The marginal rate of substitution between two goods must be equal the ratio of prices of the goods the consumer to achieve maximum satisfaction. A consumer achieves maximum satisfaction, when the MRS is equal to the ratio because otherwise the consumer could trade one good for another at market prices to obtain a higher level of satisfaction.
If new items meet customers' needs equally, the marginal rate of substitution in economics measures the quantity of new goods consumers are willing to buy compared to a comparable good.
The change in good X (dx) divided by the change in good Y is the marginal rate of substitution formula (dy). Since it is always negative, the amount of good that is sacrificed is good X. Gained in exchange is always positive Y.
The marginal rate of substitution (MRS), which assumes that two items give the same level of value and satisfaction, establishes whether or not a consumer would switch from one good or service to another.
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