Question

can be described by the utility function U(r, y)102. Prices Sally the Sleek's preferences are pz 2 and py 4. (a) If Sally initially consumed 10 units of and 5 units of y, how much could she save if she consumed 8 more (small) units of x and kept utility constant?1 Therefore, can it be optimal to (b) Sally decides that she wants a level of U 27. What is the minimum she would have to spend c) What is the cost of one additional (small) unit of extra utility in that case? [If you use decimals, consume the bundle (10,5)? (4]) in order to attain that utility? (4) round to two decimal places after the zero.] (2)

Answer 1

v(x, y) = x^3 y^2/1024 P_x = 2 P_y = 4 x = 10 & y = 5 Budget = 2(10) + 5(4) = 40 U = (10)^3 (5)^2/1024 = 24.419 If sally consume x = 10 + 8 = 18 then (18)^3 y^2/1024 = 24.414 y^2 = 25000/(18)^3 = 4.28669 y = 2.0704 Budget required = 2.0704 (4) + 18(2) = 44.2817 Thus $ 4.2817 mass of spent when x = 18 If U^bar = 27 At Eqn MRs = P_x/P_y = > 3x^2 y^2/2x^3 y = > 3y/2x = 2/4 3y = x & U = 27 = x^3 y^2/1024 = > 27 = (3y)^3 y^2/1024 27 times 1024/27 = y^5 = > y = 4 & x = 12 Budget = 2(12) + 4(4) = 24 + 16 = 40 In order to get U = 28, 28 = 27/1024 y^5 y^0 = 4.029 & x = 12.087 Cost = 4.029 (4) + 12.087 (2) = 16.116