Question

The city of Crawfordville, Florida has a very bad problem with the mosquito population from late April through late September almost every year. The City generally sprays the mosquito population to deal with the problem. The data below, collected and maintained by the City of Crawfordville’s Finance Department, shows the City’s market data for spraying for mosquitoes. The price is measured in thousands of US dollars per spraying and both quantities are measured in dozens of spraying events events per year, from 2003-2016.

The Rafferty Analytic Group, LTD., Port St Lucie, Florida, is a firm that specializes in chemical spraying l data collection. The firm at the request of the City Council has studied the Crawfordville population and discovered the City generates an externality of $15 for each and every spraying for mosquitoes. This is due to the mist that is created by the spraying which is a general irritant to the nose, eyes and lungs of the residents, the fact that people need to wash their cars after the spraying (unless they keep them in a garage), and are not allowed outdoors for 6 hours in the area once sprayed.

1. In one clearly and accurately labeled graph, created using Excel, graph the market data as collected by the City Council as well as the market failure that the Rafferty Group has discovered. This will be graph # 7. (45 pts)

2. Referencing only your graph, what equilibrium price and quantity did the market generate? (3 pts)

3. Referencing only your graph, what is the extent of market failure in this situation? What price and quantity are consistent with an efficient level of spraying? (6 pts)

4. Given that there is market failure, provide one solution for how the efficient level of mosquito spraying can be achieved. (6 pts)

Answer 1

The diagram above represents the downward sloping marginal benefit curve (PMB) and private marginal cost ( PMC) curve by the data collected by the city council. The Social Marginal cost lies left of the private marginal cost due to $15,000 of negative externalitites. Therefore, triangle EFT represents the extent of market faliure.

B) The market attains equilibrium at point E, i.e., at the intersection of the PMB and PMC. In other words, the equilibrium quantity = 8 dozens and equilibrium price = $55,000.

C) Socially optimal level of price and quantity are respectively $62,500 and 6.5 dozens. That is the price of $62,500 and quantity of 6.5 dozens are consistent with an efficient level of spraying.

Therefore the extent of market faliure = area of traingle EFT = 0.5

= 0.5 * 15,000 * (8-6.5) where 15,000 is the extent of externalities, 8 = market equilibrium output and 6.5 = socially optimum output.

=> Loss of social welfare (or extent of market failure) = 0.5(15,000)(1.5) = $11,250

D) one way to achieve efficient level of mosquito is by imposing a tax of $15,000 on production so that the Private marginal Cost shift towards to coincide with the Socail Marginal Cost. The social optimum level of output will be 6.5