Texts: Problem 2. DTE Energy is a local monopolist of retail electricity and provides electricity to homes in Ann Arbor. Suppose the electricity demand in Ann Arbor is given by:
Qa = 160,000,000 - 200,000,000P = 160M - 200M P
where P is the price (in $ per kWh), and Q is the total electricity consumption demand in kilowatt-hours (kWh) and M is one million. DTE's marginal cost of generating each kWh of electricity is $0.20. That is, its marginal cost of generating electricity is constant regardless of how much it produces.
(a) What is DTE Energy's profit-maximizing quantity and price of electricity?
(b) What is DTE Energy's mark-up and price-cost margin? [Note: compute the mark-up and margin using monopoly's variable cost i.e. ignore any fixed cost it may have]
(c) What is the consumer surplus and producer surplus in the monopoly market?
(d) If this market was perfectly competitive, what would be the equilibrium quantity and price of electricity? [Hint: take the monopoly's marginal cost curve as the market inverse-supply curve]
(e) What is the consumer surplus and producer surplus in the perfectly competitive market?
(f) What would be the deadweight loss associated with DTE Energy's market power? Show the deadweight loss on the supply & demand graph.
(g) Now suppose that DTE Energy generates most of its electricity via fossil fuels. As a result, the byproduct of electricity generation is CO2 emissions which imposes a negative externality on society. Assume that DTE Energy doesn't internalize this negative externality when thinking about its production cost. Qualitatively, how does your answer to the previous question change? That is, what happens to the deadweight loss associated with DTE Energy's market power in the presence of a negative externality?