Customer‘s safety is the future trend of the foodservice and hospitality industry

313Lecture8.ExternalitiesIslides.pdf

Home >Business & Finance homework help >Management homework help >Customer‘s safety is the future trend of the foodservice and hospitality industry

Externalities

1. Definitions

Economics 313

Externalities

Slide 2

 The Fundamental Welfare Theorems connect perfectly competitive markets and Pareto efficiency. But “perfectly” competitive markets require more that free entry and price flexibility

 In the last lecture, we saw how imperfect information can prevent efficient exchanges from taking place. In this lecture, we turn to another source of market “imperfection”: so-called “externalities”

 Key to the welfare theorems is the fact that prices convey useful information regarding preferences and costs. Even if participants don’t explicitly consider it, prices allow the “invisible hand” can guide resources into their highest value use.

 By definition, externalities are excluded from these calculations

Definition of Externality

Slide 3

 We will use the term externality to describe any cost or benefit generated by one agent that affects another agent without appropriate monetary compensation occurring

 Externalities occur when some market transaction involves costs and/or benefits that accrue to people outside the transaction  Externalities are sometimes called spillovers

 In such a case prices don’t allow agents to internalize marginal benefits and costs, and the first welfare theorems fail

Pecuniary Externalities

Slide 4

 Not externalities under our definition

 Refers to the effect one agent’s demand (or supply) has on the welfare of other agents due to the effect they have on market price

 This is a “spillover” in the sense that one person’s choices affect other people, but this is exactly how prices can guide the allocation of resources

 Externalities (in our sense) are effects that are not mediated by prices

Definition of Externality

Slide 5

 Negative Externality  A cost imposed on a third party not directly involved in the

economic transaction  Also called these external costs: external to the market  Result in “too much of a bad thing”

 Positive Externality  A benefit conferred on a third party not directly involved in

the transaction  Also call these external benefits: external to the market  Results in “too little of a good thing”

Definition of Externality

Slide 6

 Production Externality  Externality arising from the production of the good  Results in difference between Marginal Private Cost (=supply)

and Marginal Social Cost curves

 Consumption Externality  Externality arising from the consumption of the good  Results in difference between Marginal Private Benefit

(=demand) and Marginal Social Benefit curves

Nature of External Costs

Slide 7

 Could be monetary (result in out-of pocket expenses)  Climate change examples

 Farmers buying more crop insurance because of increase in adverse weather events

 Coastal communities’ investment in infrastructure to mitigate flooding  External costs can be measured in dollars

 Could be non-monetary (result in utility costs)  Climate change examples

 People are less happy at the prospect of living in a work in which polar bears become extinct

 Certain regions of the world will face upheaval due to rising sea levels  Can be measured in willingness to pay/willingness to accept

Understanding Externalities is Important

Slide 8

 Many important public debates concern externalities

 Pollution  Research and development  Smoking  Higher education  Vaccinations  Antibiotics  Electric Cars  Drug legalization  Fat taxes  …..

Where We Are Going

Slide 9

 Modelling externalities  Consequences of externalities

 Potential resolutions

 Taxes and subsidies

 Quantity mechanisms  Quotas or government provision of a public good

 Establishing firm property rights  Allowing markets to solve externalities on their own  Coase theorem

-- end of part 1 --

Externalities

2. Market Equilibrium

Economics 313

Negative Externalities

Slide 12

Price ($/MWh)

Quantity of electricity (MWh)

𝑄𝑄𝑀𝑀𝑀𝑀𝑀𝑀𝑄𝑄∗

𝑃𝑃∗

𝑃𝑃𝑀𝑀𝑀𝑀𝑀𝑀

Marginal External Cost, MEC

Supply, 𝑆𝑆 = 𝑀𝑀𝐶𝐶𝐼𝐼 (Marginal Private Cost – MPC)

Marginal Social Cost, 𝑀𝑀𝑆𝑆𝐶𝐶 = 𝑀𝑀𝐶𝐶𝐼𝐼 + 𝑀𝑀𝑀𝑀𝐶𝐶

𝑀𝑀𝑀𝑀𝐶𝐶

Demand, D (Marginal Private Benefit – MPB)

Positive Externalities

Slide 13

Price ($/degree)

