1. duopoly part i. dell and hewlett-packard are in a duopoly in the laptop computer market. the market demand for laptops is given by: = 600– and q is market quantity. both firms have a constant marginal cost of $100. a. write a total revenue function for each firm that depends on the quantities produced by both firms (i. e., total revenue for firm “i” is and “i” is either hp or dell). b. write each firm’s profit function and the condition for profit maximization. note: each firm only gets to choose its own quantity and takes the competitor’s quantity as given. this condition assumes the firms produce a la cournot competitors. c. each firm’s profit maximization condition in (b) can be written with the own firm’s quantity on one side (each firm’s “reaction” function). write both reaction functions. then solve them simultaneously to get hp’s and dell’s profit maximizing quantities. d. what is the market quantity when both firms behave as cournot competitors? what is the price in the market? e. what price and market quantity would prevail if they behaved like a cartel? note: both firms would produce half of the quantity that maximizes a monopolist’s profit.