Consider an economy with a private good and public good. The economy consists of two consumers whose utility functions are: u1(x1, y) = 1 2 ln x1 + 1 2 ln y and u2(x2, y) = 1 3 ln x2 + 2 3 ln y. The endowment of consumer 1 is w1 = 2, and the endowment of consumer 2 is w2 = 3, both in units of private goods. The production of public good uses the linear technology y = z.

1. What is the voluntary contributions equilibrium.

2. What is the Lindahl equilibrium.