Question

If I have a utility function ,u(w)=w^2, do I exhibit diminishing marginal utility?

1) Yes

2) No

Answer 1

If marginal utility is positive, then as we consume more units of the good our utility increases.

To determine whether a utility function exhibits diminishing marginal utility (that is, as our consumption of the good increases by each unit, the utility we derive from consuming that unit gradually decreases), we need to differentiate marginal utility with respect to w (according to this question).

If the differentiation gives us a negative value (<0) then we can say that the utility function is exhibiting diminishing marginal utility.

The utility function is such that-

u(w) = w^2

Differenting the utility function with respect to w (which gives us the marginal utility)

MU= u`(w) = 2w

Differentiating MU with respect to w,

MU`(w)= 2 >0 ( Increasing utility )

So, this utility function does not exhibit diminshing marginal utility.

The answer is No.