Marginal rate of substitution (M.R.S.)
The rate at which one good must be substituted for another as a consumer moves along his indifference curve. Consider the indifference curve in the diagram below. If the individual is initially at point A, representing a particular quantity of x and a particular quantity of y, we can move him or her along the indifference curve by subtracting a small amount of x and substituting for it the appropriate amount of y. What is appropriate depends on the shape of the indifference curve and varies along it. Thus in moving from A to B a relatively small increment in y is quite enough to compensate for the reduction in x. At E, however, the same reduction in x requires a much !arger increment in y to compensate. Let us denote the (supposedly very small) change in x by dx, and the appropriate change in y – required to return to the indifference curve – by dy. The marginal rate of substitution of y for x is then defined as dy/dx, i.e. the ratio of
the required change in y to the change in x. Alternatively, if we were thinking in terms of increasing x and reducing y, we could define the M.R.S. of x for y, as dx/dy. Clearly, the two expressions are reciprocal. Mathematically, the M.R.S. measures the slope of the indifference curve, and the type of curvature normally assumed implies a decreasing M.R.S., i.e. a slope which increases in absolute value but decreases in numerical value as we move from right to left.
Reference: The Penguin Dictionary of Economics, 3rd edt.