In this question you will study market provision of a public good. Consider two types of household with preferences over a public good ? and a composite good y,

Household A: Efgy-'1} = 2:31-11"? + If" Household B: tir [17,. y\") = 31x1\" + 1:5 Where households rank choices according to the total amount of the nu hllc good which is purchased privately, :r: = 1:\" + 173,. and their private consumption of the composite, y" for i = A, B. Households' feasible choices satisfy their budget constraints, Household 1:pr + 1"\" = 12:: emanate a: px + 3:\" = 15:: Finally, the industry cost function is x} 2 4x.