Question

18. (20 points) Matt's utility is given by u(x,,x2) - minfx,, x2) + minfx3, x4 Which of the following four bundles (A, B, C, and D) will he most prefer? Bundles are written (x.x2,x3,x4) a. A b. B (2, 2, 2, 2) (6, 0, 0, 2) d. D (6,1,3, 1 af(x,y,z) 19. If f(x, y.z) 3x2 + 2xyz +8y*z + Vž, find o 692when x - 1. y 2, z 3 20. If u(x1, x2) -8x1 + 4x2, find the value of MRS(8, 13). (Don't forget to include a minus sign when entering your answer!)

Answer 1

A = (2, 2, 2, 2) is correct option Because U(x_1, x_2) = min(x_1, x_2) + min(x_3, x_4) mean x_1 = x_2: x_3 = x_4 whereas min mean Both Bundle should be equal which satisfy the option A only f(x, y, z) = 3x^2 + 2xyz + 8y^3 z + squareroot z partial differential f(x, y, z)/partial differential x = partial derivative w.r.t x all other constant. = partial differential/partial differential x (3x^2 + 2xyz + 8y^3 z + squareroot z) = 6x + 2yz + 0 + 0 partial differential f(x, y, z)/partial differential x at x = 1, y = 2, z = 3 = 6 times 1 + 2 times 2 times 3 = 6 + 12 = 18 So, partial differential f(x, y, z)/partial differential x at x = 1 y = 2 z = 3 is 18 \r\n U(x_1, x_2) = 8x_1 + 4x_2 MRS(8, 13) = -MVx_1/MVx_2 = -partial differential U(x_1, x_2)/partial differential x_1/partial differential U(x_1, x_2)/partial differential x_2 = partial derivative w.r.t x_1