L5: Welfare Economics and the Evnrionment Flashcards by Frazer George

For the basic welfare economics model, what two assumptions are made?

No externalities exist in either consumption or production
All produced goods and services are private (not public) goods

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For simplicity, strip the problem down to its barest essentials:
• economy consists of two ___ (A and B);
• two _____ (X and Y) are _____;
• production of each good uses two inputs (Which are??) each available
in a fixed quantity

▪ For simplicity, strip the problem down to its barest essentials:
• economy consists of two persons (A and B);
• two goods (X and Y) are produced;
• production of each good uses two inputs (K for capital and L for labour) each available
in a fixed quantity

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▪ Marginal utility written as and defined by: , etc.

▪ Marginal product written as and defined by: , etc.

▪ Marginal utility written as and defined by: dU/dX or dU/dY

▪ Marginal product written as and defined by: dY/dL
or equivalents for product X and for Capital

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Marginal rate of utility substitution for A:
• Definition?

It varies with the levels of _____ of X and Y and is given by the ____of the ____ _____
Denote A’s ____ ____ _____ ______ as MRUS^A

. Similarly for _

Marginal rate of utility substitution for A:
• The rate at which X can be substituted for Y at the margin, or vice versa, while holding the level of A’sutility constant
• It varies with the levels of consumption of X and Y and is given by the slope of the indifference curve
• Denote A’s marginal rate of substitution as MRUSA
. Similarly for B

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The marginal rate of technical substitution in the production of X:
• Definition

It varies with the input levels for ___ and ___ and is given by the ____ of the _____
Denote the ___ ____ ____ ____ in the production of X as MRTSX .Similarly for Y

What is an isoquant?

The marginal rate of technical substitution in the production of X:
• The rate at which K can be substituted for L at the margin, or vice versa, while holding the level output
of X constant
• It varies with the input levels for K and L and is given by the slope of the isoquant
• Denote the marginal rate of substitution in the production of X as MRTSX .Similarly for Y

An isoquant, in microeconomics, is a contour line drawn through the set of points at which the same quantity of output is produced while changing the quantities of two or more inputs.

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The marginal rates of transformation for the commodities X and Y:

• The rates at which the ____ of one can be transformed into the other by ____ shifting ____
or ____ from one line of production to the other

• MRTL
is the increase in the ___ of Y obtained by shifting a small amount of ___ from use in the
___ of X to use in the _____ of Y, or vice versa

• MRTK
is the increase in the ___ of Y obtained by shifting a small amount of ___ from use in the
_____ of X to use in the _____ of Y, or vice versa

The marginal rates of transformation for the commodities X and Y:

• The rates at which the output of one can be transformed into the other by marginally shifting capital or labour from one line of production to the other

• MRTL
is the increase in the output of Y obtained by shifting a small amount of labour from use in the
production of X to use in the production of Y, or vice versa

• MRTK
is the increase in the output of Y obtained by shifting a small amount of capital from use in the
production of X to use in the production of Y, or vice versa

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Economic Efficiency

An allocation of resources is efficient if …..

▪ Inefficient allocation occurs when it is possible to improve …..

▪ A gain by one or more persons without anyone else suffering is a ___ ____

▪ When all such gains have been made, the resulting allocation is _____ optimal (or ____ efficient).

▪ Efficiency in allocation requires that three efficiency conditions are fulfilled

An allocation of resources is efficient if it is not possible to make one or more persons better
off without making at least one other person worse off.

▪ Inefficient allocation occurs when it is possible to improve someone’s position without
worsening the position of anyone else.

▪ A gain by one or more persons without anyone else suffering is a Pareto improvement.

▪ When all such gains have been made, the resulting allocation is Pareto optimal (or Pareto efficient).

▪ Efficiency in allocation requires that three efficiency conditions are fulfilled

efficiency in consumption
efficiency in production
product-mix efficiency

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▪ Efficiency in allocation requires that three efficiency conditions are fulfilled:

▪ Efficiency in allocation requires that three efficiency conditions are fulfilled

efficiency in consumption
efficiency in production
product-mix efficiency

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Consumption efficiency requires that the…

If this condition was not satisfied, it would be possible to re-arrange the allocation between A and B of whatever is being produced so as to ….?

