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THERE EXISTS A COMPETITIVE EQUILIBRIUM CORRESPONDING TO THIS DATA IF THERE EXISTS PRICE VECTOR p1* &gt

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(1)

PURE-EXCHANGE ECONOMY:

(2)
(3)

IN THE FIGURE IT IS REPRESENTED BY THE GREEN AREA AND ITS BLUE AND RED CONTOUR

. THIS MEANS THAT A AND B ARE NOT WORSE OFF AT X THAN AT THE INITIAL ENDOWMENT, AND AT LEAST ONE OF THEM IS BETTER OFF

(4)
(5)

IS THE LOCUS OF POINTS AT WHCH MRSa = MRSb

WE CAN DEFINE THE CONTRACT CURVE FOR ANY POSSIBLE INITIAL ENDOWMENT IN EDGEWORTH BOX

(6)

THEN z2 = 0 SINCE p2 > 0 WE CONCLUDE THAT

(7)

IF

OPTIMUM CHOICES TAKEN INDEPENDENTLY BY AGENTS AT THE SAME PRICES YIELD

(8)

EXPLOITING WALRAS' LAW, TO DETERMINE COMPETITIVE EQUILIBRIUM PRICES WE FIX p2 = 1 AND IMPOSE EQUILIBRIUM ON MARKET 1

AGGREGATE SUPPLY = of x1

PREFERENCES ENDOWMENT

ENDOWMENT AND PREFERENCES ARE THE DATA. THERE EXISTS A COMPETITIVE EQUILIBRIUM CORRESPONDING TO THIS DATA IF THERE EXISTS PRICE VECTOR p1* > 0, p2 = 1 such that AGGREGATE EXCESS DEMAND z1 (p1*, 1) = 0

EQUILIBRIUM EXISTS

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