You are a manager working for Omni Consumer Products. Omni is a monopolist in the market for security devices and its marginal cost is zero for any quantity. Omni faces a linear demand curve (i.e. the quantity demanded for its product is QD = a bP for some positive parameters a and b, where P is the price). Omni is considering four possible prices for its product: P1, P2, P3, and P4. The quantity of Omni's product that would be demanded is Q1 at price P1, Q2 at price P2, Q3 at P3, and Q4 at P4. It has been estimated that the price elasticity of demand is 2 at Q1, 1.5 at Q2, 1 at Q3, and 0.8 at Q4.

(a) (2 marks) For each of the four prices P1, P2, P3, and P4, classify demand according to its elasticity (e.g. elastic, inelastic) at the corresponding quantity demanded. (b) (2 marks) How do the four prices P1, P2, P3, and P4 relate to each other? That is: state which price is the highest, which is the second highest, the third highest, and the smallest. Explain your answer. (c) (5 marks) Is Omni maximising its profits by setting the price to be P1? If so, explain why. If not, state how Omni can increase its profits. (d) (6 marks) If Omni is choosing only among the prices P2, P3, and P4, what price would you advise Omni to choose? That is, which of these prices is associated with the highest profits? Explain your answer. (e) (2 marks) Assume that Omni follows your advice from part (d) and selects the price you recommended. What is the highest total fixed cost that allows Omni to enjoy non-negative economic profits? (f) (8 marks) In this part, Omni is free to choose any price. After setting its price to the profit-maximising price level, Omni experiences an unexpected rise in the wage rate and its marginal cost increases. It now equals for any quantity, where is a small positive number. How does the increase in marginal cost affect Omni's profit- maximising price: does it increase or decrease? Answer the same question for its profit-maximising quantity and its profit. Carefully justify your answers.