There are two types of neighbors on a street that have demands for a security patrol as X1= 30 - 0.5P1and X2= 20 - 0.5P2, where X is each neighbor's units/hours of patrol demands at price per unit P.The marginal cost to provide another unit of X to the neighbors is MC = 40.All the neighbors receive the benefits of any given amount of X provided, so that the good is a public good.

a.Find/write the equation to represent the total (social) marginal benefit (demand) of X. In your answer, explain the difference between finding the total (social) marginal benefit (demand) for a public good compared to a private good. (Note that these demand curves are written quantity as a function of price.). Graph the curves.

b.Find the efficient total quantity of X to provide.

c.Find the efficient "price" to charge each person.

d.Explain why the competitive market system will likely fail to supply the efficient quantity of a public good.