The given explanation about the marginal rate of substitution (MRS) is true. MRS is the rate at which a consumer is prepared/willing to forego some consumption of one good in exchange for another good whilst maintaining his/her level of utility. It is thus a measure of the opportunity cost of consuming one more unit of good Y in terms of units of good X. Marginal rate of substitution is always negative and decreases in absolute value as more and more units of one good are traded for another. The decrease in the absolute value of the MRS with increase in the consumption of one good against the other is called diminishing marginal rate of substitution.
The MRS is the gradient/slope of an indifferent curve. The indifferent curve itself measures the rate at which a consumer is ready to trade one good with another - it is a locus of points of all possible combinations of two goods X and Y that yields the same level of utility to the consumer. The indifference curve is downward sloping due to the need to tradeoff between consumption of two goods X and Y, and due to the negative slope of the MRS. It is convex to the origin due to the concept of diminishing marginal rate of substitution.
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