Marginal Utility and MRS:

Assume that our original bundle is bundle C in our previous example, and that we add one unit of good 1 so that we end up with bundle B. The marginal utility of good 1 is then,

MU₁ = ΔU/ΔQ₁ = [U(B) – U(C)]/ ΔQ₁

If we now add one unit of good 2 to bundle B, we end up with bundle A, and the change in utility is,

MU₂ = ΔU/ΔQ₂ = [U(B) – U(C)]/ ΔQ₂

The actual numbers can easily be seen to be MU₁ = 2, and MU₂ = 3. But again these numbers have no specific meaning. However, let us take the ratio of these expressions,
 
Note that the last ratio is (the negative of) the marginal rate of substitution between good 1 and 2, hence,

MRS₁₂ = - MU₁/MU₂

An important point here is that if we apply any of the transformation in the previous example, the marginal utilities would be affected by (most of) these transformations, but the MRS₁₂, which shows the shape of the indifference curves, would not.

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