Which of the following functions is not a Cobb-Douglas function?
z(x,y)=5x12y12−3x12y12.
z(x,y)=√2x0.1y0.9.
z(x,y)=4√16xy3.
z(x,y)=5x−12y32.
Correct: z(x,y)=5x−12y32 can be rewritten to the form kxαy1−α, with k>0. However, α=−12<0.
Go on.
Wrong: z(x,y) can be written in the right form:
z(x,y)=5x12y12−3x12y12=2x12y12.
Hence, z(x,y) is a Cobb-Douglas function with k=2 and α=12.
See Cobb-Douglas functions.
Wrong: z(x,y) is a Cobb-Douglas function with k=√2 and α=0.1.
See Cobb-Douglas functions.
Wrong: z(x,y) can be written in the right form:
z(x,y)=4√16xy3=2x14y34.
Hence, z(x,y) is a Cobb-Douglas function with k=2 and α=14.
See Power functions or Cobb-Douglas functions.