Question - One firm exists in the market for gadgets. The cost function and demand function are as follows,
C(q) = 6000 + 1/8 q2 + 25q
Qd(p) = 1600 - 16p
(a) Find the profit-maximizing quantity the monopolist will produce, and what price he will charge.
(b) At this price and quantity, calculate the monopolist's profit and producer surplus.
(c) Calculate the consumers' surplus.
(d) Explain why this allocation is not Pareto efficient. That is, can the consumers' or monopolist increase their surpluses without decreasing the others at any price and quantity?
(e) Find the efficient price and quantity. Calculate producer and consumers' surplus at this price and quantity.
(f) Calculate the dead-weight loss. Interpret this number.
(g) Can this market support another firm? That is, suppose a second firm enters with identical cost structure (same cost function) and the firms are (perfectly) competitive. Find the equilibrium market price and quantity where Qs = 2qs. At this price and quantity, calculate the firm's profit.