3. Find the MRS or MTRS of the following functions.
a) Utility function: U(x)= 2x1^1/3x2^2/3
dy= f1dx1+f2dx2= (2/3x1^-2/3 x2^2/3)dx1+(4/3x1x2^-1/3)dx2=0
dx2/dx1]dy=0 =2/3x1^-2/3x^2/3/4/3x1^1/3x2^1/3 = MRTS x2/2X1
b) Cobb-Douglas function: Y=3x1^alfa X2^beta
dy= (alfa3X1^alfa-1 X2^beta)dx1 + (beta3X1^alfa X2^beta-1)dx2=0
dx2/dx1=]dy=0 =-alfa3x1^alfa-1X2^beta/beta3X1^alfa X2^beta-1 = MRTS alfaX2^beta/betaX1^alfa
c) Utility function: U(x)= X1X2
dy=(X1^-1X2)dx1 + (X1X2^-1)dx2=0
dx2/dx1=]dy=0 =X1^-1X2/X1X2^-1 = MRTS X2/X1
5. Show that:
a)f(x1,x2)=(2x1+2)