Please help with calculating the MRS!?

Question

I have a utility function:

U(X,Y) = 2X +12lnY

This appears to be a function for perfect substitutes so MUx would be 2, easy enough. Now onto MUy. I know that the derivitive of a lorgorithm such as lnX would be 1/X. Does this mean that MUy would be 12/Y --- (12*1/Y)?

Giving an MRS of 2/(12/Y)? I think I have the MUY and subsequent MRS wrong since i should be getting an MRS that looks like a/b where a and b are the positive constants infront of X and lnY. Can anyone help me with this?

Answer 1

No, you are right, MUy is 12/Y.

MUx/MUy = 2/(12/Y) = (2/1)/(12/Y) = 2Y/12, or Y/6.