Edgeworth-Bowley Box Diagram
Consumer Preferences
X and Y are economic goods. More of X is always better than less of X. More of Y is
always better than less of Y.
Y
G
D
B
E
C
A
F
X
When comparing bundles of X and Y–
- Bundle B is preferred to A, because it has more of X and Y.
- Bundle C is not preferred to A, because it has less of X and Y.
- Bundle D is preferred to A, because it has more of Y and the same X.
- Bundle E is not preferred to A, because it has less of X and the same Y.
Bundle G may or may not be preferred to A, as it has more Y but less X.
Bundle F may or may not be preferred to A, as it has more X but less Y.
To determine how to rank A, G, and F we have to know about a specific consumer’s
preferences. In other words, we have to know how much a consumer values a unit of X
relative to a unit of Y. To do this, economists use indifference curves.
Y
H
G
A
F
If
Ia
Ig
X
Indifference Curves
- An indifference curve shows all the combinations of goods X and Y that
achieve the same level of total utility or satisfaction.
- For instance, points A and H are both on the same indifference curve (Ia), so
the consumer gets the same level of satisfaction from both bundles, even
though the two bundles have different amounts of X and Y.
- Since we know the indifference curve (Ia) above represents all the points as
good as A, we can now compare points A and G. Point G lies below the
indifference curve Ia, and an indifference curve going through point G (Ig)
would be closer to the origin than Ia, and therefore Point A is preferred to
point G.
- Since we know the indifference curve (Ia) above represents all the points as
good as A, we can now compare points A and F. Point F lies above the
indifference curve Ia, and an indifference curve going through point F (If)
would be farther from the origin than Ia, and therefore Point F is preferred to
point A.
- Rules for drawing indifference curves:
o Slope Down
o Convex
o Don’t Cross
Edgeworth-Bowley Box Diagram
XBa
B
Y
a
YAa
YBa
Ia
Ib
A
XAa
X
Assumptions
1. All of the X and Y available are either possessed by A or B. There is total
scarcity in that the only way A can get an addition unit of X or Y is if person B
loses a unit of X or Y.
2. Point a represents an initial possible allocation of goods X and Y amongst person
A and B.
3. Person A and B inhabit different corners of the box diagram. Each gets more X
and Y the further away they move from their corner.
4. At Point “a”, the level of utility achieved by A and B can be represented by
drawing the indifference curves of A and B through point a, with the relevant
curve convex to its possessor’s origin corner.
Trade within the Edgworth-Bowley Box
B
Y
c
a
d
Ia
b
Ib
A
Rules for Trade
For trade to occur, it must be consistent with rational self interest, and therefore must
follow the Pareto principle. The Pareto principle holds that for a trade to occur, it must
make at least one of the traders better off and the other no worse off. Such a trade is said
to be a “Pareto Improvement” or a “Pareto Improving Trade”.
If we begin a point a, all of the points in the shaded area and on the curves Ia and Ib that
are immediately adjacent to the shaded area are Pareto improvements and therefore,
represent trades that could occur. For instance, moves for point a to point b, c or d would
represent Pareto improvements, and therefore would occur voluntarily. To confirm that
points b, c, and d represents Pareto improvements, one can draw indifference curves for
A and B at each of these points, and show that at least one party is better off (On an
indifference curve further from his origin) and the other no worse off (On the same
indifference curve as he began).
B
Y
c
a
Iac
d
Iad
Iaab
b
Ibd
Ibac
Ibb
A
X
Pareto Optimality
Pareto Optimality occurs when you reach at point at which no additional Pareto
improving trades can be made. All moves from a Pareto optimal point would make at
least one party worse off, and therefore would be vetoed.
Graphically, a Pareto optimal point is a point at which there is a tangency between the
indifference curve for person A and B. A tangency between the curves leaves no area for
Pareto improving trades to occur.
On the above graph, points b, d and c are all Pareto optimal points (tangencies between
the indifference curves). Once A and B exchange to reach any of these points (b,d,c) the
possibilities for additional trading are exhausted.
The number of Pareto optimal points is not limited to b, c and d. There are an unlimited
number of possible optimal points (tangencies) between the original indifference curves.
If these points where all identified and plotted, they would form a line like the one in the
graph, connecting b to c. The line representing all the possible Pareto optimal points is
called the Contract Curve.
Important Ideas from the Edgeworth-Bowley Box
1) No matter what distribution you start with, the rational self interest of the two
parties will cause them to trade until they reach the contract curve, meaning that
all beneficial trades are exhausted.
2) Even in a world of total scarcity, where more X for A means less X for B,
mutually beneficial trades exist which improve the total level of utility. No X or
Y is created, yet swapping X and Y improve utility.
3) Though rational, self-interest will cause the parties to trade to the contract curve,
it is impossible to predict where on the curve they will end up.
4) All points on the contract curve are equally good from the perspective of the
economist, since all possible utility enhancing trades have been made, no matter
which party benefited more and which one less. All that matters is that all
mutually beneficial trades have happened.