Consider the market for electricity in Tustin Beach, and assume it is competitive. Electricity is used to power tramways and electric cars. The hypothetical demand and supply equations are given by:
Supply: QS = -10 + 5 P; QS is in MWh (megawatt hour); P is in $ per MWh. Demand: QD = 80 - 4 P; QD is in MWh; P is in $ per MWh. In the above, QS and QD are respectively the quantity supplied and demanded of electricity. As you know, the supply function is also the marginal private cost (MPC) curve, and the demand function also represents the marginal private benefit (MPB) curve.
Suppose that producing electricity (from coal in the case of Tustin Beach) creates an externality (pollution) that results in damages (to health, visibility, and nature). These damages can be represented by the marginal external cost (MEC) curve:
MEC(QS) = 3/20 QS; MEC is in $ per MWh (so 3/20 is in $/MWh2) where QS is in MWh. In the rest, we omit the argument of MEC. As you know, total social costs (TSC) are such that (we also omit QS as argument of TSC and TPC):
TSC=TPC+TEC.
a. Find the price and the quantity of electricity produced under a market equilibrium.
b. Find consumer and producer surplus at market equilibrium along with total external costs. What is the value of net social welfare?
c. Find the socially optimum quantity of electricity to produce along with the corresponding price.
d. Justify that the objective of a benevolent government should be to maximize TPB(Q)-TSC(Q), by choosing the right level of Q. Then, write, interpret, and solve the resulting first order necessary condition for an optimum (remember the first order condition we gave in class).
e. Find the equation of TEC(QS), TPC(QS) and TSC(QS). Assume that TEC(0)=0 and TPC(0)=100.
f. Find the equation of TPB. Assume that TPB(0)=0. Since we suppose that TEB(Q)=0 (i.e., there are no external benefits from producing electricity), TPB=TSB.
g. If the government decided to implement the solution above using a system of transferable permits, how many permits should be distributed to polluters? What would the price of a permit at equilibrium be?