def. Marginal Rate of Substitution. asks “How much of can you give me for one unit of ?”

  • means MRS of good for good , i.e. “one unit of for how many units of ?""

x_{1},x_{2} changes spots in the nominator/denominator in the final formula.

  • The tangent of Utility Function at a certain point is the MRS at that specific point (more accurately, its absolute value of the tangent)
  • Convexity Assumption causes MRS to decrease (=Diminishing MRS) rightward (the more of good we consume, the more we would like ).
  • When two people have different MRS, then they can trade for both of their utility.
    • e.g. ,
    • ⇒ they can trade at any rate where to both of their benefit.

Deriving the MRS Formula

We’re looking for a place on the scalar field provided by where the gradient is zero. ⇒ Thus we need to find a point where the following is true:

By the definition of MRS it’s the gradient of a indifference curve, i.e. the gradient of a level curve in the field:

Changes in MRS

  • MRS can change due to exogenous factors; in this case the whole indifference curve will change accordingly too.
  • e.g. After 9.11., air travel is perceived by consumers to be less safe.

  • Observe that air travel becoming less safe, causes the MRS to decrease, as one is willing to trade less money for flying by air.
  • You can think of this from a different perspective by instead of thinking of air safety as an exogenous factor, actually quantifying air safety as a measure as well, and graphing it together.
  • Graphing air safety as the third axis shows that we can in fact visualize the decrease in MRS of air miles and $‘s of other consumption.