Please provide all the calculations and explanations necessary to explain your answer.

You have just been hired as the chief economist for Aarons (an eraser manu- facturer) who currently enjoys a patented technology that allows it to produce erasers faster and at a lower cost than your only rival, Zacharys. Aarons has used this advantage to be to enable them to be the first mover in the eraser market and as such can choose to operate at the profit-maximising output level. Aarons cost function is CA(QA) = 2QCA, where as Zacharys cost function is Cz(Qz) = 40z and the inverse demand function for erasers is P = 500 - 2Q. (8 Marks) (a) Given the above information calculate the profit-maximising output lev- els for both Aarons and Zacharys. (2 Marks) (b) Given the above information calculate the equilibrium price in this mar- ket. (2 Marks) (c) Calculate the amount of profit each firm earns. (2 Marks) (d) Your firm has decided to merge with Zacharys, determine the offer that would enable the merger to be profitable to you firm. (2 Marks)