Download 13 assumed that only interior allocations are Pareto

assumed that only interior allocations are Pareto-optimal, that is, both households receive
positive amounts of both goods. This need not be the case in general; with appropriately
shaped indifference curves also allocations on the boundary of the Edgeworth-box may turn
out Pareto-efficient.
h
can be interpreted as the (maximum) amount of good 2, which can be
Remember that MRS1,2
taken away from household h, if it receives an additional unit of good 1, in order that it
h
remains indifferent. Similarly, MRS1,2
can be interpreted as the (minimum) amount of good
2, which must be given to household h if one unit of good 1 is taken away from it, in order
that it remains indifferent.
2
The intuition, why the condition MRS11,2 = MRS1,2
must be satisfied for a Pareto-efficient
2
allocation can be seen from the following example: Assume that MRS11,2 ≠ MRS1,2
, e. g. that
2
MRS11,2 = −1 , while MRS1,2
= −2 . Then obviously, household 1 remains indifferent, if it gives
up one unit of good 1 in return of one unit of good 2, but household 2 is even willing to give
up two units of good 2, if it receives one more unit of good 1. Thus, if one unit of good 1 is
transferred from household 1 to household 2 and one unit of good 2 the other way round,
household 2 is better off, while household 1 stays indifferent. (Obviously, if two units of good
2 are transferred to household 1 in exchange for one unit of good 1, then household 2 is
indifferent and household 1 is made better off; and there are infinitely many possibilities in
between.) Such Pareto-improving transfers are possible, whenever the marginal rates of
substitution are not equal for both households.
We can illustrate the utility positions of the households by deriving the utility possibility curve
from the contract curve (Figure II.3).
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