Econ8100 Monopoly

1 Monopoly A monopoly firm faces a market given by the inverse demand function p = a - bq where p is the price the monopoly receives if it sells quantity q of output. The firm's cost function is given by c (q ) = 1.1 Find the profit-maximizing quantity of output, price and the corresponding profit for this firm. 1.2 Find out the consumer and producer surplus of the equilibrium that you calculated in 1.1. [You may want to draw a diagram to indicate them] 1.3 Find out the consumer and producer surplus of the competitive equilibrium outcome. What are the competitive equilibrium price and quantity? 1.4 From your answers to 1.2 and 1.3, show that the monopoly is not efficient. 1.5 Suppose the government imposes a profits tax t on the monopoly. Find the profit-maximizing quantity of output, price and the corresponding profit for the firm. What are the impacts of the profits tax on the quantity of output, price, and the monopoly's profit? 1.6 Suppose the government subsidizes the monopoly at a rate of t , so that consumers pay a price p = a - bq, but the firm receives a price (1 + t )(a - bq). For what level of t will the firm produce the efficient quantity you calculated in 1.3? 1.7 Consider and evaluate the following two possible policy proposals: Proposal 1: "A monopoly produces an inefficiently low ouput, subsidies to the firm can induce the monopoly to produce more output and hence efficiency can improved. Therefore, we should subsidize monopolies." Proposal 2: "As we have seen, a monopoly cannot pass the tax along to the consumers. Therefore, we should tax monopolies