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 per year, from 2003-2016.
P 85 75 65 55 45 35 25
Qs 14 12 10 8 6 4 2
Qd 2 4 6 8 10 12 14
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.
a. 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.
b. Referencing only your graph, what equilibrium price and quantity did the market generate?
c. 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? d. Given that there is a market failure, provide one solution for how the efficient level of mosquito spraying can be achieved.

What's the formula that should be used in the graph?

Answer 1

(a) The below diagram shows the downward sloping private marginal benefit curve (PMB) and private marginal cost (PMC) curve out of the data collected by City COuncil (given data table). Due to $15,000 of negative externality, the social marginal cost curve lies left to the PMC as shown in the digram. Hence, the extent of market failure (or the amount of welfare loss is shown as the area of the shared triangle EFT.

welfare loss Price PMB 0 1 2 3 4 5 6 9 10 11 12 13 14 15 7 8 Quantity

(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 as observed from the diagram.

(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.

Hence, the extent of market failure = area of the shaded triangle = 0.5 * ET * (difference betwwen market and socially optimal output)

= 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 is to impose a tax of amount $15,000 on producion so that the PMC shifts to coincide with SMC. This will result in an socially optimum level of output i.,e., 6.5