Monopoly

Monopoly

What is monopoly?

It is a situation in which there is one seller of a product for which there are no good substitutes.

Why do monopolies exist?

1. Economies of scale – costs are lowest when one firm supplies all the product (Natural Monopoly)

2. Legal Barriers such as patents (exclusive right given to inventor/innovator for a specified period of time) and exclusive franchises or licenses

3. Control of an essential resource needed for production

Since the monopolist is the only supplier of the product, the demand curve for the industry is the same as the demand curve for the monopolist’s product.

quantity

price

Demand

The firm’s profits are maximized where MR = MC.

$

Q*0

TC

TR

Q

$

Q

MC ATCP*

D

Q*

MR

ATC*

That is where the slopes of the TR & TC curves are the same & where the gap between the TR & TC curves is the largest.

In long run equilibrium, a monopolist produces the output level where LR MC = MR.

Unlike the perfectly competitive firm, however, the monopolist can have positive profits in the LR since high barriers to entry keep competitors out of the monopolist’s industry.

Lerner Index

This index measures the amount of control a firm has over the price of its product or the extent of its monopoly power.

L = (P – MC) / P

The index is between 0 & 1.

For a perfectly competitive firm, P = MC & L = 0.

Multiplant Monopoly

Suppose a firm has more than one plant.

How does it determine how much to produce in each plant?

As usual, the answer involves equating MR & MC.

Example

Suppose we have our MC for our two plants, A and B, and the price from the demand for our product.

OutputMC for Plant A

MC for Plant B

MC for Firm

Price TR MR

0 --- --- --- 18

1 1 3 16

2 2 7 14

3 4 10 12

4 9 12 10

5 10 15 8

Example

We can easily calculate our TR = PQ …


MC for Plant B

MC for Firm

Price TR MR

0 --- --- --- 18 0 ---

1 1 3 16 16

2 2 7 14 28

3 4 10 12 36

4 9 12 10 40

5 10 15 8 40

Example

and our MR.


MC for Plant B

MC for Firm

Price TR MR

0 --- --- --- 18 0 ---

1 1 3 16 16 16

2 2 7 14 28 12

3 4 10 12 36 8

4 9 12 10 40 4

5 10 15 8 40 0

Example

The firm produces the least expensive units first. So it makes the 1st and 2nd units in plant A.So the MC to the firm of making the 1st and 2nd units is the same as the MC of making the 1st and 2nd units in plant A.


MC for Plant B

MC for Firm

Price TR MR

0 --- --- --- 18 0 ---

1 1 3 1(from A)

16 16 16

2 2 7 2(from A)

14 28 12

3 4 10 12 36 8

4 9 12 10 40 4

5 10 15 8 40 0

Example

It makes the 3rd unit in plant B,


MC for Plant B

MC for Firm

Price TR MR

0 --- --- --- 18 0 ---

1 1 3 1(from A)

16 16 16

2 2 7 2(from A)

14 28 12

3 4 10 3(from B)

12 36 8

4 9 12 10 40 4

5 10 15 8 40 0

Example

the 4th unit in plant A,


MC for Plant B

MC for Firm

Price TR MR

0 --- --- --- 18 0 ---

1 1 3 1(from A)

16 16 16

2 2 7 2(from A)

14 28 12

3 4 10 3(from B)

12 36 8

4 9 12 4(from A)

10 40 4

5 10 15 8 40 0

Example

and the 5th unit in plant B.


MC for Plant B

MC for Firm

Price TR MR

0 --- --- --- 18 0 ---

1 1 3 1(from A)

16 16 16

2 2 7 2(from A)

14 28 12

3 4 10 3(from B)

12 36 8

4 9 12 4(from A)

10 40 4

5 10 15 7(from B)

8 40 0

Example

So we can see that the MC for the firm as a whole is built from the MC values from the two plants.


MC for Plant B

MC for Firm

Price TR MR

0 --- --- --- 18 0 ---

1 1 3 1(from A)

16 16 16

2 2 7 2(from A)

14 28 12

3 4 10 3(from B)

12 36 8

4 9 12 4(from A)

10 40 4

5 10 15 7(from B)

8 40 0

Example

Then the firm produces the output that equates the firm’s MC to MR. So the firm produces 4 units. (MR and MC happen to be 4 as well. MR and MC don’t have to be the same as the output level. MR and MC just have to be equal to each other.)


MC for Plant B

MC for Firm

Price TR MR

0 --- --- --- 18 0 ---

1 1 3 1 16 16 16

2 2 7 2 14 28 12

3 4 10 3 12 36 8

4 9 12 4 10 40 4

5 10 15 7 8 40 0

Note: The monopolist does not have a supply curve.A supply curve

indicates the price at which the firm would be willing to provide various quantities.

However, the monopolist determines the profit- maximizing output from MR=MC and then sets the price from the demand curve.

So there is no independent supply curve.

MC

D

P

QQcQm

Pm

MR

Suppose we want to compare the perfectly competitive industry and the monopolistic

industry.

Recall that in perfect competition, the firm’s supply curve is the MC curve above the minimum of the AVC curve. The supply curve for the perfectly competitive industry is the horizontal sum of the individual firms’ supply curves.

So, if we want to compare the monopolistic industry and the perfectly competitive industry, the monopolist’s MC curve would be comparable to the perfectly competitive industry’s supply curve.

