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Competitive Markets

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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

Profit Maximization

Profit Maximization Condition

The Firm’s short run total cost curve is

STC = 100 +20Q + Q2.

The short run Marginal cost curve is

SMC = 20 + 2Q

If SFC = 100, while SVC = 20Q + Q2

Find AVC , Minimum level of average variable cost, supply curve

Fixed Cost + Sunk Cost

TFC = SFC + NSFC

The Firm’s short run total cost curve is

STC = 100 +20Q + Q2.

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

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 + 150Q2 , 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?

P demand curve is given by

P

S

SAC

S’

P1

P2

D

Q2f

Q1f

Q

Q

Q1

Q2

Comparative Statics in short runIncrease in the number of firm

Price demand curve is given by

MC2

SAC2

LMC

MC1

P1

SAC1

LAC

Quantity

Q1

Q2

Long Run – Plant AdjustmentFree Entry and Long Run demand curve is given by

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 demand curve is given by

P

LMC

SMC

S

SAC

LAC

P*

D

D(P*) = n*Q*

Q*

Q

Q

Free Entry and Long Run3. Demand equals Supply.

D( P* ) = n Q*

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

AC( Q ) = 40 – Q – 0.01Q2.

And a corresponding long run marginal cost curve

MC( Q ) = 40 – 2Q + 0.03Q2.

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.

P – run average cost

P

LMC

S

SAC

S’

LAC

A

P2

B

P1

D’

D

Q

Q

Q1f

Q2f

Q1

Q2

Long Run Market Supply CurveP – run average cost

P

LMC

S

S’

LAC

A

P2

SL

B

P1

D’

D

Q

Q

Q1f

Q2f

Q1

Q2

Industry Long Run Supply CurveConstant Cost

Increasing Cost – run average cost

P

P

LMC2

S

LMC1

LAC2

S’

LAC1

P2

P3

SL

P1

D’

D

Q2

Q

Q

Q1f

Q2f

Q1

Industry Long Run Supply CurveProblem 1 – run average cost

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

STC ( Q ) = 16 + Q2

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 is the firm’s short run supply curve?

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 + Q2

The corresponding long run average cost function is

AC ( Q ) = 40 – 6Q + (1/3)Q2

The market demand curve for propylene is

D ( P ) = 2200 – 100P

a ) What is long run equilibrium price in the industry? is the firm’s short run supply curve?

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 is the firm’s short run supply curve?

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?