1.Suppose that two individuals, Jon and David, form a community and would  like to construct a communal fort that would protect them from attacks.  They both consume good X, a private good, and the protection of the fort, P. One unit of good X costs 1 unit of currency, and one unit of P costs 2 units of currency. Both Jon and David have an income of 100 and a utility function of the form:

U = log(Xi) + 2 × log(PJ + PD)
The budget constraint for each is given by:
Xi + 2 × Pi = 100

(a)  Find the amount of protection Jon will provide as a function of how  much David provides, and explain why the relationship is the way it is.

(b) How much protection P will be privately provided in this case?

(c)  Explain the economic intuition behind this amount, and compare it to  the socially optimal amount without solving for the socially optimal  amount.

2Roads are typically viewed as a public good. However, some highways are  financed by tolls levied on drivers instead of through taxes. Discuss  why this model works for some roads and not others in terms of the  properties of public goods.

3Suppose someone observes that people in areas where residents have more  education tend to donate more money for local parks than do people in  areas where residents are less well educated, and the observer concludes  that education increases altruism. Use what you have learned in this  course to evaluate the validity of this conclusion.