Consider 3 agents, i = 1,2,3 with utility function ui(xi,G)=lnxi+ilnG. Suppose that each agent has capital i=1 , which can be invested in the production of the private good or towards the production of the public good. Suppose the production technology for all goods are linear, i.e., f(z)=z for all z0 (and the total investment in public good equals the sum of individual investments).

1) What is the Lindahl equilibrium?

2) Consider the case in which i=1i . Suppose we wish to have a social planner implement the equilibrium allocation, but she cannot observe i . All agents must report their value of i to the planner, and the planner assumes that the reports she receives are truthful. Suppose agents 2 and 3 report the truth, that i=1 . Show that agent 1 can benefit from misreporting his value of i