18 public goods the consequences of strategic voting behavior and the role of government
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18. Public Goods, the Consequences of Strategic Voting Behavior, and the Role of Government. 18.1 Public Goods and the Free-Rider Problem Defined private goods are characterized by excludability: consumption is restricted to certain people (e.g. those who pay) and

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18. Public Goods, the Consequences of Strategic Voting Behavior, and the Role of Government

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18. Public Goods, the Consequences of Strategic Voting Behavior, and the Role of Government

18.1 Public Goods and the Free-Rider Problem Defined

private goods are characterized by

excludability:consumption is restricted to certain people (e.g. those who pay) and

rival consumption: consumption by one agent decreases quantity available for consumption by others

public goods are characterized by nonexludability and nonrival consumption, e.g. national defense

some goods are neither purely private nor purely public: e.g. cable TV: excludable, but nonrival, park: nonexcludable, but to some extent rival consumption

The Free-Rider Problem

due to nonexcludability, agents have no incentive to contribute to the public good, but instead to free-ride

e.g. when asked for the private willingness to pay for national defense, one has an incentive to underreport, because contributing has only a tiny private benefit

obviously this leads to an inefficient outcome, because this would result in having no national defense, although many people have a positive willingness to pay for it

18.2 The Pareto-Optimal Conditions for an Economy with Public Goods

if a public good is provided, all consumers will consume the same quantity

individual demand for public good can be derived as usual

the societal demand for the public good is the vertical sum of the individual demand functions, because each unit is consumed by all agents and hence the marginal benefit to society is the sum of the individual marginal benefits

the optimal quantity is where the societal marginal benefit equals the societal marginal costs (Fig 18.1)

the condition for a Pareto-optimum in an economy with private and public goods are

  • for each customer the MRS between two private goods has to be equal to the price ratio

  • the MRTS of inputs are equal for all goods

  • the MRT of private for public goods has to equal the sum of the MRS for all agents

    the third condition follows from the fact that the MRT states how many units of the private good society would have to forego for a unit of the public good and the sum of the MRS state how many units of the private good all agents together would be willing to give up

18.3 The Lindahl Solution to the Public Goods Problem

a mild government intervention, it only acts as a coordinator:

markets for private goods organized as competitive markets

assume that agents report their preferences truthfully

then the government determines for each agent a cost share of the public good, agents announce their demand

in a Lindahl equilibrium prices and cost shares are such that no agent would like to change the demand for private or public good, demand equals supply for private good and everybody demands the same quantity of the public good (necessary because of nonexludability)

so for public goods, agents may face different prices, but all demand the same quantity, for private goods all face the same price but may demand different quantities

to determine Lindahl equilibrium, derive for each agent the private consumption path and thus the demand curve (dependent on the cost share), measure cost share of person 1 from bottom and that of person 2 from top, quantity on horizontal axis (Fig 18.2)

then if public good is a normal good demand curve is downward-sloping for person 1 and upward-sloping for person 2

equilibrium is at intersection, this indicates shares such that demanded quantities are equal

Lindahl equilibrium is Pareto-optimal, because agent with share s faces ppu=s MCpu, he chooses MRSpr for pu = ppu/ ppr

hence the sum of the MRS is equal to

MCpu / ppr = MCpu / MCpr = MRTpr for pu, as required

(ppr= MCpr because the market for private goods is competitive)

The Weakness of the Lindahl Solution

the assumption that all agents report their preferences truthfully is crucial

but they have an incentive to underreport their demand or even to complete free-ride:

at the equilibrium quantity x, for his given equilibrium share s an agent chooses for this given price his optimal bundle between private and public good and is just indifferent

the derivative of the total expense on the public good is s

but now consider the reporting stage: by reporting a lower demand, such that the equilibrium quantity decreases, the agent also reduces his share, hence the derivative of the total expense is s+(ds/dx)x;

thus the agent is better off by reporting a demand such that the quantity is lower

hence the Nash-equilibrium of the demand reporting game is inefficient

Is the free-rider problem a real problem?

