Two individuals A and B have identical preferences over two goods: X (a pure public good) and Y (a private good). Preferences are represented by U i(XA + XB , Yi) = 4 ln(XA + XB ) + 3 ln(Yi) for i = {A, B}. The price of X is pX = 4 per unit and the price of Y is pY = 1 per unit. Each individual has I = 700 dollars to spend on X and Y . 1. First, consider the private market outcome. a) Use "MRS equals price ratio" for A to solve for a relationship between XA + XB and YA. b) Use A's budget constraint to solve for a relationship between YA and XA. c) Exploit symmetry (XA = XB = X) to find the private provision of X for each individual. d) Find the private market levels of XA + XB , YA, and YB . 2. Next, consider the socially optimal outcome. a) Use the social optimality condition to solve for a relationship between XA + XB and YA + YB . b) Use the joint budget constraint to find the socially optimal XA + XB . c) Find the socially optimal levels of YA and YB . 3. The government wants to implement Lindahl pricing to reach the socially optimal level. a) At the socially optimal allocation, what is each individual willing to pay per unit for the socially optimal XA + XB units? b) What is the total willingness to pay per unit for the socially optimal XA + XB units? Is this enough to fund the provision of the socially optimal XA + XB units?