Develop indifference curves

Document Sample
Develop indifference curves Powered By Docstoc
					Indifference Curve Analysis

  1. Develop indifference curves
  2. Develop budget constraint
  3. Some basic analysis: a. changes in
      prices; b. changes in income;
      c. the Engels Curve
  4. The Food Stamps Problem
Indifference curve:

 A collection of points for which the
  consumer is indifference between
  each of them and some reference
  point.

 Typically shown in the context of a two
  good world on a two-dimensional graph.
OG
                               Indifference
                     .B         curve
         D
     .
                 A
             .
                          .E
             C            .F

                              Food
 What sense does the indifference
 curve make? A heuristic approach.
The axiomatic approach to indifference
curves is a search for a minimum set
of assumptions regarding consumer
behavior through which to generate
indifference curves.

Standard axioms:

1. More is preferred to less—nonsatiation
2. Completeness—all points in a relation
3. Transitivity– A  B; B  C;  A  C
Og




        .A
               .C
               .     U1
              B     U2
                           Food
 Why indifference curves
 cannot cross (and still obey
 the axioms for preferences).
OG
     U1


              B


          A           U1

                           Food
  he
 T axioms imply that indifference
 curves must be unbroken, ie
 continuous.
The budget equation:

B = pogOG + pfF

OG = B/pog – pf/pogF

Meaning: The budget equation will depict
a curve in OG-Food space that is downward
sloping (note: its derivative –pf/pog is
negative).
OG




             Budget constraint


                                  Food
                    B/p f
               ,
 If budget is B then the most OG
 possible to buy is B/p o, and similarly
 the most Food possible is B/p f . T he
 budget constraint connects these
 two intercepts.
OG




            . E
                                 Budget
                          UE      line


                                  Food
     Consumer equilibrium
     in indifference curve analysis
Applying calculus to find an expression
for the slope of the other curve, the
indifference curve:

OG/F = - (U/F) /(U/OG)

or, using an equivalent notation:

OG/F = - MUf/ MUog
OG




            . E
                                 Budget
                          UE      line


                                  Food
     Consumer equilibrium
     in indifference curve analysis


At an equilibrium, tangency implies that
the slope of the budget constraint equals
the slope of the indifference curve: Hence,
Consumer equilibrium requires that

pf/pog = MUf /MUog
or
MUf /pf = MUog /pog


In words: The marginal utility per dollar
 of expenditure must be equal for each good.
OG




               E
           E2 . 3
           .
     .E1




                              Food
     F1       F3

 As income increases, Food demanded
             his
 increases. T is shown in indifference
 curve analysis as successive, new
 equilibria.
Income



                       Engel’s Curve




                                  Food
           F1   F2    F3

    Consider the shape of the Engels
    Curve as related to the income
    elasticity of demand.

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:13
posted:1/15/2012
language:
pages:16