Question 3(30 pts): Umbrella Academy (Firm A) and Sparrow Academy (Firm B) are operating under a Cartel that controls the production of superhero costumes. The market demand is given as p=420Q. Umbrella Academy's cost function is given as Ca=20qa+1.5qa2, while the cost function of Sparrow Academy is Cb=10q2+21qb2. a. (5pts) Find the cartel's marginal revenue and marginal cost functions b. (5 pts) Find the cartel's optimal total output and price c. (10 pts) How will the allocation of output be among the two firms? Calculate the cartel's total profit also. d. (10 pts) What is the effect of the Cartel to the welfare of the society? (Hint: Calculate for the CS and PS first, then the welfare). Question 3(30 pts): Umbrella Academy (Firm A) and Sparrow Academy (Firm B) are operating under a Cartel that controls the production of superhero costumes. The market demand is given as p=420Q. Umbrella Academy's cost function is given as Ca=20qa+1.5qa2, while the cost function of Sparrow Academy is Cb=10q2+21qb2. a. (5pts) Find the cartel's marginal revenue and marginal cost functions b. (5 pts) Find the cartel's optimal total output and price c. (10 pts) How will the allocation of output be among the two firms? Calculate the cartel's total profit also. d. (10 pts) What is the effect of the Cartel to the welfare of the society? (Hint: Calculate for the CS and PS first, then the welfare)