Quantity of College Degrees

𝑄𝑄𝑀𝑀𝑀𝑀𝑀𝑀 𝑄𝑄 ∗

𝑃𝑃∗

𝑃𝑃𝑀𝑀𝑀𝑀𝑀𝑀

marginal external benefit, MEB

Social Demand (marginal social benefit), M𝑆𝑆𝑆𝑆 = 𝐷𝐷 + 𝑀𝑀𝑀𝑀𝑆𝑆

𝑀𝑀𝑀𝑀𝑆𝑆

Supply, 𝑆𝑆 = 𝑀𝑀𝐶𝐶𝐼𝐼 (marginal private cost – MPC)

Demand, D (marginal private benefit – MPB)

Concept Check

Slide 14

 Which of the following illustrates the concept of a negative externality?

A. A professor plays a vigorous game of racquet ball B. A flood wipes out a farmer’s entire corn crop C. A professor plays loud music at 2am D. The government intervenes in the market E. Bees kept for making honey pollinate fruit trees

Concept Check

Slide 15

 When positive externalities are present in a market

A. Producers will not be affected by consumers B. Underproduction will occur C. Supply is too high D. The market will operate smoothly E. Overproduction will occur

Concept Check

Slide 16

 If x2 units of output are produced, which area represents net social benefits?

A. f B. g + m C. m D. f + g + m E. f - j

Concept Check

Slide 17

 If output falls from x1 to x2 units, which area represents the change in social costs?

A. j + h + n. B. h + n. C. n. D. j. E. h.

Concept Check

Slide 18

 If x2 units of output are produced, which area represents (total) external costs?

A. j B. j + h C. j + h + g D. g E. There are no external costs at x2 units of output

-- end of part 2 --

Externalities

3. Spillovers between firms

Economics 313

A production externality

Slide 21

 A machine shop, 𝑀𝑀, has opened beside a daycare, 𝐷𝐷. Unfortunately for the daycare, the machine shop can get pretty noisy.

 The noise from the machine shop is affecting the children’s ability to sleep, and it’s costly for the machine shop to limit noise during nap time at the daycare.

 Both businesses operate in perfectly competitive input and output markets

Cost Functions

Slide 22

 Let 𝑚𝑚 be the output of the machine shop, and 𝑠𝑠 be the level of sound it produces during naptime. Let 𝑑𝑑 be the output of the daycare.

 The cost functions for the two firms are 𝐶𝐶𝑀𝑀(𝑚𝑚, 𝑠𝑠) where 𝜕𝜕𝐶𝐶𝑀𝑀 𝜕𝜕𝜕𝜕

> 0, 𝜕𝜕𝐶𝐶𝑀𝑀 𝜕𝜕𝑠𝑠

< 0

and 𝐶𝐶𝐷𝐷(𝑑𝑑, 𝑠𝑠) where 𝜕𝜕𝐶𝐶𝐷𝐷 𝜕𝜕𝑑𝑑

> 0, 𝜕𝜕𝐶𝐶𝐷𝐷 𝜕𝜕𝑠𝑠

> 0

Profit Maximisation

Slide 23

 𝑀𝑀 chooses 𝑚𝑚 and 𝑠𝑠 to maximise profit. max 𝜕𝜕,𝑠𝑠

𝑝𝑝𝜕𝜕𝑚𝑚 − 𝐶𝐶𝑀𝑀(𝑚𝑚, 𝑠𝑠)

by solving the first order conditions

𝑝𝑝𝜕𝜕 = 𝜕𝜕𝐶𝐶𝑀𝑀 𝜕𝜕𝑚𝑚

0 = 𝜕𝜕𝐶𝐶𝑀𝑀 𝜕𝜕𝑠𝑠

Since the “price of noise” is zero.  Similarly, the FOC for D is

𝑝𝑝𝑑𝑑 = 𝜕𝜕𝐶𝐶𝐷𝐷 𝜕𝜕𝑑𝑑

because the daycare cannot choose the level of noise.

