A modest sized city is currently considering ways of providing broad band intern

Question

A modest sized city is currently considering ways of providing broad band internet service to its citizens which is not currently available. Based on analyses from other cities, they estimate that market demand in their city is P = 20 - .1Q, where Q is measured in thousands of households served and P is the price of monthly service in 10s of dollars. The marginal cost of supplying the service is P = 1 + .001Q. A group of city counselors believes the city should own and operate the system for the purpose of making a profit. Thus, the city would be the monopoly provider. If these city counselors get their way, what will be the price and output of broad band service in the city Sketch your answer as well as calculate it numerically. What is the city's mark-up over marginal cost What is the price elasticity of demand at this outcome How is this number related to the markup you calculated in part1 If instead the city instead decides to provide the service at the efficient level, what would be the price and output Compare the monopolist vs. the efficient outcome, what is the DWL involved in allowing the city to act as a monopolist Again, provide a sketch of your answer in addition to the calculations. If the city counselors who want the city to act as the broad band internet monopoly find that basically no senior citizens take advantage of service but everyone else does, what would be the profit-maximizing lower price that they could offer to the senior citizens How many senior citizen households would now also buy the service What is the DWL now If instead of supplying broadband, the monopolist was producing a product that generated substantial pollution as a byproduct of production but was currently unregulated, would the dead weight loss you calculated in part c be as large Why or why not Use a new graph to illustrate your answer.

Explanation / Answer

d.

P = 20 – 0.1Q

TR = PQ

      = (20 – 0.1Q) × Q

      = 20Q – 0.1Q^2

MR = Derivative of TR

       = 20 – 0.2Q

Profit maximizing condition: MR = MC

20 – 0.2Q = 1 + 0.001Q

0.201Q = 19

Q = 19/0.201

Putting the value of Q in the demand function, P = 20 – 0.1(19/0.201) = 212/20.1

Therefore, the price is 212/20.1 and the quantity (number of senior citizen) is 19/0.201

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