Experimental Evidence: yes, in particular with repetition contributions to a public good decrease; contributions are even lower with a negative frame

18.4 Theoretical Solutions to the Free-Rider Problem

The Demand Revealing Mechanism

aim: create incentive for people to reveal their demand for public goods

assume four people have willingness to pay for three different plans (with equal costs) as follows:







choose the plan with highest total WTP (B)

tax: look for each person whether their WTP affects choice

if yes, tax them the difference between the total WTP, excluding their own, between the plan that would be chosen if they were excluded and the plan that is chosen when they are included (that amount equals the externality they have on the others by changing the choice)

it is optimal to report the true WTP, because the stated WTP does not influence how much one has to pay, but only if one has to pay; and one changes the choice exactly for those cases where the tax is at most equal to the difference in one’s own WTP

The Weakness of the Demand-Revealing Mechanism

it is not balanced-budget, i.e. the government may run a surplus which cannot be redistributed, because that would change the incentive

the mechanism yields the desired information, but it cannot be optimally used

18.5 The Role of Government

the above examples suggest a role of government is to aggregate preferences to find a socially optimal solution

there are, however, problems with that

18.6 The Problem of Preference Aggregation: Arrow’s Impossibility Theorem

when individual preferences are aggregated into social preferences, these should be rational, i.e. complete and transitive

The Voting Paradox

assume three person-society, all have rational preferences

person 1: x y z, person 2: z x y, person 3: y z x

then (truthful) majority voting yields: x y and y z, BUT z x, hence social preferences are not transitive, Condorcet-cycle

Arrow’s impossibility theorem states that there is no voting mechanism that fulfills the following desirable conditions

  • Group Rationality: social preferences should be complete and transitive

  • Unrestricted Domain: every kind of rational individual preferences should be allowed as inputs to the aggregation

  • Pareto Optimality: If all people prefer x to y then also according to the social preferences x is preferred to y

  • Independence: social ranking of x and y depends only on individual rankings of x and y but not on how they are ranked to other alternatives

  • Nondictatorship: The voting mechanism should not exclusively reflect the preferences of one person

    Hence a voting mechanisms that fulfills 1-4 must be dictatorial, that is the social preferences match those of one individual for all choice alternatives

    Rescue: it is enough to give up 2.: e.g. if issue is one-dimensional and each person has a preferred level and likes the decision less the further it is away (single-peaked preferences), then majority voting yields transitive social preferences

18.7 The Problem of Vote Manipulation

Finding a satisfactory voting mechanism is further complicated by strategic manipulation

Agenda Manipulation

if the voting mechanism does not give rise to a complete transitive order, then the order in which alternatives are voted upon determines the outcome

hence the chairperson can manipulate the outcome by setting the agenda appropriately

e.g. if majority voting yields x y, y z, and z x, then a chairperson who prefers z would select the agenda such that first x versus y is voted upon and then the winner versus z.

Strategic Voting

a person may have an incentive not to vote truthfully (e.g. for her second choice over her first choice), in order to achieve e.g. her second choice instead of something worse

example: assume person 1 has preferences: x y z, and the agenda is as above, i.e. first x versus y is voted upon and then the winner versus z

if person 1 votes truthfully, the result will be z, her least preferred choice

by voting for y instead of x in the first vote, the result will be y (if the others vote truthfully), which she prefers over z

hence truthful voting is not a Nash-equilibrium for the given individual preferences and agenda

strategic voting is not restricted to majority voting (e.g. also for Borda count)

Gibbard-Satterthwaite theorem: the only voting rule to choose one out of more than two alternatives that cannot be manipulated is dictatorial

18.8 The Government as Institutional Architect

if the government knew the environment (i.e. a complete description of the economy including the preferences of the members) perfectly, it could just implement a desirable (e.g. Pareto-optimal) outcome (if there is agreement on what is desirable)

because there is no complete information about the environment, the government has to find an indirect implementation via a voting mechanism

since voting mechanisms can be manipulated, the government has to take this into account when designing institutions

hence the aim is to find a voting mechanism such that for each environment the Nash-equilibrium yields an outcome that is in the set of acceptable outcomes

18.9 Rent-Seeking – The Economics of Interest Groups

individuals or groups engage in lobbying, in order to bias government decision on their behalf, rent seeking

example: if the government grants a single license for the provision of a good this firm can act as a monopolist and will make extra-normal profits (or rent) of R

hence a firm would be willing to pay up to R to obtain license

Competitive Rent Seeking

two firms are bidding for a rent R

equilibrium depends on whether (a) loser gets a refund and (b) higher bribe wins for sure or only with higher probability

refund for loser and sure win for higher bribe: both pay R

no-refund and sure win: no pure-strategy equilibrium

no sure win: both bid less than R

rent seeking increases the welfare loss of monopoly

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