Optimality

Slide 24

 Now imagine that the owner of 𝐷𝐷 decides to buy the machine shop. What should they do? Choose 𝑑𝑑, 𝑚𝑚 and 𝑠𝑠 to maximise total profit.

max 𝑑𝑑,𝜕𝜕,𝑠𝑠

𝑝𝑝𝜕𝜕𝑚𝑚 + 𝑝𝑝𝑑𝑑𝑑𝑑 −𝐶𝐶𝑀𝑀 𝑚𝑚, 𝑠𝑠 − 𝐶𝐶𝐷𝐷(𝑑𝑑, 𝑠𝑠)

by solving the first order conditions

𝑝𝑝𝑑𝑑 = 𝜕𝜕𝐶𝐶𝐷𝐷 𝜕𝜕𝑑𝑑

𝑝𝑝𝜕𝜕 = 𝜕𝜕𝐶𝐶𝑀𝑀 𝜕𝜕𝑚𝑚

0 = 𝜕𝜕𝐶𝐶𝑀𝑀 𝜕𝜕𝑠𝑠

+ 𝜕𝜕𝐶𝐶𝐷𝐷 𝜕𝜕𝑠𝑠

The reason why the “decentralized” equilibrium is inefficient is clear in the final condition: maximising overall profits (i.e. efficiency) requires the effect of noise on the cost of the daycare to be included.

The noise “market”

Slide 25

𝑀𝑀𝐶𝐶𝐷𝐷 = 𝜕𝜕𝐶𝐶𝑀𝑀 𝜕𝜕𝑠𝑠

−𝑀𝑀𝐶𝐶𝐷𝐷= − 𝜕𝜕𝐶𝐶𝑀𝑀 𝜕𝜕𝑠𝑠

Noise

Recall that 𝜕𝜕𝐶𝐶𝑀𝑀 𝜕𝜕𝑠𝑠

< 0

𝑠𝑠∗𝑠𝑠𝑒𝑒

-- end of part 3 --

Externalities

4. The tragedy of the commons

Economics 313

Sheep keeping on common land

Slide 28

 A much discussed case of externalities. Name comes from Hardin, G. 1968. The tragedy of the commons. Science 162, 1243–8.

 The idea is that common property is subject to overuse.

 Imagine that it costs $𝑚𝑚 to buy a sheep in a competitive lamb market, and that it produces wool that can be sold in a competitive market.

 Villagers can graze the sheep on the community land.

Sheep keeping on common land

Slide 29

 Assume that the production of wool depends on the number of sheep grazing on the common. Let 𝑓𝑓(𝑠𝑠) be the total value of wool when there are 𝑠𝑠 sheep on the field.

 The efficient number of sheep will maximise the surplus

max 𝑠𝑠

𝑓𝑓 𝑠𝑠 − 𝑚𝑚𝑠𝑠

so 𝑓𝑓′ 𝑠𝑠 = 𝑚𝑚

Sheep keeping on common land

Slide 30

 If villagers decide independently how many sheep to keep they will think about the return they get when they put a sheep out to graze.

 This is the “average product” 𝑓𝑓(𝑠𝑠) 𝑠𝑠

 They will add sheep until the average product equals the cost of a lamb. Each new lamb lowers the average product (assuming diminishing returns), so sheep are added until

𝑓𝑓(𝑠𝑠∗) 𝑠𝑠∗

= 𝑚𝑚

Tragedy of the Commons

Slide 31

𝑀𝑀𝐶𝐶𝑠𝑠𝑠𝑒𝑒𝑒𝑒𝑠𝑠 = 𝑚𝑚

Sheep𝑠𝑠 ∗𝑠𝑠𝑒𝑒

𝑓𝑓(𝑠𝑠) 𝑠𝑠

𝑓𝑓𝑓(𝑠𝑠)

𝑁𝑁 commuters can either take the train or drive their cars. All they care about is the length of time it takes to get to work.

The train takes 60 minutes no matter how many passengers are riding, but the time to drive depends on how many commuters choose to drive.

Assume that payoffs are equal to the negative of the commuting time.

The commuter game

# of cars time

1 21 55 75 5 25 60 80

10 30 65 85 15 35 70 90 20 40 75 95 25 45 80 100 30 50 85 105 35 55 90 110 40 60 95 115 45 65 100 120 50 70 105 125

Do you drive or take the train?

A: Drive B: Train

Train takes 60 minutes

Nash Equilibrium

To find a Nash Equilibrium we can test some candidates.

Is everyone riding the train a Nash Equilibrium?

