4.4 Public goods The table below shows how much each small town in a county of 10 small towns is willing to pay each year for additional sheriff deputies to provide law enforcement services to the county as a whole. Each town's Total county's Yearly salary # of Sheriff's willingness to willingness to needed to deputies willing pay for pay for attract qualified to work for this additional additional deputies salary deputies ($ per deputies year) ($ per year) 20,000 16,000 160,000 35,000 14,000 140,000 50,000 12,000 20,000 65,000 4 10,000 100,000 80,000 5 8,000 80,000 95,000 6 6,000 60,000 110,000 4,000 40,000 125,000 8 2,000 20,000 1. In the graph below plot the individual towns' demand for sheriff deputies, the supply of deputies (the number of deputies willing to work at each salary level) and the total county demand for deputies. Yearly Salary [,DOD's of $) 12 105 75 45 30 15 1 2 3 5 6 7 8 9 10 # of sheriff's deputies2. Explain each how your graph illustrates each of the following in the market for public security in this county: a. The marginal private benefits (of each individual town) b. The marginal social benefits (of the entire county) C. The marginal social cost3. Identity each of the following from your graph above: a. The number of deputies that would be hired if the residents of each town were asked to voluntarily contribute to the deputies' salaries : b. The socially optimal number of deputies that should be hired : c. The salary needed to hire the socially optimal number of deputies : 4. Explain why...r the number of deputies hired. if left to the free market. will be less than the socially optimal leyel. 5. What are the characteristics of the law enforcement services provided by sheriff's deputies that make this an example of a public good?6. What is the n'friee-rider problem\" and how does help explain why no deputies will be hired if residents of each town are asked to voluntarily pay for it? T. What is the solution to the market failure illustrated and explained above