MRS is the amount of consumption of one good that is given up to increase consumption of another good. Since amount of one good will decrease (-) and the amount of the other good will increase (+), the sign is negative.
Mathematically,
MRS = - (MU1 / MU2), where MU: Marginal utility
Negative sign of MRS is also understood when we look at the indifference curve (IC). The IC slopes downward, so it has a negative slope as we move along the IC, reflecting the fact that as we consume more of 1 good, we consume less of the other. Since MRS is the slope of IC, the sign of MRS is negative.
Why is there a negative sign? can you please explain the derivation of this formula? 10:35...