Marginal rate of substitution(yx) question

For utility function U= ln(x)+Y How do I determine if MRS(yx) is diminishing or not for this question? I got Mu(x)=1/x and Mu(y)= 1 MRS(yx)=Mu(y)/Mu(x)= 1/1/x = x

Does this mean that MRS(yx) is diminishing and why? I checked around online but I couldn't find examples where MRS just equals a variable. And does it also satisfy the law of diminishing Mu?

1 Answer

Wauw, I'm completely baffled by the questions on this site. Many of them are extremely basic.

The indifference curves (for u = 100 and depending on whether you express y as function of x or x as a function of y are):

As the MRS is the magnitude of the slope of the indifference curve we have that (see graph) when expressing x as a function of y that the slope of the indifference curve becomes much steeper as x becomes larger. Remember that x is on the second axis. This is in accordance with mrs(yx) = x. As x becomes larger (moving up along the second axis) the slope becomes steeper (or MRS becomes larger).

In the second example (which I think is much simpler) MRS(xy) = 1/x and as x becomes larger clearly the slope is going towards 0.

Regards

• Indeed many questions are basic. To discourage those, we do not provide answers. – Giskard Feb 6 at 21:40