the same cost function as above.

1. If the firms compete as Cournot Duopolists, what is Firm 1's Best Response Function?

q₁^BR = ____(390-2.5q₂)/5_________

1. What will be the Cournot Duopoly equilibrium quantities of soda sold and price of soda?

q₁ = ____52______ q₂ = _____52_________ p = ______140_______

1. How much profit does each firm make?

₁ = ___6560________ ₂ = _____6560_______

1. What is the deadweight loss from the Duopoly?

DWL = ____3380_____

Suppose the owners of Firm 1 and Firm 2 decide to form a cartel, with each firm selling an equal amount of food.

1. What price and quantity of soda will they choose to sell if they seek to maximize the combined profits?

q₁ = _____39_______ q₂ = _______39_______ p = ______205______

1. If Firm 1 believes Firm 2 will adhere to the cartel agreement, what output level maximizes Firm 1's profit? In other words, what would be firm 1's best response?

q₁ = __58.5________