The monotonicity assumption tells us that cosuming more of a good is always better or for any normal goods or for any "good" commodity, the marginal utility derived from that good is always positive or greater than zero. i.e MU of a particular good is positive.
Marginal rate of substitution tells us the rate at which we must give up some units of good Y to get one extra unit of good X. This is shown by the slope of the indifference curve. A negative slope means that as we move along an indifference curve, we sacrifice smaller and smaller amount of good y to get one extra unit of good X. This is known as the diminishing marginal rate of substitution between two goods.
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