Mathematical Derivation of the MRS Formula
Starting from the principle that total utility remains constant along an indifference curve, provide a step-by-step mathematical explanation for why the Marginal Rate of Substitution (MRS) is equal to the ratio of the marginal utilities of the two goods. Assume a consumer's preferences are represented by a utility function U(x, y), where x is the good on the horizontal axis and y is the good on the vertical axis.
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Mathematical Derivation of the MRS Formula
A consumer's preferences over two goods, Good X (on the horizontal axis) and Good Y (on the vertical axis), are described by a utility function. Arrange the following steps in the correct logical sequence to derive the formula for this consumer's Marginal Rate of Substitution (MRS).