Assume that the firm has had an analyst successfully parse it's demand into an a group and b group with inverse demand functions: Qa=100-Pa and Qb= 120-0.5 Pb.

Assume the firms' cost function is : C = 2,000 + 20Q (where Q=Qa+Qb).

A) Identify the firms' optimal price and quantity for group a, and profit or surplus to the producer.

B) Identify the firm's optimal price and quantity for group b and profit or surplus to the producer

C) Which group is more price responsive? How can you tell for sure?

D) Now consider a separate case where a firm cannot differentiate between its' markets but knows that costs and demand are given by C = $20,000 + $15Q and Q=5500-100P respectively. How might you approach this firm's dilemma of profit maximization? Please present your solution