Competitive Markets

Structure

• Fragmented • Undifferentiated Products : Homogeneous • Perfect Information about Price • Equal Access to Resources

Three Implication

• • •

Price Takers Law of one Price Free Entry & Free Exit



Max



Profit Maximization

   ( ) 

Profit Maximization Condition

d



dq

 0

d



dq dq



dq MR



dq MC



dq MR



MC

)  )

TR,TC TR TC 0 0

MC > MR MC < MR Profit

Q MC MR = P

MC = MR MC > MR

Q

Price Firm AR = P = MR Price Industry Q D Q

Price P1 C Excess Profit 0 B A MC AC AVC MR = P Q Q

P1 C Price 0 A MC AC AVC MR = P Q Q

Price C P1 Loss 0 B A MC AC AVC MR = P Q Q

Price C P1 0 Loss A B Q MC AC AVC MR = P Q

Price P1 0 C Loss B A MC AC Q AVC MR = P Q

P1 P2 P3 P4 0 Price MC AC AVC Shut Down Point Q

P1 P2 P3 P4 0 Price Firm’s Supply MC AC AVC Shut Down Point Q

Example The Firm’s short run total cost curve is STC = 100 +20Q + Q 2 . The short run Marginal cost curve is SMC = 20 + 2Q If SFC = 100, while SVC = 20Q + Q 2 Find AVC , Minimum level of average variable cost, supply curve

Fixed Cost + Sunk Cost

TFC = SFC + NSFC

ANSC=AVC+ NSFC Q

Price C P1 0 A B Q MC AC ANSC AVC Minimum ANSC = P Q

Example The Firm’s short run total cost curve is STC = 100 +20Q + Q 2 . The short run Marginal cost curve is SMC = 20 + 2Q If SFC = 36, while NSFC = 64 Find ANSC , Minimum level of average non sunk cost, supply curve

p P Firm Supply and Market Supply Firms P Market Q1 Q2 Q Q1+Q2 Q

P* Short Run perfectly Competitive equilibrium

S ( 1

P

* )  S ( 2

P

* ) 

P SAC P

 n

P

* )  ( * )

S Q* Q D(P*) D Q

The Market consists of 300 identical firms, and the market demand curve is given by

D(P) = 60 – P.

Each firm has a short run cost curve

STC = 0.1 + 150Q 2

, all fixed cost are sunk. The corresponding short run marginal cost curve

SMC = 300Q.

The corresponding average variable cost curve is

AVC = 150Q.

You should verify that the minimum level of AVC is 0. Thus, a firm will continue to produce as large as price is positive Find Short run equilibrium in market, at equilibrium, do the firm make positive profit?

P1 P2 Comparative Statics in short run Increase in the number of firm P SAC P S S’ Q2 f Q1 f Q Q1 Q2 D Q

P1 Price

Long Run – Plant Adjustment

MC2 SAC2 LMC MC1 SAC1 LAC Q1 Q2 Quantity

P1 P2 P* Price Long Run Supply Curve LMC LAC Quantity Q* Q2 Q1

P1 P2 P* Price Long Run Supply Curve LMC LAC Quantity Q* Q2 Q1

Free Entry and Long Run 1. Long Run Profit is maximized with respect to output and plant size.

P* = MC ( Q* ) 2. Economic profit is Zero.

P* = AC ( Q* )

P* Free Entry and Long Run 3. Demand equals Supply.

P D( P* ) = n Q* P LMC SMC LAC SAC S Q* Q D(P*) = n*Q* D Q

In this market, each firm and potential entrant has a long – run average cost

AC( Q ) = 40 – Q – 0.01Q

2 .

And a corresponding long run marginal cost curve

MC( Q ) = 40 – 2Q + 0.03Q

2 .

Where Q is thousand units per year. The Market demand curve is

D( P ) = 25,000 – 1,000P,

Where D(P) is also measured in thousand units. Find the long run equilibrium price, quantity per firm, and number of firms.

P2 P1 P Long Run Market Supply Curve P LMC LAC SAC S S’ A B Q1 f Q2 f Q Q1 Q2 D D’ Q

P2 P1 P Industry Long Run Supply Curve Constant Cost P LMC S S’ LAC A B S L D’ D Q1 f Q2 f Q Q1 Q2 Q

P Industry Long Run Supply Curve Increasing Cost P P2 P3 P1 LAC 2 LAC 1 LMC 2 LMC 1 S S’ S L D’ D Q2 Q1 f Q2 f Q Q1 Q

Problem 1

The bolt industry currently consists of 20 producers, all of whom operate with identical short run total cost function

STC ( Q ) = 16 + Q 2

Where Q is the annual output. The corresponding short run marginal cost curve is

SMC ( Q ) = 2Q

The market demand for the bolts is

D ( P ) = 110 – P

Where P is the market price

a ) Assuming that all of the firm fixed cost is sunk, what is the firm’s short run supply curve?

b ) What is the short run market supply curve?

c ) Determine the short run equilibrium price and quantity in the industry.

Problem 2

Propylene is used to make plastic. The propylene industry is perfectly competitive, and each producer has a long run marginal cost function given by

MC ( Q ) = 40 – 12Q + Q 2

The corresponding long run average cost function is

AC ( Q ) = 40 – 6Q + (1/3)Q 2

The market demand curve for propylene is

D ( P ) = 2200 – 100P

a ) What is long run equilibrium price in the industry? b ) At this price, how much would an individual firm produce?

c ) How many firms are in the propylene market in long run competitive equilibrium.

d ) Suppose the demand curve shifted so that it is now

D ( P ) = A – 100P.

How large would A have to be so that in the new long run competitive equilibrium, the number of propylene firms was twice what it was in the initial long run equilibrium?.

Problem 3

The long run total cost function for producers of mineral water is

TC ( Q ) = cQ

Where Q is the output of individual firm expressed as thousand liters per year. The market demand curve is

D ( P ) = a – bP

Find the long run equilibrium price and quantity in term of a, b, c, . Can you determine the equilibrium number of firms? If so, what is it? Why not?