Public Finance

John Anderson

            Henry George theorem in public finance.

            The public revenue that provides for the collective goods of an optimally-sized community equals the land rent of that community.

            The utility function is U(G,X), where G is a collective and X a private good.

            Output Y is a function of N workers: Y = f(N) = XN + G.

Y = f(N) = XN + G. Then:

(1) ∂f/∂N = X  

(2) X = {f(N)-G} / N

(3) ∂f/∂N = {(f(N)-G)/N}

(4) G = f(N) - Nf’(N)

R (rent) is the difference between total product Y and total wages:

(4) R = f(N) - Nf'(N) = G.

A community chooses the level of public goods that maximizes land rent.

Land value maximization leads to an efficient amount of public goods.

3. Welfare economics and public goods

Says no folk tales of entrepreneurs providing public goods.

But knowledge is a public good: Galileo, Newton, Einstein

Civic goods: Ebenezer Howard, Walt Disney

Says markets, i.e. private enterprise, can efficiently provide individually-used goods,

but not collectively-used goods.

Free riders. Really?

Also, says reputation is a public good.

But reputations are generated by the private sector.

Defines public goods are nonrival and non-excludable.

Private goods are rivalrous.

Lighthouse example.

Nonexcludable at sea, but excludable at the harbor.

A tie-in to an excludable service.

Technology can affect whether a service is excludable,

such as sensors that activate lighthouses.

Says there is no way to make listeneres pay for radio programs,

but they do for satellite radio, and radio programs could be encrypted.

In many cases, charging admission is not desired, such as for a local park.

Impure public goods? Better:


Congestible                Non-rival

swimming pool           political association    excludable

population growth      wildlife existence       global

Club goods: congestible, excludable

Most government works are territorial.

The goods increase demand to be in that space.

People are willing to pay a higher rent.

So they pay for the good in land rent.

Users of goods are therefore not free riders.

Is government necessary for club goods?

Is government necessary for non-excludable goods?

Allocation of goods

Individually used goods: market demand is the horizontal sum of quantities.

Price rationed.

Market demand more elastic than individual demands (62)?

Collective goods: total demand is the vertical sum of willingness to pay.

Can we discover the willingness to pay?

- Demand revelation -

Welfare economics

= well being

Conditions for theorems:

perfect competition: price takers, full markets, full information.

First fundamental theorem of welfare economics:

A competitive market equilibrium is maximally efficient.

Second fundamental theorem of welfare economics:

Any efficient allocation can be provided by a competitive market.

The Second Fundamental Theorem of Welfare Economics states that society can obtain any efficient allocation of resources by creating initial endowments.

Measurements of economic welfare

Consumer and producer surplus.

The social surplus is maximized at the market-clearing quantity and price.

4. Externalities

An externality is an act which changes the utility of others without compensation.

P. 85:

Says: the private market fails to allocate properly when there are externalities present.

But also: the external benefit or damage occurs outside the market.

If these effects were subject to the market, they would be priced,

            and there would be no allocation problem.

Confused statement: It is the absence of a market that causes these effects to result in an inefficient allocation by the market.

Better: the problem of externalities is also said to involve the absence of markets.

P. 90: Externalities exist because of poorly determined property rights.

P. 86: positive and negative externalities.

Should positive externalities be paid for? By whom?

Research has positive externalities. Market failure?

Research has

Beekeper whose apiary is next to an orchard.

The market will not compensate for the positive externalities; market failure.


Steven Cheung, ‘The Fable of the Bees: An Economic Investigation’ Journal of Law and Economics 16 (1973), pp. 11-33.

Cheung showed that contracts to place beehives in orchards were common long before economists began calling pollination an uncompensated externality of producing honey.

R. Coase, Nobel-prize winning economicst:

‘The Lighthouse in Economics’, Journal of Law and Economics 17(2) (1974), pp. 357-376.

            Tracing the history of lighthouses, Coase pointed out that examples of shipping companies being charged for the services provided by lighthouses had long existed, if only the textbook writers had looked for them.

            In this and other work, Coase showed that private actors routinely have found negotiated ways around problems that economists have been invoking as market failures and as cause for public sector intervention.


Corn farmer uses fertilizer, causes ground water contamination.

The social cost is greater than the private cost.

But who owns the groundwater?

P. 90: Says, public goods are a special case of externalities.

FF: Not so for club goods, where users pay.

For non-excludable goods, people could pay, such as for religion.

Public goods are often but not necessarily externalities.

Negative externalities

Efficient quantities are always where marginal cost equals marginal benefit or revenue.

Where social cost is greater than consumer cost,

the quantity is greater than optimal.

The optimal amount of pollution is not zero,

but where the marginal cost of reducing pollution equals the marginal benefit.


Regulation, command and control

P. 102: does not result in efficient allocation.

One rule for all does not take into account individual costs and benefits.

The parry paper concludes that the cost of regulations can be greater than that of pollution.

Emissions permit trading.

The government sets a limit to pollution, requires permits to pollute, and then lets owners trade.

More efficient than regulation.

Carbon taxes: can be on inputs or outputs.

Taxing inputs, such as gasoline, has a deadweight loss.

Focusing the tax on the emissions has no deadweight loss if labor and capital were not taxed.

Parry: pre-existing taxes put quotas at a severe disadvantage relative to carbon taxes.

There is a tax-interaction effect, resulting in higher costs and lower real wages.

A five percent reduction in emissions is seven times more costly with a quota than with a tax.

Carbon quotas or grandfathered permits may not be able to generate positive gains,

unless the benefits from reducing pollution are enourmous.

Pigouvian taxes, after economist Pigou

A tax on the negative externality equal to the damage caused.

The efficient solution.

Also, the revenue can offset other taxes, creating a double dividend.

Permit trading does not generate periodic government revenue.

Parry paper, tax is more efficient than quota.

The “green tax shift.”

The Kyoto protocol of 1997, or UN Framework on Climate Change

Developing countries such as China and India were excluded from reducing emissions.

Private solutions

P. 100: The Coase theorem

The classic example, steam-powered train that throws off sparks on the fields of crops that catch fire.

The Coase theorem: negotiation will achieve the efficient outcome, regardless of the assignment of property rights.

But if there are high transaction costs, then negotiation will not be effective.

Also, pollution as a nuisance, could be subject to lawsuits, although now regulation precludes it.