No: if (any) one commuter deviates and chooses to drive, his or her payoff rises: with a time saving of 39 minutes.

The unique NE is when 40 commuters drive.

In the NE all commuters spend 60 minutes traveling.

If we persuaded 1 additional driver to ride the train, that person would still spend 60 minutes on the commute. No worse off….

The other 39 drivers would each gain 1 minute of time, for a total saving of 39 minutes.

The Nash equilibrium is not socially efficient

The commuter game

How about a getting 10 of the drivers to ride the train?

30 drivers spend 50 minutes each.

Drivers are better off and train riders no worse off.

The commuter game

The socially efficient number of drivers is 20.

Each driver takes 40 minutes.

A 21st driver would save 19 minutes, but cost 20 minutes delay to other 20 drivers.

=>Total commuting time rises.

If one more driver rode the train, her time would increase by 20 minutes, but save only 1 minute for each of the remaining 19 drivers.

=>Total commuting time rises.

The commuter game

-- end of part 4 --

Externalities

5. Addressing Inefficiencies

Economics 313

Three basic policy approaches

Slide 41

 Price mechanisms  The application of (Pigouvian) taxes or subsidies

 Quantity mechanisms  Quotas or government provision of a public good

 Create a market with property rights  Allowing markets to solve externalities on their own  Coase theorem

We will discuss the third case extensively next lesson….

Pigouvian Tax

Slide 42

 In the noise example, producers of 𝑠𝑠 treated it as if it were free

What if we created a tax on noise? Say, 𝑡𝑡 per unit.

max 𝜕𝜕,𝑠𝑠

𝑝𝑝𝜕𝜕𝑚𝑚 − 𝐶𝐶𝑀𝑀 𝑚𝑚, 𝑠𝑠 − 𝑡𝑡𝑠𝑠

Now the first order conditions are

𝑝𝑝𝜕𝜕 = 𝜕𝜕𝐶𝐶𝑀𝑀 𝜕𝜕𝑚𝑚

𝑡𝑡 = − 𝜕𝜕𝐶𝐶𝑀𝑀 𝜕𝜕𝑠𝑠

What should we choose for 𝑡𝑡?

Pigouvian Tax

Slide 43

We want choose the value of 𝑡𝑡 that makes the firm’s first order conditions be the same as the Social Optimum (that we found when both firms had a common owner)

0 = 𝜕𝜕𝐶𝐶𝑀𝑀 𝜕𝜕𝑠𝑠

+ 𝜕𝜕𝐶𝐶𝐷𝐷 𝜕𝜕𝑠𝑠

𝑡𝑡 = 𝜕𝜕𝐶𝐶𝐷𝐷 𝜕𝜕𝑠𝑠

The noise “market”

Slide 44

𝑀𝑀𝐶𝐶𝐷𝐷 = 𝜕𝜕𝐶𝐶𝑀𝑀 𝜕𝜕𝑠𝑠

−𝑀𝑀𝐶𝐶𝐷𝐷= − 𝜕𝜕𝐶𝐶𝑀𝑀 𝜕𝜕𝑠𝑠

Noise

The tax lowers the cost reduction from noisy production

𝑠𝑠∗𝑠𝑠𝑒𝑒

𝑡𝑡𝑒𝑒

↓

Add a toll on driving:

Tax worth the equivalent of 20 minutes in travel time.

The commuter game

# of cars time

1 21+20 55 95 5 45 60 100

10 50 65 105 15 55 70 110 20 60 75 115 25 65 80 120 30 70 85 125 35 75 90 130 40 80 95 135 45 85 100 140 50 90 105 145

With a toll on driving equal to the utility cost of 20 minutes in the commute the NE will have

20 drivers taking 40 minutes plus paying the “20 minute” toll.

and everyone else riding the train.

The commuter game

As in the old NE total disutility of commuting would be N commuters times 60 “minutes”.

But now we would have collected 20 X 20 minutes worth of tax revenue.

Correcting inefficiencies leads to a “free lunch.”

