substituting the zero profit condition above so that

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Unformatted text preview: B = 0.3 X = 0.5 YA = 0.2 YB = 0.3 Y = 0.5 Solving for equilibrium quantities XA = 0.5 XB = 0.5 X = 0.5 YA = 0.2 YB = 0.3 Y = 0.5 And the prices that consumer A and consumer B are willing to pay for the same amount of public good X PXA = 0.2r + 0.6w 2X PXB = 0.8r + 0.4w 2X = 0.8 = 1.2 INCENTIVE MECHANISM So we have addressed the issue of optimal allocation of public goods (Samuelson) and the issue of pricing public goods (Lindahl) but if you can recall the beginning of the class, we said there were three issues surrounding public goods. The third issue is the free rider do we get people to reveal their willingness to pay for a public good? For that matter, how do we get them to be willing to pay anything at all? So to have an appropriate solution to the Lindahl pricing method above, we need a truthful reporting of individual's willingness to pay for the public good. If people do not truthfully reveal the prices that they are willing to pay for the public good, X, the method of vertical summation will yield an incorrect market demand for the public good. Consequently, the market equilibrium condition Demand = Supply will give us an incorrect equilibrium quantity of the public good in the economy. Presumably, with an under-reporting of WTP there will be an under-provision of the public good in the market. Why might people lie about or otherwise mis-report their willingness to pay for public goods? 249 By their very nature, public goods are available to all consumers in the economy regardless of whether they contribute to the cost of their production or not. We cannot exclude those who do not pay nor can we distribute the public good to only those that pay. Consumers generally learn quickly that if they do not reveal their demands for public goods, they can get away with paying less than what they should have paid for their consumption of the public goods (or even not pay at all). On the other hand, they cannot be prevented from enjoying the public goods and so there are economic incentives fo...
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