Let Y be a public good, and X be a private good which can be either consumed or used in the production of the public good. There are three households. Each household has an endowment of 100 units of the private good and zero units of the public good. Preferences of the households are given by: u1(x1, y) = x1 + 2(y) 1/2, u2(x2, y) = x2 + 6(y)1/2, u3(x3, y) = x3 + 8(y) 1/2. The public good is produced according to the production function y = f(x) = (1/2)x

a) What is the marginal cost of Y (in terms of the private good X)?

b) Find the set of Pareto-efficient allocations.