Consumption efficiency requires that the marginal rates of utility substitution for the two
individuals are equal:

MRUSA = MRUSB

If this condition was not satisfied, it would be possible to re-arrange the allocation as
between A and B of whatever is being produced so as to make one better-off without
making the other worse-off.

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▪ Efficiency in production requires that …

▪ If this condition was not satisfied, it would be possible to re-allocate inputs to production so
as to produce …

▪ Efficiency in production requires that the marginal rate of technical substitution be the same
in the production of both commodities. That is
MRTSx = MRTSy
▪ If this condition was not satisfied, it would be possible to re-allocate inputs to production so
as to produce more of one of the commodities without producing less of the other.

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▪ Consumption and production affect ____ and ____ in an uncompensated or unpaid way

▪ We are interested in effects from one agent to another which are unintended and where there is no ___or ___

▪ External effects can be classified according to what sort of economic activity they ___ ____ and what sort of economic activity they __ ___

▪ Given that two economic activity, consumption and production, this gives rise to the sixfold classification

▪ Illustrative utility or(and) production function(s) for the affected agent(s&raquo_space; see table on slides

▪ Consumption and production affect utility and output in an uncompensated or unpaid
way

▪ We are interested in effects from one agent to another which are unintended and
where there is no compensation or payment

▪ External effects can be classified according to what sort of economic activity they
originate in and what sort of economic activity they impact on.

▪ Given that two economic activity, consumption and production, this gives rise to thesixfold classification

▪ Illustrative utility or(and) production function(s) for the affected agent(s&raquo_space; see table on slides

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How would write the utility/production functions for :
(Arising in : Affecting)

Consumption : Production
C : C
C : C,P
Production : C
P : P
P : C, P

Lecture 5 Slide 11. (refer to slide 5 for help with notation)
(X and Y are inputs, U= utilities from commodities)
(Arising in : Affecting)

Consumption : Production > X (Kx, Lx, Ya)
C:C > UA (Xa, Ya, Xb)
C:C,P > Ua (Xa, Ya, Xb) and Y(Ky, Ly, Xb)
P:C > Ua (Xa, Ya, X)
P:P > X (Kx, Lx, Y)
P: C,P > Ua (Xa, Ya, Y) and X (Kx, Lx, Y)

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Write the following in terms of their function:

B’s consumption of X affects the utility that A derives from given levels of consumption of X and Y.
A’s consumption of Y affects the production of X, for given levels of capital and labour input.
B’s consumption of X affecting both A’s utility and the production of Y.
The amount of X produced, as well as A’s consumption of X, affects A’s utility. Think of production and consumption of diesel
Production of Y determining, for given capital and labour inputs, the amount of X produced.
The level of Y affects both A’s utility and the production of X

Consumption : Production > X (Kx, Lx, Ya)

C:C > UA (Xa, Ya, Xb)

C:C,P > Ua (Xa, Ya, Xb) and Y(Ky, Ly, Xb)

P:C > Ua (Xa, Ya, X)

P:P > X (Kx, Lx, Y)

P: C,P > Ua (Xa, Ya, Y) and X (Kx, Lx, Y)

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Explain each of the following functions:

Consumption : Production > X (Kx, Lx, Ya)

C:C > UA (Xa, Ya, Xb)

C:C,P > Ua (Xa, Ya, Xb) and Y(Ky, Ly, Xb)

P:C > Ua (Xa, Ya, X)

P:P > X (Kx, Lx, Y)

P: C,P > Ua (Xa, Ya, Y) and X (Kx, Lx, Y)

Write the following in terms of their function:

A’s consumption of Y affects the production of X, for given levels of capital and labour input.
B’s consumption of X affects the utility that A derives from given levels of consumption of X and Y.
B’s consumption of X affecting both A’s utility and the production of Y.
The amount of X produced, as well as A’s consumption of X, affects A’s utility. Think of production and consumption of diesel
Production of Y determining, for given capital and labour inputs, the amount of X produced.
The level of Y affects both A’s utility and the production of X

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In practical terms, you can think of real-life examples of the above externalities such as (3)

C:C
C:P
PP
P:C

In practical terms, you can think of real-life examples of the above externalities such as

(a) smoking and playing music loudly
(b) The production and consumption of diesel from fossil fuels
(c) firm’s chemical discharge into rivers and waterways
(d) deforestation and uncontrolled wildfires.

