THE BERTRAND MODEL BERTRAND MODEL IN 1883 A

THE BERTRAND MODEL

BERTRAND MODEL Ø IN 1883 A FRENCH MATHEMATICIAN JOSEPH BERTRAND CRITICISED COURNOT MODEL FOR ASSUMING THE SUPPLY OF RIVAL AS CONSTANT. Ø IT BASED ON THE ASSUMPTION THAT PRICE OF RIVAL AS CONSTANT Ø IT IS A DUOPOLY MODEL. Ø IT BASED ON FOLLOWING ASSUMPTIONS.

ASSUMPTIONS Ø Ø Ø THERE ARE TWOINDEPENDENT SELLERS[INTERDEPENDENCE IS IGNORED] HOMOGENIOUS PRODUCT TOTAL OUTPUT MUST BE SOLD OUT, PERISHABLE , NON DURABLE NO. OF BUYERS IS LARGE EACH SELLER KNOWS THE MARKET DD CURVE OF THEPRODUCT COST OF PRODUCTION ASSUMED TO BE ZERO BOTH HAVE IDENTICAL DD AND COST EACH SELLER DECIDES ABOUT THE QTY HE WANTS TO PRODUCE AND SELL IN EACH PERIOD EACH IS IGNORENT ABOUT HIS RIVALS PLAN ABOUT OUTPUT EACH SELLER TAKES ABOUT THE PRICE OF RIVAL AS CONSTANT THE ENTRY OF FIRM IS BLOCKED EACH SELLER AIMS AT OBTAINING MAXIMUM PROFIT

MODEL Ø Ø Ø Ø Ø THERE ARE 2 SELLERS IN THE MARKET FIRST “A”ENTER THE MKT. CONSIDER HIMSELF AS A MONOPOLIST. FIX THE PRICE OF HIS PDT AS MONOPOLY PRICE THEN “B” ENTER THE MARKET WITH THE PERSUMPTION THAT “A” CONTINUE THIS PRICE AND REDUCE HIS PRICE THAN “A”. TAKE SOME OF THE CUSTOMERS OF A. “A “ THINK THAT “B” WILL COTINUE THIS PRICE. AND CHARGE PRICE THAN “B” PRICE WAR TILL CONTINUE TILL BOTH REACH THE PERFECT COMPITITION ABOVE PC –DOESN’T EXIST. BELOW PC ONE WHO INCCUR LOST PC IS THE STABLE EQM POINT TOTAL OUTPUT EQUALLY SHARED.

DIAGRAMATICAL EXPLANATION Ø Ø Ø “OD” PRICE AXIS OF BOTH A &B “DA” DD CURVE OF A “DB” DD CURVE OF B AB PERFECT COMPITITIVE LEVEL MAX OUTPUT A CAN SELL “OA”- B CAN SELL “OB” THEY SHARE MKT JOINTLY THEY SELL=12[OA+OB]=OE+OC NO COLLUSSION A CHARGE “OP” PRICE AND SELLOE QTY B ENTER THE MKT AND CHARGE PRICE LOWER THAN CHARGE BY A OP 1 PRICE WITH OF QTY THEN “A “REDUCE PRICE THAN B AT OP 2 PRICE WITH OG QTY AGAIN “B” REDUCE THE PRICE OP 3 AND SELL OH THE PRICE WAR TILL CONTINUE BOTH REACH “AB” LEVEL.

IN TERMS OF REACTION CURVE Ø A- A’S REACTION CURVE Ø B- B’S REACTION CURVE Ø HORIZONTAL AXIS MEASURES A’S PRICE AND VERTICAL AXIS MEASURES “B” S PRICE Ø 45 DEGREE SHOW EQUALITY BETWEEN A&B Ø A CHRGE LOWER PRICE”OA 1” Ø B REACTS BY CHARGING HIGHER PRICE OB 1 THAN A Ø A REACT BY CHARGE HIGHER PRICE OA 2 THEN B Ø ACTION AND REACTION PROCESS BW 2 SELLERS TILL CONTINUE EQM POINT “E” Ø OA 3=OB 3

CRITICISM Ø Ø IT IS A STATIC MODEL ZERO COST OF PRODUCTION IS UN REALISTIC IT IS A CLOSDE MODEL EACH DUOPOLIST CAN ACT WITHOUT ANY PRICE REDUCTION FROM THE OTHER IS UNREALISTIC. IT IS NO LEARNING BY DOING MODEL