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100A GENERAL EQUILIBRIUM (CH 16) IN CONSUMER MARKET
IN INITIAL DISCUSSION (CHS 3,4 AND 5) WE DEALT WITH
INDIVIDUAL CONSUMERS AND OR INDIVIDUAL
MARKETS…EACH CONSUMER WAS IN EQUILIBRIUM
(MAXIMIZING HIS/HER SATISFACTION)---THAT ASPECT OF THE
THEORY IS REFERRED TO AS PARTIAL EQUILIBRIUM
ANALYSIS
DISCUSSION NOW TURNS TO LOOKING AT ALL CONSUMERS IN
ALL MARKETS--FOR ANALYTIC PURPOSES;
1. WE PICK ANY 2 CONSUMERS AND ANY 2 MARKETS….THUS,
WE IN EFFECT ARE INCLUDING EVERYONE AND
EVERYTHING, AND
2. ASSUME ALL GOODS WILL BE CONSUMED BY EITHER OR
BOTH PARTIES…
>>>>>CONSTRUCTION OF THE EDGEWORTH BOX DIAGRAM
(MEANT TO HELP, BUT STUDENTS CAN GET CONFUSED IN THE
CONSTRUCTION)
BASIC PROBLEM IS THAT YOU HAVE TO TWIST AND TURN TO
SEE SECOND CONSUMER…but don’t give up!
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Y
Sally
a
d
b
e
c
Frankie
Toys
IN THE ABOVE DIAGRAM, WE ASSUME THAT THE TOTAL
OUTPUT OF TOYS AND OTHER GOODS (y) ARE CONSUMED BY
FRANKIE AND SALLY…..
ANY DISTRIBUTION OF THE TWO GOODS IS POSSIBLE, BUT…
SOME ARE “BETTER” THAN OTHERS…..
“BETTER” IN THE SENSE THAT SUCH A DISTRIBUTION CAN’T BE
ALTERED WITHOUT HURTING AT LEAST ONE PERSON----THERE
ARE SEVERAL SUCH POSSIBILITIES. for example, if Sally had all the
Toys and all of the other goods, than any alteration towards Frankie would
hurt Sally (assuming selfish motivation).
However, in the diagram above, note that point A is a distribution that can
be altered without hurting either party; a movement to C would not hurt
Frankie, but would help Sally (from A to D, Frankie would be better off, and
Sally no worse off). And, a movement to B would make them both better
off. Thus, point A is what is referred to as an INEFFICIENT
DISTRIBUTION
Note also, that once at D, it is impossible to alter the distribution without
hurting Sally or Frankie. (we don’t know if this is the case at B or C without
more info—i.e., more indifference curves). We do know, however, that D is
heaven, or in economist’s jargon, PARETO OPTIMAL (B and C are Pareto
preferred over A)
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WHERE A MOVEMENT WOULD BENEFIT ONE PARTY WITHOUT
HARM TO THE SECOND PARETO PREFERRED OR PARETO
SUPERIOR
WHERE IS WOULD BE IMPOSSIBLE TO MOVE WITHOUT
HARMING AT LEAST ONE PARTY PARETO OPTIMAL….D is such
a point…..
WHERE A MOVEMENT WOULD BENEFIT ONE PARTY AT THE
EXPENSE OF ANOTHER…EVEN THOUGH SUCH A MOVEMENT
MIGHT SEEM FAIR….
PARETO EFFICIENCY REFERS TO JUST THAT, EFFICIENCY,
NOT EQUITY [BRIEF DISCUSSION OF REAL OR THEORETICAL
COMPENSATION]
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CONCEPT OF THE CONTRACT CURVE
Note that D is a point where the indifference curves of both Sally and
Frankie are TANGENT!!!! The series of such points of tangency are
referred to as the CONTRACT CURVE…..
