Answer to Question #293196 in Microeconomics for Umkal

Question

Given U(x, y)=10x0.6y0.4 a) Marginal utility of the two commodities when x-2 and y= 3 (1 points). b) Find Marginal Rate of Substitution when x-y-2 (0.5 points).

Answer 1

a) Marginal utility of the two commodities when x = 2 and y = 3 is:

$MUx = U'(x) = 6y^{0.4}/x^{0.6} = 6.14,$

$MUy = U'(y) = 4x^{0.6}/y^{0.4} = 3.91.$

b) The Marginal Rate of Substitution when x = y = 2 is:

$MRS x,y = -MUx/MUy = \frac{6×3^{0.4}/2^{0.6}}{4×2^{0.6}/3^{0.4}}= -1.57.$