If the formula for my marginal rate of substitution at any c

If the formula for my marginal rate of substitution at any commodity bundle(x,y) only depends on my consumption level of X, what can you conclude about my indifference curves in the (X,Y) plane?

Solution

Say, U=10=(xy)^(1/2); or, y=100/x

So, MRS=dy/dx=-100/x^2

Hence, this is a non-homothetic utility function as MRS does not depend on both y and x.