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Suppose A & B live in adjacent flats, A likes metal and B does not, but B can hear A practicing.

▪ Where M represents wealth and 𝑆
𝐴 denotes the hours that A plays music for in a week:

What is the Utility of A and B

Suppose A & B live in adjacent flats, A likes metal and B does not, but B can hear A practicing.
▪ Where M represents wealth and 𝑆
𝐴 denotes the hours that A plays music for in a week:

𝑈𝐴 = 𝑈𝐴(𝑀𝐴, 𝑆𝐴)
𝑈𝐵 = 𝑈𝐵(𝑀𝐵, 𝑆𝐴)

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Are the derivates positive or negative?

FOC of Utilities wrt to M and S

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dUa / dMa > 0

dUb / dMa > 0

dUa / dSa > 0

dUb / dSa < 0

Draw the graph for the Consumption - consumption Externality relating to the previous example:

Suppose A & B live in adjacent flats, A likes metal and B does not, but B can hear A practicing.

▪ Where M represents wealth and 𝑆
𝐴 denotes the hours that A plays music for in a week:

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Lecture 5 slide 13

In relation to the Consumption-Consumption Externality graph:

A plays for 𝑆0 hours with total
benefit of ____. B’s total
suffering is ____

▪ The absence of market results in
music output of ___ since A does not in fact have
to ____ to play in their flat

▪ Inefficient because ____ > ____.
The efficient outcome is at __
where ___ _ ___

▪ Where ___ > ____, A is prepared
to compensate for an hourly
increase more than B’s
willingness to accept.

▪ Where ____ > ____, B is prepared
to pay for an hourly decrease
more than A’s willingness to
accept

No compensation because B does not have a ___ ___ to no noise pollution. A _____
would support bargaining and yield S*

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A plays for 𝑆0 hours with total
benefit of a+b+d. B’s total
suffering is b+d+c

▪ The absence of market results in
𝑆0 since A does not in fact have
to pay to play in their flat

▪ Inefficient because MEC>MB.
The efficient outcome is at S*
where MEC=MB.

▪ Where MB>MEC, A is prepared
to compensate for an hourly
increase more than B’s
willingness to accept.

▪ Where MB

Coase Theorem: Suitable assignment of property rights would allow ____ to correct for ____

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Coase Theorem: Suitable assignment of property rights would allow bargaining to correct for externalities

Suppose that A has a legal right to play metal for as long as he likes. This right can be ____.
Here the right is vested in the generator. In the interest of the victim, it could offer ___ to
A not to exercise the full right. Bargaining over the payment. Either assignment will lead to
an ____ ___

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Suppose that A has a legal right to play metal for as long as he likes. This right can be traded.
Here the right is vested in the generator. In the interest of the victim, it could offer money to
A not to exercise the full right. Bargaining over the payment. Either assignment will lead to
an efficient outcome

Using the C-C Externality Diagram:

The Coase theorem:- given an externality situation, due to incomplete private property rights, a feasible solution is to create ____ ____ for either the victim or the generator.

Either assignment will lead to an efficient outcome.
▪ Where B (the victim) gets the right there is an Noise reduction of (__ − __) and A pays B an amount equal to the area of _____ = value of B’s suffering at the efficient outcome S*

▪ For the case where A (the polluter) gets the property right there is an noise reduction of (__ − __) and B pays A an amount equal to the area of ___=value of A’s loss as compared with the no-property-rights situation

▪ Either assignment will not necessarily have the same
implications for equity. Said nothing about the initial wealth of A & B. Should the assignment of the right be based on equity conditions? Does not necessarily follow that externality sufferers are relatively poor and generators rich

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Using the C-C Externality Diagram:

The Coase theorem:- given an externality situation, due to incomplete private property rights, a feasible solution is to create property rights for either the victim or the generator.

