The Marginal Rate of Substitution (MRS)

(1) The geometry of the MRS     In the diagram to the right, consider two points on Uo: Point Milk Donuts A 1 10 B 2 5     How much has each of the following changed in the move from A to B? Milk consumption? DM = Donut consumption? DD = Utility? DU =

    The slope of an indifference curve is called the marginal rate of substitution (MRS).
    It tells us the rate at which good X can substitute for good Y without affecting utility.

    The MRS = the maximum amount of Y which a consumer is willing to give up to get another unit of X

(2) the mathematics of the MRS

    Even though we can’t directly measure MUs, we can show that they do determine the slope of Uo:

    DU = MUx^.DX + MUy^.DY

    Along Uo, DU = 0 =>

    -MUy^.DY = MUx^.DX =>

    |-DY/DX| = MUx/MUy

(3) the logic of the MRS

	General case:	|	Example here:
	MUx = the utility gained from an extra X	|	MUx = 10 utils
	MUy = the rate that utility falls when giving up Y	|	MUy = 2 utils
		|
	=> MUx/MUy	|	10u/(2u per Y)
	= total Y you can give up for 1X without losing any utility	|	5Y for 1X
	= |-DY/DX| (the size of the slope of Uo)	|