TY - GEN

T1 - Markets with production

T2 - 16th ACM Conference on Economics and Computation, EC 2015

AU - Garg, Jugal

AU - Kannan, Ravi

PY - 2015/6/15

Y1 - 2015/6/15

N2 - The classic Arrow-Debreu market model captures both production and consumption, two equally important blocks of an economy, however most of the work in theoretical computer science has so far concentrated on markets without production, i.e., the exchange economy. In this paper we show two new results on markets with production. Our first result gives a polynomial time algorithm for Arrow-Debreu markets under piecewise linear concave (PLC) utilities and polyhedral production sets provided the number of goods is constant. This is the first polynomial time result for the most general case of Arrow-Debreu markets. Our second result gives a novel reduction from an Arrow-Debreu market M (with production firms) to an equivalent exchange market M such that the equilibria ofMare in one-to-one correspondence with the equilibria of M. Unlike the previous reduction by Rader [Rader 1964] where M is artificially constructed, our reduction gives an explicit market M and we also get: (i) when M has concave utilities and convex production sets (standard assumption in Arrow-Debreu markets [Arrow and Debreu 1954]), then M has concave utilities, (ii) whenMhas PLC utilities and polyhedral production sets, then M has PLC utilities, and (iii) whenMhas nested CES-Leontief utilities and nested CES-Leontief production, then M has nested CES-Leontief utilities.

AB - The classic Arrow-Debreu market model captures both production and consumption, two equally important blocks of an economy, however most of the work in theoretical computer science has so far concentrated on markets without production, i.e., the exchange economy. In this paper we show two new results on markets with production. Our first result gives a polynomial time algorithm for Arrow-Debreu markets under piecewise linear concave (PLC) utilities and polyhedral production sets provided the number of goods is constant. This is the first polynomial time result for the most general case of Arrow-Debreu markets. Our second result gives a novel reduction from an Arrow-Debreu market M (with production firms) to an equivalent exchange market M such that the equilibria ofMare in one-to-one correspondence with the equilibria of M. Unlike the previous reduction by Rader [Rader 1964] where M is artificially constructed, our reduction gives an explicit market M and we also get: (i) when M has concave utilities and convex production sets (standard assumption in Arrow-Debreu markets [Arrow and Debreu 1954]), then M has concave utilities, (ii) whenMhas PLC utilities and polyhedral production sets, then M has PLC utilities, and (iii) whenMhas nested CES-Leontief utilities and nested CES-Leontief production, then M has nested CES-Leontief utilities.

KW - Market equilibrium

KW - Piecewise linear concave utilities

UR - http://www.scopus.com/inward/record.url?scp=84962086343&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84962086343&partnerID=8YFLogxK

U2 - 10.1145/2764468.2764517

DO - 10.1145/2764468.2764517

M3 - Conference contribution

AN - SCOPUS:84962086343

T3 - EC 2015 - Proceedings of the 2015 ACM Conference on Economics and Computation

SP - 733

EP - 749

BT - EC 2015 - Proceedings of the 2015 ACM Conference on Economics and Computation

PB - Association for Computing Machinery, Inc

Y2 - 15 June 2015 through 19 June 2015

ER -