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  Marginal Utility and MRS

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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