Either assignment will lead to an efficient outcome.
▪ Where B (the victim) gets the right there is an S reduction of (S0 − S) and A pays B an amount equal to the area of triangle b= value of B’s suffering at the efficient outcome S

▪ For the case where A (the polluter) gets the property right there is an S reduction of (S0 − S*) and B pays A an amount equal to the area of triangle d=value of A’s loss as compared with the no-property-rights situation

▪ The Coase theorem cannot be used to address the externalities problem through the
assignment of property rights for two reasons:
(i)

(ii)

▪ Externality problems that are of serious ___ concern involve many generators and/or many sufferers so it is difficult and expensive to relate one agent’s suffering to another agent’s ____

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▪ The Coase theorem cannot be used to address the externalities problem through the
assignment of property rights for two reasons:

(i) The case for property rights solutions is based solely on efficiency
(ii) Even with clearly defined property rights bargaining is costly

▪ Externality problems that are of serious policy concern involve many generators and/or
many sufferers so it is difficult and expensive to relate one agent’s suffering to another
agent’s actions

E.g., Y is a paper mill which discharges S into a river upstream from a laundry which extracts
water from the river to clean linen, X.

𝑋 = 𝑋(𝐾x, 𝐿x, 𝑆)

𝑌 = 𝑌(𝐾y, 𝐿y, 𝑆)

Are the derivatives for X and Y positive or negative? (2)

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dY / dS > 0

dX / dS < 0

▪ Property rights could be assigned to the downstream sufferer (x) or to the upstream generator (y). ____ could then lead to the efficient outcome. This simply requires the ____ axis to be relabelled with _. Without a ___-___ property right S is too ___ for efficiency

▪ Property rights could be assigned to the downstream sufferer (x) or to the upstream generator (y). Bargaining could then lead to the efficient outcome. This simply requires the horizontal axis to be relabelled with S. Without a well-defined property right S is too high for efficiency

▪ For profits in the production of X (the sufferer) we have: is the derivative positive or negative?

πX = PxX (Kx,Lx,S) - PkKx - PlLx 'revenue (PxQ) minus the price of Capital and Labour' dπx / dS < 0

The impact of a small increase in S on profits is the MECx. For profits in the production of Y (the polluter), the impact of a small increase in S is the MBy: is the derivative positive or negative?

πY = PxY (Ky,Ly,S) - PkKy - PlLy 'revenue (PxQ) minus the price of Capital and Labour' dπy/dS > 0

In the Prod:Prod Externality what is an alternative way of internalising the externality?

An alternative way of internalising the externality would be for the firms to collude to maximise their joint profits. The Y producer would choose its level of KY, LY and S in the light of the consequences for the output of X for given KX and LX

Why is collusion to internalise a pollution externality so rare? Think about when/why firms would do this

Collusion will occur if both firms believe that their share of joint profits will be larger. ▪ While joint profit maximisation can internalise an externality as required for efficiency thereare very few cases of firms colluding or merging to internalise a pollution externality. There is no reason to suppose joint profit max and internalising a pollution externality will coincide

Production-Consumption Externality: Here the externality impacts on 2 agents and the resource is __-__ and ___-___ in consumption. Emissions arise in the production of Y and adversely affect the ____ of A and B This production-consumption case most closely resembles the common pollution policy problems.

Production-Consumption Externality: Here the externality impacts on 2 agents and is non-rival and non-excludable in consumption. Emissions arise in the production of Y and adversely affect the utilities of A and B This production-consumption case most closely resembles the common pollution policy problems.

Production-Consumption Externality: Emissions arise in the production of Y and adversely affect the utilities of A and B e.g., a fossil fuel burning electricity plant located in an urban area. Ua = dUa/dS _ 0 Ub = dUb/dS _ 0 Y = dY/dS _ 0

Lecture 5, Slide 22

Production-Consumption Externality: ▪ Emissions arise in the production of Y and adversely affect the utilities of A and B e.g., a fossil fuel burning electricity plant located in an urban area. ▪ Private bargaining and the assignment of property rights will not deal with the externality problem. Why?

