Show that the utility functions V(X,Y) = XaY1-a and U(X,Y) = a ...

[naturalchemist]

Show that the utility functions V(X,Y) = XaY1-a and U(X,Y) = a ln(X) + (1-a)ln(Y) represent the same ordering of bundles.
 
  What will be an ideal response?

Question 2

A specific tax in a monopoly market equal to the marginal harm of pollution
 
  A) will increase welfare.
  B) will decrease welfare.
  C) will leave welfare unchanged.
  D) All of the above are possible.

[macagnavarro]

Answer to Question 1

ln(V(X,Y)) = ln(XaY1-a) = ln(Xa) + ln(Y1-a) = U(X,Y)
Because ln(x) is a monotonic increasing function, the preference ordering is preserved.

Answer to Question 2

D