The commuter game: efficient taxation

Externalities Example: Pigouvian Tax

Slide 49

 More generally, impose a tax equal to the marginal external cost

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

x50

MEC=Tax, T

𝑥𝑥𝑆𝑆 (MPC)

𝑀𝑀𝑆𝑆𝐶𝐶 = 𝑀𝑀𝑃𝑃𝐶𝐶 + 𝑇𝑇

𝑇𝑇

𝑥𝑥𝐷𝐷 (MSB)

Externalities Example: Pigouvian Tax

Slide 50

 The outcome is efficient with the correctly set tax

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

x50

MEC=Tax, T

𝑥𝑥𝑆𝑆 (MPC)

𝑀𝑀𝑆𝑆𝐶𝐶 = 𝑀𝑀𝑃𝑃𝐶𝐶 + 𝑇𝑇

𝑇𝑇

𝑥𝑥𝐷𝐷 (MSB)

Quotas and quantity mechanisms

Slide 51

 Price mechanisms have advantages in that they allow for firms to respond optimally and make the most efficient changes. They do require politicians to impose “taxes”

 Quantity mechanisms work more directly on the “good” or “bad” that is creating the inefficiency. These can afford more certainty as to levels, but require monitoring and in some cases for governments to make specific choices over production technology

 Quotas are a specific limitation to production. These need in general to be allocated, and some form of auction might be used

The noise “market”

Slide 52

𝑀𝑀𝐶𝐶𝐷𝐷 = 𝜕𝜕𝐶𝐶𝑀𝑀 𝜕𝜕𝑠𝑠

= 𝑡𝑡

−𝑀𝑀𝐶𝐶𝐷𝐷= − 𝜕𝜕𝐶𝐶𝑀𝑀 𝜕𝜕𝑠𝑠

Noise

The quota is a quantity restriction directly limiting the level of sound

𝑠𝑠∗𝑠𝑠𝑒𝑒

�̅�𝑠

Slide 53

 You could also implement a quota of 40 units of x

Externalities Example: Quota

Slide 53

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

x50

MEC

𝑥𝑥𝑆𝑆 (MPC)

𝑀𝑀𝑆𝑆𝐶𝐶

𝑥𝑥𝐷𝐷 (MSB)

𝑥𝑥𝑆𝑆 with quota

-- end of part 5 --

Externalities

6. Numerical Examples

Economics 313

Externalities with Equations

Slide 56

Ariel produces aluminum cubes, facing costs of 𝑐𝑐𝐴𝐴 𝐴𝐴 = 𝐴𝐴2

10 ,

where A is the number of cubes produced.

Bjorn grows beets next to Ariel’s factory, facing costs of 𝑐𝑐𝑆𝑆 𝐴𝐴, 𝑆𝑆 = 5𝑆𝑆 +

𝐵𝐵2

100 + 𝐴𝐴

20 , where B is the number of beets

produced.

Which of the following statement is true: A. Aluminum production generates a negative externality on

beet production B. Aluminum production generates a positive externality on

beet production

Question

Slide 57

Firm A: costs of 𝑐𝑐𝐴𝐴 𝐴𝐴 = 𝐴𝐴2

Firm B: costs of 𝑐𝑐𝑆𝑆 𝐴𝐴, 𝑆𝑆 = 5𝑆𝑆 + 𝐵𝐵2

100 + 𝐴𝐴

Assume competitive price of A is $30 and price of B is $15. Suppose the socially optimal 𝐴𝐴∗ = 100 and 𝑆𝑆∗ = 500.

What is the tax per A at the socially optimal A, that would induce efficiency? A. 30 B. 15 C. 10 D. 25 E. 20

Question

Slide 58

Firm A: costs of 𝑐𝑐𝐴𝐴 𝐴𝐴 = 𝐴𝐴2

Firm B: costs of 𝑐𝑐𝑆𝑆 𝐴𝐴, 𝑆𝑆 = 5𝑆𝑆 + 𝐵𝐵2

100 + 𝐴𝐴

Assume competitive price of A is $30 and price of B is $15. Suppose the socially optimal 𝐴𝐴∗ = 100 and 𝑆𝑆∗ = 500.

What is the tax per A at the socially optimal A, that would induce efficiency? A. 30 B. 15 C. 10 D. 25 E. 20

The MEC of A at any point is the partial derivative of the cost function of B with respect to A: 1

10 𝐴𝐴

So at the socially optimal A: T=10

-- end of part 6 --