Question

5.         What would be the marginal utility of x (MU_x) and the marginal utility of y (MU_y) if the      utility function is expressed by?

U = 5 x^0.35 y^0.65

            Also, calculate the numerical values of those marginal utilities, and the MRS when:

            x = 10, and y=40

6.         As a student, David’s lunch has always been bagel and cream cheese. He rarely could afford           to buy a decent meal. Now that he graduated and got a good paying job, he has been going to    a good restaurant for lunch, and very seldom eats bagel and cream cheese anymore. Draw his         Income-Consumption Curve (I-CC), and show where his equilibrium point would be

Answer 1

5.

U = 5x^0.35 y^0.65

MUx = Partial derivative of U with respect of x

         = (5 × 0.35){x^(0.35 – 1)}y^0.65

         = 1.75 × x^(-0.65) × y^0.65

         = 1.75y^0.65 / x^0.65 (Answer)

MUy = Partial derivative of U with respect of y

          = (5 × 0.65){y^(0.65 – 1)}x^0.35

         = 3.25 × x^0.35 × y^(-0.35)

         = 3.25x^0.35 / y^0.35 (Answer)

Numerical values:

MUx = 1.75y^0.65 / x^0.65

          = 1.75 × 40^0.65 / 10^0.65

          = 1.75 × 10.99864 / 4.46683

          = 4.309 (Answer)

MUy = 3.25x^0.35 / y^0.35

         = 3.25 × 10^0.35 / 40^0.35

         = 3.25 × 2.23872 / 3.63681

         = 2 (Answer)

MRSxy = MUx / MUy

              = 4.309 / 2

              = 2.1545 (Answer)

MRSyx = MUy / MUx

              = 2 / 4.309

              = 0.464 (Answer)