Two individuals A and B have utility functions defined over two goods, a private good ‘x’) and a public good, ‘F’. The utility function of an agent ‘i’ is defined by ui = 2 log xi + log F where F =FA + FB. Each agent has 200 units of private goods x, as his endowment and 1 unit of private good can be transformed into 1 public good F.
Answer the following
(a) Find the Nash equilibrium values of FA and FB?
(b) What is the Pareto optimal level of F?
(c) In what condition the Pareto optimal level of F will not depend on the number of private goods?
(d) What would be the consumption of x by each agent if they contribute equally towards the public good (F)?
(e) Would it change if an agent had a larger endowment of x to begin with?
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