Negative Externalities (Market)
2. (From Final 2010) Colorado Department of Transportation oversees snow removal in Colorado, but this task is performed by private companies that use a sand/salt mixture that work as freezing-point depressants. The monthly inverse demand for sand/salt mixture is $P = 90 - \frac{1}{10}Q$, where price is measured in dollars, and quantity in tons. The market for sand/salt mixture is perfectly competitive, and the price (inverse supply) is equal to $20 per ton: $P = 20$.
a. How many tons of salt/sand mixture will be purchased? Calculate the consumer surplus and the producer surplus and illustrate your answers on a graph.
Unfortunately, the use of sand/salt mixture has a negative external effect on drivers. First, it increases the cost of car maintenance because the sand/salt mixture corrodes vehicles and damages windshields. Second, it increases the cost of car insurance because the salt in the mixture attracts deer, elk, and Big Horn sheep and therefore increases the probability of vehicle-animal collisions/injuries.
It has been estimated that the marginal external cost (MEC) of each additional ton of sand/salt mixture used on the roads of Colorado is equal to $15. That is, $MEC = 15$.
b. What is the total external cost (TEC) to drivers at the equilibrium quantity that you found in a.?
c. What is the equation for the marginal social cost (MSC) of sand/salt mixture consumption?
d. What is the socially optimal level of consumption? Illustrate both the socially optimal level of salt/sand mixture and the market level of salt/sand mixture (answer to part a.) on a new graph.
