Question

Use the following table to indicate whether the marginal rate of substitution (MRS) of each utility function increases, decreases, or is constant as x increases. MRS Increases with Utility Function Ux,y)- 3x y U(x,y) = MRS Decreases with x Constant MRS MRS Increases withx x-y U(x,y) =

Answer 1

MRS = MO_x/MU_y = partial u/partial x partial u/partial y (i) U (x, y) = 3x + y MRS = 3 implies constant MRS U (x, y) = squareroot xy MRS = squareroot y 1/2 squareroot x/squareroot x 1/2 squareroot y implies y/x MRS decreases with x U (x, y) = squareroot x + y MRS = 1/2 squareroot x/1 = 1/2 squareroot x Declares with xr\n U (x, y) = squareroot x^2 - y^2 MRS = 1 (2x)/2 squareroot x^2 - y^2 implies x/squareroot x^2 - y^2 times squareroot x^2 - y^2/2y 1 (- 1) 2y/2 squareroot x^2 - y^2 MRS = x/2y MRS Increases with x U (x, y) = xy/x + y MRS = y [partial (x/ x + y)/partial x]/x [partial/partial y (y/x + y) implies y[1 (x + y) - (x)/(x + y)^2/x [1 (x + y) - y/(x + y)^2 = y^2/x^2 \r\n MRS decreases with x increases Now checking the strictly diminishing
Similarly the fifth part can solved.