IMPERFECT COMPETITIONBASIC MATHEMATICS

致华北电力大学

发言人卜若柏

Robert Blohm

http://www.blohm.cnc.net

2007 年 5 月 25 日

2

1FIRMS HAVE PROFIT ON THE CONVEX PORTION OF THEIR PRODUCTION

POSSIBILITIES FRONTIER

PRODUCTIONPOSSIBILITIES

FRONTIERPPF

QUANTITYx

QUANTITYy

–0

–

+

+

Y-intercept b indicates profit is positive or negative

PRICE LINES TANGENT TO PPF

bxp

py

y

x

yxy bpxpyp

xyy xpypbp Profit is the value ypy of output

minus the value xpx of input

: SLOPE = px/py

3

TOTALREVENUE = MR

TOTALREVENUECURVES

= AR

AR=MRLINEAR:

QUANTITYSOLD

AR : AVERAGE REVENUE

NON-LINEAR

TOTALCOST

TOTALREVENUE

QUANTITYSOLD

TOTALCOST

CURVESMC

=

NON-LINEAR

AC

AC= MC

: SLOPE

OUTSIDE THE PERFECTLY COMPETITIVE TEXTBOOK WORLD OF STRAIGHT LINES ,CURVES ARE NON-LINEAR .

AC : AVERAGE COSTMC : MARGINAL COST

LINEAR :

=

MR : MARGINAL REVENUE

: SLOPE

2

4

IMPERFECT COMPETITORS PRODUCE THE PROFIT-MAXIMIZINGQUANTITY AND PRICE OFF THE AVERAGE REVENUE CURVE

p pc

q pc

PERFECT COMPETITIONONLY AT A HORIZONTAL SUPPLY AND DEMAND CURVE

WHERE MARGINAL EQUALS AVERAGE

MC

AC

AR

MR

QUANTITY

$ / UNIT

q

p

DEMAND CURVEVALUE CURVE

SUPPLY CURVE

MC: MARGINAL COST

AC: AVERAGE COSTAR: AVERAGE REVENUE

MR: MARGINAL REVENUE

q : PERFECTLY COMPETITIVE QUANTITY pc

p : PERFECTLY COMPETITIVE PRICE pc

: PERFECTLY COMPETITIVE SUPPLY AND DEMAND CURVE

3

5

Q

ACTUAL AND PERCEIVEDDEMAND CURVE

IMPERFECT COMPETITION :ONCE THE (PERCEIVED) DEMAND CURVE SLOPES ,

AVERAGE AND MARGINAL REVENUE DIVERGE

ARMR

QUANTITY

$ / UNIT

5/6c

A QUINTOPOLY

1 2/3

1/3

ACTUAL DEMAND CURVE

PERCEIVED DEMAND CURVE

AR

MRQ

$ / UNIT

2/5

4/5c

A QUADROPOLY

1 3/5

AR

MR

1/2

3/4c

A TRIOPOLY

1 1/2

AR

MRQ

2/3

2/3c

A DUOPOLY

1 1/3 1

AR

MR

QUANTITY

1

1/2c

A MONOPOLY

PERCEIVED AGGREGATE DEMAND CURVE STEEPENS AS THE INDUSTRYCOMPRISES FEWER STRATEGIC PLAYERS.

EACH PLAYER IS EFFECTIVELY A SMALL MONOPOLIST, LEAVING ONE-AND-THE-SAME RESIDUAL PORTION OF DEMAND UNSERVED.

p = c

PERFECTCOMPETITION :

FLAT HORIZONTALSUPPLY AND DEMAND

CURVE$ / UNIT

1Q

MR : AGGREGATE PERCEIVED MARGINAL REVENUEAR : AGGREGATE PERCEIVED AVERAGE REVENUE

p

pp

p

p

qq

qq

qq

4

一、 Competitive Equilibrium

Profit:

Profit maximization:

If , Demand curve: Competitive quantity: ,

5

CR

0cpMCMRdq

dC

dq

dR

dq

d

AR0pcpMR

qcqp

0cMC q1)q(pAR

q10)q(p 1q

二、 Monopoly equilibrium 6

Profit:

Profit maximization:

CR q)q(cq)q(p

MCMRdq

dC

dq

dR

dq

d

0dq

dcq)q(c

dq

dpq)q(p

二、 Monopoly equilibrium (cont.d) 7

If , , &

Demand curve: Marginal Revenue curve:

Monopoly quantity & price:

0)q(cC

q1)q(pAR

0dq

dpq)q(pMR

0MC

0q21qq1MR

2

1q

2

1p

三、 Duopolistic competition8

Profit: ,

Profit maximization (when ):

111 CR 1211211 q)qq(cq)qq(p

111

1

1

1

1

1 MCMRdq

dC

dq

dR

dq

d

0dq

)qq(dpq)qq(pMR

1

211211

222 CR

2212212 q)qq(cq)qq(p

0qq21q)qq(1 21121

0)qq(cC 211

三、 Duopolistic competition (cont.d)9

Profit maximization (when ):

Demand curve:

222

2

2

2

2

2 MCMRdq

dC

dq

dR

dq

d

0dq

)qq(dpq)qq(pMR

2

212212

0)qq(cC 212

0qq21q)qq(1 12221

)qq(1)qq(pAR 2121

12 q1q2

三、 Duopolistic competition (cont.d)10

Duopolistic quantity & price:

02

q

2

1q21MR

1

111

0q2

3

2

11

3

1

3

2

2

1q1

三、 Duopolistic competition (cont.d)11

Duopolistic quantity & price:

03

1q21MR 22

0q23

22

3

1

2

1

3

2q2

3

1

3

1

3

11p

三、 Duopolistic competition (cont.d)12

Marginal Revenue Curve incorporating the quantity chosen by the other competitor:

By symmetry:

Joint Marginal Revenue Curve (at half the slope of the Duopolist’s), & quantity produced by the Duopoly:

22 q23

2MR

11 q23

2MR

2121 q3

2MR

3

2q 21 ,0MR 21 When.

2,12,1 q23

2MR

三、 Duopolistic competition (cont.d)13

Demand Curve seen by each Duopolist perceiving itself as a Monopolist in its market seqment (i.e. slope of is halved):

Demand Curve seen by the Duopoly when each Duopolist perceives itself as a Monopolist in its market segment (i.e. slope of is halved):

212,1 q3

2AR

2121 q2

1

3

2AR

2,1MR

3

2q 21 ,0AR 2,1 When.

3

11

3

4q 21 ,0AR 21 When.

2,1AR