Consider a standard Fisher Economy. Assume that the population is divided between groups of individuals (we will call them Group A and Group B) and that there are three times as many individuals in Group A as compared to Group B. Suppose the two Groups (A and B) have the following endowments (10, 20) and (20, 10), respectively. Also assume that utility is given by 1 U(CIC2) = C? + \"CZ a. Write down the consumer's generalized, constrained maximization problem for each group. Graphically illustrate autarky for a typical member of each group. Be specific. What are the equations of the budget constraints from your graphs? b. Write down the appropriate Lagrangian equation for Group A individuals. (you do not need to solve it!) c. Derive the savings function for both groups of individuals. Do these savings functions satisfy our assumptions. Dene equilibrium in words. Write down the market clearing equation and illustrate it graphically. d. Solve for equilibrium (be complete\"). How does Group A's and Group B's behavior differ in equilibrium? Graphically illustrate equilibrium for a typical member of each group. Does the savings market clear