[IN FRANK--P. 560 AND ON--CONTRACT CURVE GOES THROUGH
THE ORIGINS…NOT NECESSARY, WHERE ONE CONSUMER
MIGHT BE AT A CORNER SOLUTION]
Y
Sally
contract curve
Frankie
Toys
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QUESTION IS, UNDER WHAT CIRCUMSTANCES WILL THE
DISTRIBUTION OF GOODS BE PARETO OPTIMAL, I.E., ON THE
CONTRACT CURVE?? [FRANK, p. 561-63, GOES THROUGH THE
PROCESS OF TWO CONSUMERS TRADING WITH EACH
OTHER…FAIR ENOUGH, BUT NOT AS REALISTIC AS IT MIGHT BE,
AND A BIT COMPLEX IN THE GRAPHS…]
SIMPLER ROUTE IS TO ASSUME THAT ALL CONSUMERS FACE
THE SAME PRICES, AND THAT ALL GOODS ARE CONSUMED…,
BUT THIS INTRODUCES MORE GRAPHICAL CONSTRUCTION
PROBLEMS….but let’s go for it.
---UNDER PREVIOUS ASSUMPTIONS REGARDING
MAXIMIZATION, ALL CONSUMERS SEEK THE GREATEST LEVEL
OF SATISFACTION, I.E., ON THEIR RESPECTIVE BUDGET
LINES…..that is, ALL THEN CONSUMING WHERE: MRSyx = Px/Py
IF WE ASSUME THAT SALLY AND FRANKIE FACE THE SAME SET
OF PRICES, REGARDLESS OF WHAT THEIR RESPECTIVE INCOMES
MIGHT BE, THEN THE FOLLOWING TWO DIAGRAMS SHOULD BE
FAMILIER…
Y
Y
y1
y1
o t1
Sally
o
Frankie
t1
Both Sally and Frankie are maximizing (Frankie’s doing a lot better in terms
of consumption—not necessarily in utility—and they are each consuming
their respective amounts of Y and Toys (oy1 and ot1) NOW THE FUN!!
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If we add the total amount of Y and of toys that the two are consuming, and
construct and Edgeworth Box, we get the following:
Sally
Y
0
D
0
TOYS
Frankie
VOILA!! We have “created” a point “D” (pareto optimal)….
Implying that as long as both consumers MAXIMIZE THEIR UTILITY and
FACE THE SAME SET OF RELATIVE PRICES, THE RESULTING
DISTRIBUTION OF GOODS CAN’T BE IMPROVED UPON (in the sense
that you can’t make one person better off without hurting the other).
and despite the seemingly abstract nature of all of the above, there are real
world EXAMPLES:
1) COMMODITY DISCOUNTS (note earlier discussion in Frank—p. 78,
figure 3-6
2) QUANTITY LIMITATIONS---like housing discrimination, or
3) PRICE DIFFERENTIALS BASED ON RACE
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ALL OF THE ABOVE DISCUSSION FOCUSES TOTALLY ON
ECONOMIC EFFICIENCY…I.E., IT TAKES INCOME LEVELS AS
GIVEN…..THAT IS, THE ISSUE OF EQUITY (FAIRNESS,
DISTRIBUTION…) IS ESSENTIALLY IGNORED,
BUT CAN’T (OR SHOULDN’T) BE IN POLICY ISSUES
FOUR BRIEF POINTS ON THESE QUESTIONS
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1) GOODS CAN BE EFFICIENTLY DISTRIBUTED FOR ANY INCOME
DISTRIBUTION---i.e., any where along the contract curve
2) THERE IS NO OBVIOUS ANSWER REGARDING “OPTIMAL”
INCOME DISTRIBUTION, GIVEN THE ASSUMPTION REGARDING
SELF-INTERESTED BEHAVIOR
3) ISSUES AT CONFLICT WHEN HAVING TO CHOOSE BETWEEN
EFFICIENCY AND EQUITY WITHOUT EFFICIENCY…
B
A
Note that while point A is an efficient distribution, B is a bit “fairer.”
Which should the policy maker select??? Frankie (solid lines) would
be happier at B, the “inefficient” point, but not Sally.
4) INTRODUCTION OF “ALTRUISM” INTO THE UTILITY
FUNCTION MAY LEAD TO DIFFERENT SET OF
CHOICES…PARTICULARLY AT THE EXTREMES OF INCOME
INEQUALITY, for example, in extremes of distribution, altruistic behavior
might dominate…i.e., B preferred to A on the part of everyone in diagram
above…not unlike the case of the Limo Liberal discussed earlier in the
course.