▪ Emissions arise in the production of Y and adversely affect the utilities of A and B e.g., a fossil fuel burning electricity plant located in an urban area. ▪ Private bargaining and the assignment of property rights will not deal with the externality problem. This is because the market cannot be used to supply a public good due to its nonexcludability. Non-excludable goods are public goods that cannot exclude a certain individual or group of individuals from using them. ▪ A market would be able to supply a public good if the makers could exchange the right for exclusive control over defined bundles of the good for the rights to exclusive control over defined bundles of something else. The exchange is usually for money. But it can only work if the maker can deny access to those who do not pay. Correcting this market failure requires ongoing intervention by a government agency (e.g., EPA) ▪ An entity that can get the revenue required to cover the costs of production other than from the sale of the good must supply it Nonrivalrous means that when one person uses a good, it does not prevent others from using it.

Production-Consumption Externality: ▪ A market would be able to supply a public good if the makers could exchange the right for ___ ___over defined bundles of the good for the rights to ___ ___over defined bundles of something else. The exchange is usually for money. But it can only work if the maker can .....?? Correcting this market failure requires ongoing intervention by a ____ ____ (e.g., EPA) ▪ An entity that can get the revenue required to cover the costs of production other than from the sale of the good must _____ ___

Production-Consumption Externality: ▪ A market would be able to supply a public good if the makers could exchange the right for exclusive control over defined bundles of the good for the rights to exclusive control over defined bundles of something else. The exchange is usually for money. But it can only work if the maker can deny access to those who do not pay. Correcting this market failure requires ongoing intervention by a government agency (e.g., EPA) ▪ An entity that can get the revenue required to cover the costs of production other than from the sale of the good must supply it

Draw the Production-Consumption Externality diagram: | that internalises the SMC with a tax

L5 slide 24

Production-Consumption Externality: DIAGRAM ▪PMC is the ___ ___ ___ which refers to ___ ___ that the producer of Y takes account of. ▪MEC is the sum of the ....? ▪PMC+MEC=SMC. We see that SMC is ____ than ___ because of the additional component ▪To maximise profit, producer of Y will produce at ___ where __=__. This is not the efficient level of output as ....?

▪PMC is the private marginal cost which refers to input costs that the producer of Y takes account of. ▪MEC is the sum of the willingness to pay of the 2 sufferers to reduce pollution by a small amount ▪PMC+MEC=SMC. We see that SMC is steeper than PMC because of the additional component ▪To maximise profit, producer of Y will produce at Y0 where PMC=Py. This is not the efficient level of output as it ignores the costs borne by A and B

Production-Consumption Externality: DIAGRAM ▪ The efficient level of output is __ where ...? ▪ To correct this ___ ___ the EPA can tax S. PMCT is PMC+t. The appropriate t is: ?? ▪ So, t should be set equal to the ___ at the ___ levels of Y and S. In order to set t, the EPA would need to identify __ and calculate the corresponding ___. Calculating ___ would require the EPA to know how the MEC varies with S i.e., must know the ____ ____ of A and B

Production-Consumption Externality: ▪ The efficient level of output is Y* where SMC=Py ▪ To correct this market failure the EPA can tax S. PMCT is PMC+t. The appropriate t is: 𝑡 = 𝑆𝑀𝐶∗ − 𝑃𝑀𝐶∗ = 𝑀𝐸𝐶∗ ▪ So, t should be set equal to the MEC at the efficient levels of Y and S. In order to set t, the EPA would need to identify Y* and calculate the corresponding MEC*. Calculating MEC* would require the EPA to know how the MEC varies with S i.e., must know the utility functions of A and B

Recall the ideal conditions required for markets to achieve efficiency (8)

(i) Markets exist for all goods and services produced and consumed (ii) All markets are perfectly competitive (iii) All transactors have perfect information (iv) Private property rights are fully assigned for all resources and commodities (v) No externalities exist (vi) All goods and services are private goods (vii) All utility and production functions are ‘well-behaved’ (viii) All agents are maximisers

The second-best problem: So far, we have assumed that firms sell their ____ in competitive markets and they are ____ ___ ▪ Second best theorem: If there are 2 or more sources of ___ ____, correcting just one of them will not necessarily improve ___. It may make things worse ▪ Policy should take into account the multiple sources of ___ ___. The policy should recognise that all the failures ____ be corrected i.e., a ‘second best’ package of government interventions. This package does the best that can be done given that not all sources of failure can be corrected

