Question

Mosquito control is a pure public good. Suppose there are 2 identical individuals, Alan and Ben in the economy, and each has the following marginal private benefit from mosquito control: MPBi=50 – Qi. The marginal cost of mosquito control is MSC=MPC=MC=$10 per unit.

a. What is the socially optimal level of mosquito control Q? (Hint: You need to vertically sum the individual private benefits: MSB=MPB1+MPB2.) Illustrate your answer on a graph showing MSB and MSC and labelling all the points carefully.

b. Suppose that mosquito control is not publicly provided. Rather, Alan and Ben provide it themselves. If only one of them provides mosquito control, what will be the quantity of mosquito control provided?

c. Using marginal cost-benefit analysis, find out how much mosquito control Alan will provide if Ben provides 10 units? What if Ben provides 15 units? What if ben provides 20 units? (Hint: For Ben his MPB = 50 –QB – QA and for Alan his MPB = 50 –QA – QB where QA and QB are how much Alan and Ben has produced accordingly.)

d. What kind of externality does Alan impose on Ben (or Ben on Alan) when producing some of the public good and why? Explain.

e. Is there a free-rider problem in the private provision of mosquito control? Explain.

Now suppose that Alan and Ben have only two choices, either to provide no mosquito control, QL= 0, or provide QH=20. Each player derives a benefit from the provision of mosquito control and also incurs a cost of providing either low or high quantity of mosquito control. If both of them chose QH, they receive a payoff of 50 each. If both chose QL, the payoff for each of them is (-100). If one of them produces QH, and the other QL, the former receives (-300) and the latter receives 100.

f. Draw the payoff matrix of the game, labelling the players and their strategies.

g. Find the Nash equilibria of the game. Are there any dominant strategies? Explain your logic.

h. Explain why the total quantity of public good is different in part (a) where you identified the efficient level of mosquito control and in parts (b) to (g) where the amount provided reflected the private decisions of Alan and Ben.

Answer 1

1.Detailed calculations of a b and c are given in the image

a) At social optimum Marginal social benefit has to equal marginal social cost. The social optimum mosquito control is 90 units.

b) If only one pays for mosquito control, naturally marginal private benefit is equated too marginal private cost to arrive at the optimum of 40 units of mosquito control.

c) As Ben increases his share in mosquito control, Alan spends lesser and lesser on mosquito control and begins to enjoy larger and larger levels of positive externality from Ben's share.

d) Alan imposes a positive externality on ben by producing some of the public good, mosquito control. This is a positive externality because, ben does not have to pay for it but gets to enjoy the benefits of mosquito control bought by Alan.