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.

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

e) There is a free rider problem in private provision because people would have an incentive to under report the value of the benefits they derive from the mosquito control. Since it is a public good and everyone would be receiving it, whether they pay or not, it would lead to free rider problem.

f) Alan

Ben

	Ql	Qh
Ql	(-100,-100)	(100,-300)
Qh	(-300,100)	(50,50)

There are two players Alan and Ben and there are two strategies, either to provide mosquito control Qh or not provide mosquito control Ql

The payoffs are given in the matrix above.

g) When Ben chooses Ql, it is better for Alan to choose Ql and when Ben chooses Qh, Alan is better off by choosing Qh. So in both cases, Alan is better off choosing Ql ie no provision.

When Alan chooses Ql, Ben is better off choosing Ql as the payoff is higher and when Alan chooses Qh, Ben would still choose Ql. So the nash equilibrium would be (Ql, Ql)

Both Alan and Ben have a dominant strategy of choosing Ql ie no provision.

This is because both would want to get the benefits derived but would not want to incur the cost.

h) The efficient level of mosquito control would be different from the private decisions, because the efficient one is based on the costs and benefits of the society as a whole. When the provision of mosquito control is done, there would be positive externalities, because there would be less mosquitos and hence less diseases from them. But when there is private decision, it would be based on only the costs and benefits of the individual ie MPC and MPB and so the answers would be different.

(You can comment for doubts)