The second-best problem: So far, we have assumed that firms sell their outputs in competitive markets and they are price takers. ▪ Second best theorem: If there are 2 or more sources of market failure, correcting just one of them will not necessarily improve efficiency. It may make things worse ▪ Policy should take into account the multiple sources of market failure. The policy should recognise that all the failures cannot be corrected i.e., a ‘second best’ package of government interventions. This package does the best that can be done given that not all sources of failure can be corrected

Draw the second-best problem DIAGRAM

The second-best problem DIAGRAM: SLide 28

The second-best problem DIAGRAM: Polluting firm is a ___ producing Y ▪Given an uncorrected externality the monopolist will produce __ (using __=___). If efficiency is our concern, there are too main problems with Y0: 1) Too low because monopolist is setting __=__ instead of ___: YC is the relevant output for PMC=Py 2) Too high as monopolist is ignoring ____. YT is the output level for SMC=Mry 3) Efficiency requires __=__ with output at __ ▪Suppose the EPA ___ the firm so that SMC becomes relevant for the firm. As a result output will go from __ to ___ with price going from ___ to ___ ▪There are gains and losses from the tax. A gain from the reduction in pollution, Area =. The price increase gives rise to a loss in CS, Area =

The second-best problem DIAGRAM: Polluting firm is a monopolist producing Y ▪Given an uncorrected externality the monopolist will produce Y0 (using PMC=MR). If efficiency is our concern, there are too main problems with Y0: 1) Too low because monopolist is setting MC=MR instead of price: YC is the relevant output for PMC=Py 2) Too high as monopolist is ignoring externality. YT is the output level for SMC=Mry 3) Efficiency requires SMC=Price with output at Y* ▪Suppose the EPA taxes the firm so that SMC becomes relevant for the firm. As a result output will go from Y0 to Yt with price going from Py0 to Pyt ▪There are gains and losses from the tax. A gain from the reduction in pollution, abcd. The price increase gives rise to a loss in CS, Pyt e f Py0

The second-best problem DIAGRAM: It cannot be presumed that the gain will be larger than the loss. This depends on the ___ and positions of __,__ and __. The EPA would need to have all this info to establish whether imposing the ___ would involve a net gain ▪ The EPA could induce SMC=Price at Y* if it could use 2 instruments: (i) to correct for the underproduction due to ___ = __ and (ii) a tax to ____ ___ ____ by making SMC relevant ▪ EPAs do not have the power to correct for the ___-___ through the regulation of ___

The second-best problem DIAGRAM: It cannot be presumed that the gain will be larger than the loss. This depends on the slopes and positions of PMC, SMC and DyDy. The EPA would need to have all this info to establish whether imposing the tax would involve a net gain ▪ The EPA could induce SMC=Price at Y* if it could use 2 instruments: (i) to correct for the underproduction due to PMC=MRy and (ii) a tax to internalise the externality by making SMC relevant ▪ EPAs do not have the power to correct for the under-production through the regulation of monopoly

The second-best problem: It can be shown that an EPA can set a second-best tax rate given complete info about a firm’s ___ and ___ functions, and also how pollution varies with the firm’s ___ (Baumol & Oates, 1988). Such a tax guarantees that the gains from its imposition will ___ its losses ▪ It may not move a firm to __ but it will guarantee that ____ > PYt e f Py0 ▪ The second-best tax rate depends on the damage done by the pollutant, the firm’s __ and the ____ __ ____ ▪ With many polluting monopolies the EPA would be faced with setting different tax rates for each firm because of the different ___ that they face in their output markets ▪ Unlikely to be politically ___, even if the EPA had the info to calculate the different rates

The second-best problem: It can be shown that an EPA can set a second-best tax rate given complete info about a firm’s cost and demand functions, and also how pollution varies with the firm’s behaviour (Baumol & Oates, 1988). Such a tax guarantees that the gains from its imposition will exceed its losses ▪ It may not move a firm to Y* but it will guarantee that abcd > PYt e f Py0 ▪ The second-best tax rate depends on the damage done by the pollutant, the firm’s costs and the elasticity of demand ▪ With many polluting monopolies the EPA would be faced with setting different tax rates for each firm because of the different elasticities that they face in their output markets ▪ Unlikely to be politically feasible, even if the EPA had the info to calculate the different rates

L5: Welfare Economics and the Evnrionment Flashcards

(42 cards)