The correct answer is $\boxed{\frac{{{\text{Change}}\,{\text{in Y commodity}}}}{{{\text{Change}}\,{\text{in X commodity}}}}}$.
The marginal rate of substitution (MRS) is the rate at which a consumer is willing to give up one good in exchange for another good, while maintaining the same level of satisfaction. It is a measure of the relative marginal utilities of two goods.
The marginal utility of a good is the additional satisfaction that a consumer gains from consuming one more unit of that good. The marginal utility of a good decreases as the consumer consumes more of that good.
The MRS is calculated by dividing the marginal utility of one good by the marginal utility of another good. For example, if the marginal utility of good X is 10 and the marginal utility of good Y is 5, then the MRS of X for Y is 2. This means that the consumer is willing to give up 2 units of good Y to obtain 1 unit of good X.
The MRS is a useful concept for understanding consumer behavior. It can be used to predict how consumers will respond to changes in prices and incomes. It can also be used to analyze the optimal consumption bundle for a consumer.
The other options are incorrect because they do not measure the marginal rate of substitution. Option A is the marginal utility of good X. Option B is the marginal utility of good Y. Option C is the change in the quantity of good X divided by the change in the quantity of good Y. This is the slope of the consumer’s indifference curve. The slope of the indifference curve is not the same as the MRS. The MRS is the negative reciprocal of the slope of the indifference curve.