Question

1) Consider the following mechanism as a solution to the public goods prob- lem. The public good, G, is discrete (if it is provided it must be provided at G 1. There are two agents i = 1,2 who have reservation prices for the public good rwhich are not known by the government. c is the cost of providing the public good and s is agent i's cost share such that s s2 = 1. Each agent reports a net valuation for the public good b'. Each agent believes that if and only if bb2 >0 the public good will be provided. Would you expect this mechanism to yield truthful revelation of preferences? Explain. Most marks will be given for your explanation

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Answer 1

A good is considered as public good if is satisfies non-rival and non-excludable criterion. Here, G is a discrete public good that must be provided at the level of 1.

Now, suppose the agents reveal their reservation prices as r1 and r2 but they always have incentive not to reveal their actual preference as there is always a chance of free ride. The preference is revealed by valuation of the good and if the sum of the values of all agents are at least equal to zero, G will be provided. However, if the agent reveals less valuation for G, he also has to bear less share of cost. So the challenge for the government to design a mechanism so that each individual reveal their preferences truthfully.

The possible mechanism can be Vickrey-Groves-Clarke (VCG) mechanism. Using an numerical example, satisfying the given circumstances, we will explain the mechanism.

For sake of simplicity, let us assume that G is a public park. Net valuations for the park to agent 1 & 2 are $20 & $90, respectively. The cost of building the park (c) = $100. If the cost is splitted equally, each member will pay $100/2=$50.

Given the cost $60, 1st agent's net valuation is ($20-$50=) -$30 and 2nd agent is ($90-$50=) $40.

The park will be built because, net valuation ($20+$90=$110) exceeds the cost ($100).