Consider an economy with two individuals, A and B, with quasi-linear preferences over a private good x_i with i = A,B, and over a public good, G, represented by the utility function U(x_i, G) = x_i + lnG. Each of them has income m_i with i = A, B that can be spent on the private good x_i or contributed to the public good, G. Each individual's contribution is g_i. One unit of individual contribution is used to produce one unit of the public good, G . The social planner has a Rawlsian social welfare function given by: W(U_A,U_B) = min{5U_A, 5U_B}. a) Write the budget constraint for each individual, A and B. b) Derive the Lagrangean corresponding to the optimization problem of individual B. c) Calculate the first order conditions. d) Derive the best response function for individual B, g_B. e) Calculate the demand functions for x_i (the private good) and G (the public good)