How do output and price compare in the monopolistic industry versus the perfectly

competitive industry?Recall that output and price in the perfectly competitive industry are determined by the intersection of the supply and demand curves.

So in perfect competition, output and price are Qc and Pc respectively.

In monopoly, as we stated earlier, output and price are Qm and Pm .

MC or S

D

P

Q

Pc

Qc

MRmonopolist

Qm

Pm

How do output and price compare in the monopolistic industry versus the perfectly

competitive industry?Note that Qm < Qc andPm > Pc .That is, the monopolistic industry produces a lower level of output and charges a higher price than the perfectly competitive industry does.

MC or S

D

P

Q

Pc

Qc

MRmonopolist

Qm

Pm

Welfare loss of monopoly compared to perfect competition

Recall that consumer surplus is the area above the price & below the demand curve.

Producer surplus is the area below the price & above the supply curve or, in the case of the monopolist, above the MC curve.

MC or S

D

P

Q

Pc

Qc

MRmonopolist

Qm

Pm

In the perfectly competitive case, quantity & price are determined by the intersection of the supply & demand curves.

Then consumer surplus is the purple triangle.

Producer surplus the green triangle.

MC or S

D

P

Q

Pc

Qc

MRmonopolist

Qm

Pm

In monopoly, the quantity is where MR = MC & the price comes from the D curve above that quantity.

Consumer surplus is the pinkish triangle.

Producer surplus is the yellow region.

MC or S

D

P

Q

Pc

Qc

MRmonopolist

Qm

Pm

The difference in the combined consumer & producer surpluses is the light purple area.

This is the loss of welfare when monopoly is compared to perfect competition.

MC or S

D

P

Q

Pc

Qc

MRmonopolist

Qm

Pm

Natural Monopoly

a situation in which ATC declines continually with increased output.

So a single firm would be the lowest cost producer of the output demanded.

ATC doesn’t turn upward until a very high output level, beyond the amounts that consumers will buy.

ATC

$

quantity

Remember: the MC curve is below the ATC curve when ATC is sloping downward.

ATCMC

$

quantity

Draw the demand and MR curves.

ATCMCMR

D

$

quantity

Natural Monopoly:operating freely

ATCMC

D

$

quantityQ*

P*

MR

Regulation

marginal cost pricing (P = MC)

average cost pricing (P = ATC)

Natural Monopoly: marginal cost pricing regulation

ATCMC

D$

quantity

Pm

Qm

MC pricing uses the price where MC intersects D. But at that point, P < ATC .Firm has a loss! So this won’t work.

MR

Natural Monopoly: Average Cost Pricing Regulation

In this situation, the firm sees the demand curve for its product as the orange line.The MR curve would be the bright blue line.The firm would equate MR to MC and produce QR.

QR

$

Q

MCATC

D

MR

PR

If the government uses average cost pricing to regulate a monopolist, the price PR is set where the demand curve intersects the ATC curve.

Since P = ATC, the firm will have zero economic profits.So this can work.

Example

A monopolist faces the following situation.

Demand: P = 300 – 3 Q

TC = Q3 – 21 Q2 + 333 Q + 180

(a) Determine the profit-maximizing output, price, TR, TC & profit if the monopolist operates without regulation.

(b) Determine the output, price, TR, TC & profit if the monopolist is regulated using average cost pricing.

(a) monopolist operating without regulation Demand: P = 300 – 3 QTC = Q3 – 21 Q2 + 333 Q + 180

To maximize profits, the firm will set MR = MC.

TR = PQ = 300 Q – 3 Q2

MR = dTR/dQ = 300 – 6Q

MC = dTC/dQ = 3Q2 – 42 Q + 333

Equate MR = 300 – 6Q to MC = 3Q2 – 42 Q + 333

300 – 6Q = 3Q2 – 42 Q + 333

0 = 3Q2 – 36 Q + 33

Dividing through by 3, we find

0 = Q2 – 12 Q + 11

0 = (Q – 1) (Q – 11)

So Q = 1 or Q = 11

It can be shown using the second derivative of the total profit function that profit is maximized at Q = 11 and minimized at Q = 1.

So at the maximum, where Q = 11:

P = 300 – 3 Q = 300 – 3(11) = 300 – 33 = 267

TR = PQ = (267)(11) = 2937

TC = Q3 – 21 Q2 + 333 Q + 180 = (11)3 – 21 (11)2 + 333(11) + 180 = 2633

Profit = TR – TC = 2937 – 2633 = 304

(b) Monopolist regulated by average cost pricing

Demand: P = 300 – 3 QTC = Q3 – 21 Q2 + 333 Q + 180ATC = TC/Q = Q2 – 21 Q + 333 + (180/Q)Plotting points & graphing ATC & D, you see that they intersect when Q = 15. At that output, P = 300 – 3 Q = 300 – 3(15) = 255, andATC = Q2 – 21 Q + 333 + (180/Q) = (15)2 – 21 (15) + 333 + (180/15) = 255So the regulator sets the price at 255 & the firm produces 15 units of output.

With P = 255 & Q = 15:

TR = PQ = (255)(15) = 3825TC = Q3 – 21 Q2 + 333 Q + 180 = (15)3 – 21(15)2 + 333 (15) + 180 = 3825 [or TC = ATC(Q) = 255(15) = 3825]Economic profit = TR – TC = 0& firm makes just a normal accounting profit.

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Monopoly