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Two coal-fired power plants compete to provide electricity to a certain region.

Two coal-fired power plants compete to provide electricity to a certain region. Each plant has a marginal cost of $2 per megawatt (q) of electricity produced, and market demand for electricity is Q = 50 − p. 1. Find the Cournot equilibrium price and quantity for each firm. 2. Suppose that each megawatt of electricity produced at plant 1 results in 3 tons of pollution, while each megawatt of electricity produced at plant 2 results in 6 tons of pollution. Further suppose that each ton of pollution causes an externality damage of $1. What is the total externality damage in the Cournot equilibrium? 3. Suppose that the government forces plant 1 to pay an extra $3 per megawatt of electricity produced in taxes in order to pay for each ton of pollution they emit, while plant 2 pays no taxes. Find the new Cournot equilibrium price and quantities, and calculate the new externality damage. 4. Suppose that the pollution tax is levied on plant 2 instead ($6 per megawatt), while plant 1 pays no taxes. Find the new Cournot equilibrium and externality damages. 5. Calculate the Cournot equilibrium price and quantities and externality damages if both firms pay $1 for each unit of pollution emitted. 6. Suppose that coal plants competed in prices rather than quantities. How would the results change in each case in problems 1-5 above?

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