There are two individuals with demand for streetlights (Q_1)^D= 150 - P and (Q_2)^D = 200 - P

a. Since the given price attains at the point where the market supply is perfectly elastic as it shows the maximum possible change in the quantity supplied due to no or minimal change in the price. Therefore, the market is competitive, putting off this price in the demand function would imply the possible equilibrium quantity demanded.

For 1st individual, the equilibrium quantity is determined as,

QD1=150−PQD1=150−130QD1=20unitsQ1D=150−PQ1D=150−130Q1D=20units

Similarly, the equilibrium quantity of 2nd individual would be,

Q2D=200−PQ2D=200−130Q2D=70unitsQD2=200−PQD2=200−130QD2=70units

b. Streetlights are considered as a public good because it is meant for the consumption for all people in society. It is non-excludable as well as non-rival in nature. As streetlights are consumed by all and it is financed by the central authority. Since no one does not pay for it except the authorities which imply these goods as non-competing in nature.

c. Since the market demand would be the sum of the demand made by both individuals which would be determined as,

P=150−Q1D+200−Q2DP=350−(Q1D+Q2D)P=350−2QP=150−QD1+200−QD2P=350−(QD1+QD2)P=350−2Q

Thus, Q is sum total of quantities is Q1 and Q2 and the price is $130.

Let Q* be the socially optimal quantity. Hence, the socially optimal quantity would be,

P=350−2Q∗130=350−2Q∗−220=−2Q∗110units=Q∗P=350−2Q∗130=350−2Q∗−220=−2Q∗110units=Q∗

d. A public good is considered as the market failure due to the externality of the free-riding problem. The market fails to achieve the effective allocation of resources because people generally tend to make the consumption of goods without paying for that.