To fund a public good, a government doesn't need to rely on voluntary contributions; it can...

  

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To fund a public good, a government doesn't need to rely on voluntary contributions; it can just impose taxes to raise funds. The problem then is actually knowing how much of a public good is efficient, which requires knowing the marginal benefit (demand) functions of all the relevant people. It is this missing in- formation that creates the true challenge of providing public goods efficiently. To illustrate this, consider a plan where the government is going to ask everyone their marginal benefit for a good. Then, when everyone reports answers, the government will impose equal taxes on each person in order to fund the level of the public good that would be efficient based on the responses. That is, the tax will be 1/N of the total cost of providing the (apparently) efficient quantity, where N is the number of relevant people. (Note that if the goverment required each person that person's marginal benefit, then this would become exactly a voluntary contribution setup.) Three people, Alex, Bill and Chris have heterogeneous, constant marginal benefits from a public good equal to 3, 6 and 18, respectively. The total cost of the public good is 0.5G. 1. (3 points) What is the efficient level of the public good? 2. (3 points) If the government were going to tax each person equally in order to fund the efficient level of the public good, what total amount of tax would each person need to pay? 3. (3 points) Suppose that the government does not know the marginal benefits but instead asks each person to report, and then will tax accordingly, assuming the answers are true. If Alex and Bill each report their true marginal benefit honestly, what will Chris report? (Hint: to solve this, start by thinking about what quantity of the public good Chris wants given the funding mechanism, and then ask what answer Chris would give so that the government will produce the amount Chris desires.) 4. (3 points) Alternatively, suppose that Bill and Chris report their marginal benefits honestly. What will Alex report? (Assume it is feasible to report a negative number.) To fund a public good, a government doesn't need to rely on voluntary contributions; it can just impose taxes to raise funds. The problem then is actually knowing how much of a public good is efficient, which requires knowing the marginal benefit (demand) functions of all the relevant people. It is this missing in- formation that creates the true challenge of providing public goods efficiently. To illustrate this, consider a plan where the government is going to ask everyone their marginal benefit for a good. Then, when everyone reports answers, the government will impose equal taxes on each person in order to fund the level of the public good that would be efficient based on the responses. That is, the tax will be 1/N of the total cost of providing the (apparently) efficient quantity, where N is the number of relevant people. (Note that if the goverment required each person that person's marginal benefit, then this would become exactly a voluntary contribution setup.) Three people, Alex, Bill and Chris have heterogeneous, constant marginal benefits from a public good equal to 3, 6 and 18, respectively. The total cost of the public good is 0.5G. 1. (3 points) What is the efficient level of the public good? 2. (3 points) If the government were going to tax each person equally in order to fund the efficient level of the public good, what total amount of tax would each person need to pay? 3. (3 points) Suppose that the government does not know the marginal benefits but instead asks each person to report, and then will tax accordingly, assuming the answers are true. If Alex and Bill each report their true marginal benefit honestly, what will Chris report? (Hint: to solve this, start by thinking about what quantity of the public good Chris wants given the funding mechanism, and then ask what answer Chris would give so that the government will produce the amount Chris desires.) 4. (3 points) Alternatively, suppose that Bill and Chris report their marginal benefits honestly. What will Alex report? (Assume it is feasible to report a negative number.)

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Finding the Efficient Level and Equilibrium in Public Good Provision 1 Efficient Level of the Public Good The efficient level is achieved when the sum of the marginal benefits demand equals the margin... View the full answer