Explain why taking a monotonic transformation of a utility function does not change the marginal rate of substitution (MRS).

Monotonic transformation refers to changing the quantity of both the variables in a way that their ranking or order is preserved. Monotonic transformation of a utility function does not change the marginal rate of substitution as the order of preferences remains intact with the monotonic transformation. It's just the level of utility that either increases or decreases with such a transformation. The indifference curve shape remains the same. With monotonic transformation, consumer moves from a lower to higher or higher to lower indifference curve.