4. For the each of the following functions: 1) find a function for an indifferen

Question

4. For the each of the following functions: 1) find a function for an indifference curve that delivers u=u? units of total utility: 2) Calculate the derivative (dy/dx) of the function (i.e. the instantaneous rate of change).

      a. u(x,y) = 3x + 2y

      b. u(F,C) = 10FC

      c. u(F,C) = .2F2C2

5. Find the total differentials of the following functions:

      a. u(x,y) = ax + by

      b. u(F,C) = 10FC

      c. u(F,C) = .2F? C?

      d. u(x,y) = (XY)1/2

         e.  z = 2x3-11x2y +3y2

6. Find the MRS for the following utility functions:

      a. u(x,y) = 3x + 2y

      b. u(F,C) = 10FC

      c. u(F,C) = .2F2C2

Explanation / Answer

4 (a) 1. u(x,y) = 3x + 2y = u => 2y = u - 3x

2. dy/dx = -MU(x)/MU(y) = -3/2

(b) 1. 10FC = u =>C = u/10F

2. dC/dF = -10C/10F = -C/F

(c)1. 0.2F^2C^2 = u => C^2 = 5u/(F^2)

2. dC/DF = -0.4F*C^2/0.4C*F^2 => -C/F

5. (a) du = a*dx + b*dy

(b) du = 10C*dF + 10F*dC

(c) du = 0.4F*C^2*dF + 0.4F^2*C*dC

(d) du = 0.5(Y/X)^0.5*dX + 0.5(X/Y)^0.5*dY

(e) dz = (6x^2 - 22xy)*dx + (6y - 11x^2)*dy

6. (a) MRS(x,y) = MU(x)/MU(y) = 3/2

(b) MRS(F,C) = 10C/10F = C/F

(c) MRS(F,C) = 0.4FC^2/0.4CF^2 = C/F

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