Attila (A) and Francis (F), live on Coconut Island and face the problem of determining the amount of military defense they need to repel a potential invasion from neighboring islanders. Defense is a jointly consumed pure public good. They agree to finance their defense expenditures with a benefit tax based on their respective demands for the public good. The demand functions for Attila and Francis are, respectively,
PA = 46 - Q (Attila)
PF = 24 - Q (Francis)
where PA is the price per unit of the public good (unit tax) paid by Attila and PF is the price paid by Francis. The marginal cost of providing a unit of defense is flat at $30 per unit.
1. What is the optimal quantity of public good services supplied by the government to Attila and Francis?
2. What is the total cost of providing the optimal amount of the public good?
3. What tax/price does Attila pay per unit of the public good (i.e., what is PA)?
4. Suppose, now, that there is a third person, Slack, who benefits from the public good without any charge. What is the new optimal quantity of public good to provide Slack, Attila, and Francis if Slack were to be caught
5. What is the optimal tax/price to charge Slack if he were to be caught and his true demand found to be PS = 20 - Q?
How does your answer to the above questions change if Slack's true demand is found to be PS = 32 -Q?
How does your answer to the above questions change if the tax/prices (as determined in question 1-5 above) which were used to finance the public good are abolished and replaced with a general income tax. Slack, Attila, and Francis all have the same level of income and therefore pay the same amount of tax. The government continues to supply the optimal amount of public good determined in question 4 (i.e., when Slack's demand is thought to be PS = 20 - Q?
What happens to the demand for the public good in the case where the public good is only one small program among many, and is financed out the general income tax fund (so small that it does not have a noticeable effect on income tax burdens. In this situation, what is the perceived cost of each additional unit of the good, and how much is demand?
Finally, suppose that the good in question is a pure private good rather than a pure public good as in the preceding set of questions. The individual demand functions are now QA = 46 - P for Attila, and QF = 24 - P for Francis. Marginal cost is flat at $20. What is the value of QF, the quantity consumed by Francis, QA, and P.