what is the marginal rate of substitution mrs 
in economics the marginal rate of substitution mrs is the amount of one good that a consumer is willing to give up in exchange for a new good while maintaining the same level of utility mrs is used in indifference theory to analyze consumer behavior when someone is indifferent to substituting one item for another their marginal utility for substitution is zero since they neither gain nor lose any satisfaction from the trade investopedia madelyn goodnightformula and calculation of the marginal rate of substitution mrs the mrs formula is m r s x y d y d x m u x m u y where x y two different goods d y d x derivative of y with respect to x m u marginal utility of good x y begin aligned mrs xy frac dy dx frac mu x mu y textbf where x y text two different goods frac dy dx text derivative of y with respect to x mu text marginal utility of good x y end aligned mrsxy dxdy muy mux where x y two different goodsdxdy derivative of y with respect to xmu marginal utility of good x y 