Marginal Rate of Substitution:

Let us assume that we are dealing with a consumer with well-behaved preferences. If we start from point A in figure shown below and consider an increase in the consumption of good 1, by the increment ΔQ₁, we may ask by how much we must reduce the consumption of good 2 in order to keep the consumer on the indifference curve through A (i.e., to end up at point B). Well, from the figure it is clear that this decrease is equal to ΔQ₂. Note that I’ve drawn a line through points A and B. The slope of this line is equal to,

−ΔQ₂/ΔQ₁

This slope turns out to be quite important, in fact so important that economists have given it its own name: the marginal rate of substitution between good 1 and 2, (MRS₁₂). If we make ΔQ₁ very small ΔQ₂ would likewise be very small, and in this case the MRS₁₂ shows the slope of the indifference at a single point. The importance of MRS₁₂ is that is shows the extent to which the consumer wants to exchange good 2 for more of good 1. It is the “internal” rate of exchange between the two goods. Another useful interpretation is that MRS₁₂ shows how much the consumer is willing to pay (in terms of good 2) in order to acquire one more unit of good 1. It shows the marginal willingness to pay, for good 1 (in terms of good 2). The phrase “in terms of good 2j is somewhat awkward to add all the time, but it is necessary to be clear about the units we use in measuring MRS₁₂. Things become easier to interpret (and remember) in the case where x₂ stands for “all other goods”, or simply money income, because in that case MRS₁₂ shows the marginal willingness to pay for good 1 in terms of money.

The convex shape of a well-behaved indifference curve means that MRS₁₂ decreases, or “diminishes” as we slide down the indifference curve, from the left to the right. In economic terms this means that the marginal willingness to pay for an additional unit of good 1 is high when the consumer has relatively little of good 1, and a lot of good 2 (money), and that the more of good 1 he/she gets (and the less money left over) the less will be the marginal willingness to pay for an additional unit of good 1.

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