Suppose that electricity is generated by burning coal, and that the mining, processing, and burning of coal have considerable environmental and health costs associated that are not reflected in the market price. Suppose that the market demand for electricity can be represented by the equation Q^D = 14 - 0.2P (or P = 70 - 5Q^D), where the quantity demanded represents marginal benefit, and that the market supply can be represented by Q^S = 4 + 0.8P (or P = -5 + 1.25Q^S) where the quantity supplied represents private marginal cost. The price is in cents per kilowatt hour and the quantity is in terms of millions of kilowatt hours per month.

a. Show the demand (marginal benefit) and supply (private marginal cost) curves on a diagram. Make sure to label your axes, curves, and intercepts.

b. Use algebra to solve for the private equilibrium price and quantity, and show the equilibrium price and quantity on your diagram.

c. Suppose that the external cost associated with producing one kilowatt hour (kwh) of electricity is $0.25. What is the equation for the social marginal cost curve? Add the social marginal cost curve to your diagram.

d. Use algebra to solve for the socially optimal price and quantity consumed of electricity. Explain.

e. What excise tax would have to be set in order to get electricity-producing firms to produce the socially optimal level of output? What would be the burden of this tax on consumers and producers?