Suppose the utility function for good €, f and tis given by U(c, 6.t) = 2vc + 2Vf +t _ where denotes the units of clothing the units of food, and the units of traveling: Let denotes income level, pe the price of one unit of clothing. pf the price of one unit of food, and pt the price of one unit of trave veling: a) Set up the Lagrangian and derive the uncompensated (Marshallian) demand functions for all goods b) Derive the compensated (Hicksian) demand functions for all goods Suppose that initially pe pf = 1_ p = and [ = 10. Determine the substitution effect and income effect for traveling when the price of traveling increases t0 pt