lecture 1 - monopoly

Introduction; MonopolyEconomics 302 - Microeconomic Theory II: Strategic Behavior

Instructor: Songzi Du

compiled by Shih En LuSimon Fraser University

January 6, 2015

ECON 302 (SFU) Lecture 1 January 6, 2015 1 / 26

Welcome to ECON 302!

Instructor: Songzi Du

Todays class:

1 Overview of the course material2 Monopoly


Whats this class about?

Game theory

game: interaction of people.

In life you have to interact with others, therefore you have to knowhow to play games.

Applying game theory to study markets

Economics of information


Why is this class hard?

Abstract reasoning

Abstraction: focusing on one or a few aspects of a complex situation.

Using math.

You need to know differential calculus.


This Course

Read the syllabus!

My office hours: Tuesday 10:30-12:20 in WMC 4657 (but not thisweek).

TAs OHs: 2 hours/week

Textbooks: none required. See syllabus for recommended text.

Slides will be posted at http://www.sfu.ca/~songzid/302. Takeyour own notes!


Homework

7 assignments. Discuss problems with each other - most of you willlearn a lot from each other - but write your own solutions.

Due at the end of lecture on Tuesday

20% of your grade

Each problem is graded for completeness.

Use them as practices for exams.


My Expectations

Never fall behind. The class material is cumulative. You shouldunderstand everything in a weeks lecture slides by the end of theweek.

Everybody should really do the assignments and practice exams. Youcannot learn game theory by listening to lecture and readinglecture slides.

The final grade distribution will be set according to the Economicsdepartment guidelines. You will not be penalized for low classaverages on exams.

Half of the quiz and midterm points can be transferred to the final.

Read the syllabus and course policies carefully and never ask foran exception: the answer is NO.


Derivatives and Maximization

f HxL

f ' H1L

1 2 3 4 5

1

2

3

4

5

6

f (x) is the slope of the tangent line at the point (x , f (x)).At maximum of f (x), f (x) = 0.ECON 302 (SFU) Lecture 1 January 6, 2015 8 / 26

Derivatives and Maximization

(f (x) + g(x)) = f (x) + g (x)Product rule: (f (x)g(x)) = f (x)g (x) + f (x)g(x).f (x) = axk , where a and k are constants. Then f (x) = ak xk1.f (x) = ln(x), then f (x) = 1/x .Review: quotient rule and chain rule.


What Is a Monopoly?

A firm that is the only one in the market, i.e., no firm produces aclose substitute.

As a result, a monopoly does not lose all its demand when it raisesprice above marginal cost: it has market power.

A monopoly picks a point on the market demand curve.


Sources of Monopoly

Government policy

1 Directly owned/regulated by the state (ICBC)2 Patents (drugs), copyrights (music), trademarks (brand names),

licenses (nightclubs), etc.

Large efficient scale

1 Natural monopoly: decreasing average cost over the relevant range ofquantities (utilities)

2 Network externalities on the demand side (Microsoft Office)

Firm actions

1 Control of essential input (DeBeers)2 Being more efficient than other firms and/or preventing entry

(Walmart) - this is different


Profit Maximization

Today, we assume that the monopoly charges the same price to everycustomer. No price discrimination.

Notation: P = price per unit, q = quantity.

Demand curve D(P) the number of people willing to buy at priceP; their willingness-to-pay is greater than P.

Inverse demand curve: P(q), firms cost function: C (q)

Profit: pi(q) = P(q)q C (q) (Total Revenue - Total Cost)First-order condition:pi(q) = P(q) + P (q)q C (q) = MR(q)MC (q) = 0


Profit Maximization (II)

FOC: Marginal Revenue = P(q) + P (q)q = C (q) = Marginal CostThis pins down the monopoly quantity qm. Read the price off thedemand curve: Pm = P(qm).

Note: Because P (q) < 0, we have MR < P whenever q > 0.

In words: the monopolist chooses the quantity where marginalrevenue equals marginal cost and charges the maximum price thatbears that quantity.


Profit Maximization: Some Caveats

We have assumed that the demand and cost functions aredifferentiable, and the good is perfectly divisible.

We have assumed that the second-order condition (pi(q) < 0) holds,i.e. that MR intersects MC from above. We will usually deal withdecreasing MR and increasing MC , in which case this automaticallyholds.

Just like for perfectly competitive firms, you need to check that themonopoly wouldnt prefer shutting down.


Example

Demand: D(P) = 12 12PMonopolists cost: C (q) = q2

Find the monopoly price and quantity.

Monopolist solves:maxq

q 2(12 q) q2

FOC: 2(12 q) 2q 2q = 0.Monopoly quantity qm = 4, monopoly price Pm = 16.


Welfare

0 2 4 6 8 10 120

5

10

15

20

q

P

Continue with our example: MC (q) = 2q and P = 24 2q qm = 4.Set equal the marginal social cost and benefit (willingness-to-pay) 2q = 24 2q q = 6.Units between 4 and 6 yield a benefit between 16 and 12, but onlycost between 8 and 12.ECON 302 (SFU) Lecture 1 January 6, 2015 16 / 26

Welfare

Both the consumers and the monopolist would be better off if:

two additional units were produced by the monopolist and sold at aprice of 12 to consumers whose willingness-to-pay is between 16 and 12

the monopolist keep the regular price of Pm = 16, which is forconsumers whose whose willingness-to-pay is above 16

this improvement assumes that the monopolist is able to identifyconsumers who have lower willingness-to-pay. For example: pricediscounts offered to students (student ID), senior citizens (driverslicence), etc.

