Question

The utility function U(x1, x2) = lnx1 ^5 + lnx2^2 represents Cobb- Douglas preferences. Show if it is true or false. (without using graph)

Answer 1

Using product rule of log i.e. ln(ab) = ln(a) + ln(b)

So,

So, U(x1, x2) = ln(x1​​​​​5​​​x2​​2)

Now, We know using monotonic transformation of exponents we can transform the above function as

As, Monotonic transformation of a utility function represents the same preferences as the original utility function.  

We know, represents a Cobb Douglas form of where a=5 and b=2.

So the utility function will also represent Cobb Douglas preferences.

• Hence, It's TRUE