Topic 2: Public Goods

Three problems with the government running all production (socialism)

1) Information problems - how does government know what to produce? 2) Deadweight loss of large government - distortionary taxes reduce efficiency. 3) Incentive effects - behaviour changes in response to rewards/penalties created by policy

Core trade-off in policy analysis (Topic 2 prelude)

More public goods need more distortionary taxation; more social insurance induces bad incentive effects; more redistribution distorts incentives

Pure public good - definition

A good that is perfectly non-rival in consumption AND non-excludable (e.g. national defence)

Non-rival in consumption

One person's consumption does not reduce another's opportunity to consume the good

Non-excludable

Individuals cannot be prevented from consuming the good

Impure public good

A good that is non-rival and/or non-excludable to some extent but not fully (e.g. TV streaming: non-rival but excludable; crowded city sidewalk: non-excludable but rival)

Typology of goods (2x2)

Rival + excludable = private good (car); non-rival + excludable = club good (private park); rival + non-excludable = common property resource (fish stocks); non-rival + non-excludable = public good (air)

Club good

Excludable but non-rival (e.g. private park, TV streaming)

Common property resource

Rival but non-excludable (e.g. fish stocks in the sea)

Five aspects of public goods

1) Everyone consumes the same quantity but may value it differently. 2) Classification depends on market conditions and technology. 3) Non-commodities can have public good features. 4) Private goods can be publicly provided. 5) Public provision does not mean public production (e.g. garbage collection)

Publicly provided private goods

Rival and excludable goods that are provided by the government

Private goods - how to get the social demand curve

Sum individual demand curves HORIZONTALLY: add quantities at each price (everyone faces the same price but buys different quantities)

Private goods - optimality condition

MRS(ic,c) for Ben = MRS for Jerry = Pic/Pc = MC (with Pc = 1). Each individual's MRS equals MC

Why the private market equilibrium is socially efficient (no market failure)

MRS = SMB (individual marginal value = social marginal value) and MC = SMC, so at the market equilibrium SMB = SMC

Public goods - how to get social marginal benefit

Sum individual MRSs VERTICALLY: everyone consumes the same quantity, so add each person's willingness to pay (MRS) at each quantity

Samuelson Rule (Samuelson, 1954)

Efficient provision of a public good: sum of individual MRSs (public good vs private good) = MC, i.e. Sum MRS(G,X) = FG/FX = MRT

Samuelson Rule - intuition

An extra unit of the public good benefits person 1 AND person 2 AND …, so benefits are summed; an extra unit of a private good goes to only one person

Samuelson derivation - government's problem

max over x^i and G of Sum mu_i U^i(x^i, G) s.t. F(X, G) = 0, with weights mu_i > 0 summing to 1. Solutions are the Pareto efficient allocations

Samuelson derivation - FOCs

dL/dx^i: mu_i dU^i/dx^i - lambda F_X = 0; dL/dG: Sum mu_i dU^i/dG - lambda F_G = 0. Combine to get Sum (dU^i/dG)/(dU^i/dx^i) = F_G/F_X

Allocation (formal)

A level of G and a distribution of private consumption across individuals (x^1, …, x^N, G), which must satisfy the aggregate resource constraint F(X, G) = 0

Pareto efficient allocation (formal)

No other feasible allocation makes everyone no worse off and someone strictly better off. Found by maximising weighted sum of utilities subject to the resource constraint

Free riding

When an investment has a private cost but a common benefit, individuals underinvest -> market under-provides public goods relative to the Samuelson rule

Gnutella example (Adar and Huberman, 2000)

Over 70% of users only downloaded and never uploaded; top 1% of peers gave 47% of answers, top 25% gave 98% - evidence of free riding

Voluntary contribution model - set-up

Two consumers with income M^i, prices = 1, budget M^i = x^i + g^i; each consumes total public good g^1 + g^2, so U^i(M^i - g^i, g^1 + g^2)

Voluntary contribution - Nash equilibrium

Each consumer chooses g^i to maximise utility taking the other's g^-i as given; equilibrium where each choice is a best response (reaction functions cross)

Why the voluntary contribution Nash equilibrium is inefficient

Privately efficient but not Pareto efficient: when consumer 1 buys more of the public good she creates a positive externality on consumer 2 that she ignores, so consumer 2 free rides. Both increasing contributions would be a Pareto improvement

Where are the Pareto efficient allocations in the contribution diagram?

On the locus where the two consumers' indifference curves are tangent - above/to the right of the Nash point (more public good)

Limitations of the Samuelson Rule

Hard to implement: government must know or elicit preferences; financing may require distortionary taxes; it is a first-best benchmark only

Lindahl pricing

Decentralised implementation: personalised prices so each consumer pays according to their own marginal valuation, aligning private and social benefits

Lindahl pricing - advantages

Personalised prices equate individual valuations to the cost of production; corrects the gap between private and social benefits

Lindahl pricing - three problems

1) Preference revelation - incentive to lie about WTP since payment depends on it. 2) Preference knowledge - people may not know their valuation. 3) Preference aggregation - how to combine individual values into a social value

Examples of private provision of public goods

BBC licence fee (penalties for watching without one); Kazaa ranking users by upload/download ratio; Times Square Business Improvement District funding sanitation and security

Why people give to private provision

Warm glow (name on building), reciprocity (alumni), social pressure (churches), altruism (poverty relief)

What private giving funds

Religion, education, human services, health, arts, causes (environment, animal protection)

Crowd-out

Reduction in private contributions to a public good when government provision of it increases