Consider a community consisting of three persons, $i=1,2,3$. The following utility function

Consider a community consisting of three persons, a" = 1, 2, 3. The following utility function represents person is preferences over the amount of public good provisionF g: Uzi = Och/E 03'; where 051- is person is preference parameterT satisfying 0 U for 2'. = 1= 2, 3. [1) Formulate the optimization problem to solve a Paretoeicient allocation in this so ciety; taking person 1's utility function as the objective function. [2) Solve the problem formulated above and show the Paretoefcient level of the public good. (You need differentiation]