utility function is given as Cobb Douglas functional form: U=x10.5x20.5 Price the first good: p1=5$ Price the second good: p2=10$ Income: I = 500$ A) a) Find the Budget equation and derive the slope of this budget equation. b) Set up the Utility Maximization Problem (UMP) or Primal Problem and construct the Lagrangian function c) Find the Marshallian (Uncompansated) demand functions and calculate the optimal quantities of goods: x1 and x2 d) Compute Indirect Utility Function (Value Function) and maximum Utility value. e) Find the equation of the Indifference Curve (IC) and calculate the slope of this indifference curve (Marginal rate of substitution: MRS) at the optimal point (tangency point) f) Verify that at consumer equilibrium point " slope N of Indifference Curve (MRS) is equal to "slope N of Budget Constraint Equation (Relative Price Ratio) B) a) Set up the Expenditure Minimization Problem (EMP) or Dual Problem and construct the Lagrangian function b) Find the Hicksian (Compansated) demand functions and and calculate the optimal quantities of goods: x1 and x2 c) Calculate Expenditure function d) Show that both Marshallian and Hicksian demands functions initially provide identical numerical values C) a) If the price of the first good decrease to 4$(p1=4$) then find the new (final) Marshallian and Hicksian demand functions for the first and second goods b) Find the difference between new and old Marshallian demands for the first good: (x1 new x1 old). This difference is called as the "Total Effect" (TE) c) Find the difference between new Hicksian demand and old Marshallian demands for the first good. This difference is called as the "5ubstitution Efect" [5E). d) Find the difference between new Marshallian demand and and new Hicksian demand. This difference is called as the "Income Effect" (IE) e) Show that TE=SE+IE