Which of the following functions is not a Cobb-Douglas function?

z(x,y)=5x12y123x12y12.

z(x,y)=2x0.1y0.9.

z(x,y)=5x12y32.

z(x,y)=416xy3.

Which of the following functions is not a Cobb-Douglas function?

Antwoord 1 correct
Correct
Antwoord 2 optie

z(x,y)=5x12y123x12y12.

Antwoord 2 correct
Fout
Antwoord 3 optie

z(x,y)=2x0.1y0.9.

Antwoord 3 correct
Fout
Antwoord 4 optie

z(x,y)=416xy3.

Antwoord 4 correct
Fout
Antwoord 1 optie

z(x,y)=5x12y32.

Antwoord 1 feedback

Correct: z(x,y)=5x12y32 can be rewritten to the form kxαy1α, with k>0. However, α=12<0.

Go on.

Antwoord 2 feedback

Wrong: z(x,y) can be written in the right form:
z(x,y)=5x12y123x12y12=2x12y12.
Hence, z(x,y) is a Cobb-Douglas function with k=2 and α=12.

See Cobb-Douglas functions.

Antwoord 3 feedback

Wrong: z(x,y) is a Cobb-Douglas function with k=2 and α=0.1.

See Cobb-Douglas functions.

Antwoord 4 feedback

Wrong: z(x,y) can be written in the right form:
z(x,y)=416xy3=2x14y34.
Hence, z(x,y) is a Cobb-Douglas function with k=2 and α=14.

See Power functions or Cobb-Douglas functions.