Question

1. In a two goods (x and y) world, two districts (A and B) are identical, except the price of good x (Px) is higher in district A. Suppose two identical individuals (i.e. same preferences and income) live in the two districts separately and their optimal choices are interior solutions. Evaluate the following statement: ‘The MRS at the optimal choices of two individuals can be the same’. True, false, or uncertain? Explain your answer intuitively and graphically. (4/20)

Answer 1

MRS ie marginal rate is the amount of agood that a consumer is willing to consume in relation to another good,as long as the new good is equally satisfying

marginal rate economic involves theory of sloping curve called the indifference curve

indiffernce curve: indifference schedule shows quantity different combinaltion of good x and good y if the quantity of one good is increased the quantity of the other must be decreased .for example when consumer e good x moves from combination A to B the good x inceases by one unit while y decreases by 4 unit this combination also gives from the same satisfaction. if good y is not decreased his satisfaction level will go up. the scedule shows that as the consumption of good x increases the rate of sacrifice of good y deceases because of law of dimnishing marginal utility as the consumer consume more and more unit of good x it will give him less and less satisfaction hence the rate of sacrifice of good y decreases this is called marginal rate of substitution (mRs) MR: MR is defined as the rate at which the consumer is willing to sacrifice one good to obtain more unit of other good

mr= change in the quantity of the good the consumer is willing to sacrifice/ change in the quantity of the good the consumer is willing to obtain.

mr is somewhat related to indiffernce schedule : indifference schedule shows different combination of two commodities that give the consumer equal satis faction or utility. for eg:

combinations	good x (units)	good y(units)	mrs y/x
A	1	8	-
B	2	4	4y:1x
C	3	2	2y:1x

IN the given schedule A,B,,C combination of good x and good y give the consumer equal satisfaction if the quantity of one good is increased the quantity of other good is decreased for eg when consumer moves from combination a to b the good X increases by one unit, while y decreases by 4 unit this combination also give him same satisfaction if good y is not deceased the satisfaction level will go up the schedule shows that the consumption of good x increases the rate of sacrifices of good y deceases because of law of dimnishing utility as, the consumer consumes more and more unit of good x it gives him less and less satisfaction hence, the rate of sacrifice of good y decreases this is called MRS.

the INDIFFERENCE CURVE always slopes downward from left to right in other words it is negative sloped because when consumer increases consumption of good x he must reduce the consumtion of good y to maintain same satis faction from all combination of goods

indiiference curve neither touches the axis because the consumer have to consume some quantity of good x and good y each if the indifference curve is touching the x asis it means the consumer is consuming only good x which is angaist the assumption of a bundle of two goods

the indifference curve is convex toward the origin because of law of decreasing marginal rate of substitution the slope of indifference curve is nothing but mrs when consumer moves from a to b downward he is willing to give up

Hence, the slope declines as we move downward along the curve. this gives convex shape to the indifference curve.

Key points to be taken:

marginal rate of substitution are graphed along an indifference curve which is usually downward sloping and convex.en point along with the curve.

the MR is the slope of indifference curve at any given curve

when the law of dimnishing marginal rate of substitution is n effect the marginal rate of substituion envolves negative sloping showing more consumption of one good in place of other

FOR EXAMPLE:

A consumer must choose between x and y in oder to determine the marginal rate of substitution the consumer is asked what combination of x and y provides the same level of satisaction.

when these combination are graphee d the slope of the resulting line is negative. this means that consumer faces a dimnishing marginal rate of substitution the more x they have relative to y the fewer x theey are willing to consume if the marginal rate of substituion of than the invidiual would be willing to give up y x for every additonal consumption.

limitation of marginal rate of substitiution:

the marginal rate of substituion dose not examine a combination of good that the consumer would prefer more or less than other combinations this genrally limits the analyis of mrs to the two variables also, mrs does necceserliy examine marignal utility since it treats the utility ofboth comparable goods though in actuality they may have varying utility.

Hence, we can say that MRS at the optimal choce of two can be the same.