The monopoly outcome is not Pareto efficient: everyone(consumers and the monopolist) could be better off!


Welfare

0 2 4 6 8 10 120

5

10

15

20

q

P

The deadweight loss (inefficiency) is the area between the demandand marginal cost curves, from the actual quantity to the efficientquantity, = 12 (6 4) (16 8) = 8 in this example.ECON 302 (SFU) Lecture 1 January 6, 2015 18 / 26

Price, Marginal Cost and Elasticity at the MonopolistsOptimum

Remember FOC: P(q) + P (q)q = C (q)P MC = dPdq q

PMCP = dPdq qP = 1 , where is the price elasticity of demand:

= dq/qdP/P

Equivalently,

markup =P MCMC

=1

1 .

Markup over marginal cost gets lower as elasticity increases: thefirms market power decreases.

What happens when ?


Price, Marginal Cost and Elasticity at the MonopolistsOptimum

Remember FOC: P(q) + P (q)q = C (q)P MC = dPdq q

PMCP = dPdq qP = 1 , where is the price elasticity of demand:

= dq/qdP/P

Equivalently,

markup =P MCMC

=1

1 .

Markup over marginal cost gets lower as elasticity increases: thefirms market power decreases.

What happens when ?ECON 302 (SFU) Lecture 1 January 6, 2015 19 / 26

Example Continued

We found qm = 4 and Pm = 16.

Marginal cost is C (q) = ddq (q2) = 2q, so it is 8 at qm. The markup

is 100%.

Thus = PPMC =16

168 = 2.

Now lets find directly using the demand D(P) = 12 12P.

= dqdPqP

= 12416

= 2.


Estimated Price Elasticities of Demand in U.S., 1990s

Salt 0.1 Movies 0.9Matches 0.1 Housing, owner occupied, long-run 1.2Toothpicks 0.1 Shellfish, consumed at home 0.9Airline travel, short-run 0.1 Oysters, consumed at home 1.1Gasoline, short-run 0.2 Private education 1.1Gasoline, long-run 0.7 Tires, short-run 0.9Residential natural gas, short-run 0.1 Tires, long-run 1.2Residential natural gas, long-run 0.5 Radio and television receivers 1.2Coffee 0.25 Restaurant meals 2.3Fish (cod) consumed at home 0.5 Foreign travel, long-run 4.0Tobacco products, short-run 0.45 Airline travel, long-run 2.4Legal services, short-run 0.4 Fresh green peas 2.8Physician services 0.6 Automobiles, short-run 1.2 1.5Taxi, short-run 0.6 Chevrolet automobiles 4.0Automobiles, long-run 0.2 Fresh tomatoes 4.6

Source: http:

//scholar.harvard.edu/files/alada/files/price_elasticity_of_demand_handout.pdf


Why Would a Government Create a Monopoly?

Monopolies come with a deadweight loss. Why create them?

The government might take control of a monopoly that would existanyway (e.g. utilities).

The government can generate revenue or reduce expenditures byselling the right to form a monopoly (e.g. certain toll highways).

The government might want to encourage innovation through patentsand copyright. The alternative would be to subsidize, which increasesthe need for revenues and could therefore increase deadweight losseselsewhere.


What Can Government Do about Monopolies?

Divestiture: monopolies that control a key resource can be forced tosell off some of that resource. For example, AT&T had to sell off itslocal operations in 1982.

In other cases, such as natural monopolies, the government can stillaffect the price:

1 through taxes (or subsidies);2 directly through regulation.


Taxes and Monopolies

Does taxing a monopoly improve efficiency?

It does redistribute money from the monopoly (and its customers)toward the government.

Just like under perfect competition, there is a tax wedge between thecurves determining quantity.

Here, they are the MR and MC curves (rather than the supply anddemand curves).

Once you know the quantity, read the price paid by consumers(consumers price, Pc) off the demand curve.

The price received by the monopoly (monopolists price, Pm) is Pcless the tax.


Taxes and Monopolies: Per-unit Tax

Return to our example: MC (q) = 2q, P(q) = 24 2q andMR(q) = d(P(q)q)dq = 24 4q.We found qm = 4 and Pm = 16 with no taxes. Now suppose theres aper unit tax of 6.

Find the new quantity, price paid by consumers and price received bythe monopolist.

Monopolist solves maxq P(q)q C (q) 6q.24 4qm = 2qm + 6With tax: qm = 3, Pc = 18, Pm = 18 6 = 12.Per-unit tax of 6 increases the consumers price by only 2.

Does tax leads to the efficiency of P(q) = MC (q)?

No, we are even farther away from market clearance.


Taxes and Monopolies: Ad Valorem (Sales) Tax

Instead of a per unit tax of 6, in the previous example suppose theresa percentage tax (sales tax) of 100% of the price received by themonopoly (equivalently, 12 of the price paid by consumers).

Monopolist solves:

maxq

1

1 + t(24 2q)q q2,

where t = 100%, FOC: 1/2 (24 4qm) 2qm = 0, or qm = 3.Consumers price Pc is still read off the demand curve: Pc = 18.

But what does the monopoly get now? Monopolists pricePm =

11+tPc = 9.

In words: total revenue is 11+t =12 of what it was without tax at

every q. Thus so is marginal revenue MR(q) = 12 2q. SettingMR = MC gives: 12 2qm = 2qm, or qm = 3.


lecture 1 - monopoly

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