LECTURE 2 Flashcards
PURE PUBLIC GOOD =
perfectly NON-RIVAL and NON-EXCLUDABLE
NON-RIVAL =
one individuals’ consumption doesn’t affect another’s opportunity to consume.
Non-excludable =
cannot deny others the opportunity to consume.
Impure public goods =
Satisfy the 2 conditions to some extent but not fully.
Private goods =
rivalrous and excludable.
Impure public good example: non-excludable but rival.
Common property resource - rival if very crowded.
Impure public good example: excludable but non-rival.
Club good - can be made excludable.
MRSx,y =
MUx/MUy = number of units of Y willing to give up for an additional X holding utility constant.
Optimality condition for CONSUMPTION of PRIVATE goods
MRS1 = MRS2 = … = Px/Py
Optimality condition for PRODUCTION of PRIVATE goods
P = MC
Equilibrium for private goods + interp
MRS1 = MRS2 = … = MC
How do we find SMB from individual demand curves ro PRIVATE good?
Horizontal summation of individual demand curves at each price.
SMC for private good is given by…
industry supply curve.
SAMUELSON RULE FOR PUBLIC GOOD
SUM of MRS across individuals = MC of producing the public good.
How do we find SMB from individual demand curves ro PUBLIC good?
VERTICAL summation of individual demand curves at each quantity.
What is each individuals consumption of the public good?
G - the total amount of the public good produced can be consumed by everyone since its non-rival and non-excludable.
What’s F(X, G) = 0 means?
The aggregate production relationship - expressing PPF.
In an optimisation, an allocation means…
A level of G and a distribution of private consumption across individuals.
An allocation is PE if there is NO other allocation such that…(2)
- Satisfies aggregate resource constraint.
2. Makes every individual no worse off and some individuals strictly better off.
How can the government find the PE allocation i.e. find Samuelson rule?
Max SWF s.t. aggregate resource constraint.
Whats the BC for government public good optimisation?
PxX1 + PxX2 + pgG = e1 + e2 for 2 individuals.
Marginal rate of transformation =
Fg/Fi
Why is the MB of an extra unit of the public good the sum of MRS?
Because public good is nontrivial and non-excludable so the additional unit can be consumed by everyone so we sum MB across all individuals.
Whats G* when provided by a private firm? Why?
G > 0 is suboptimal as no consumer WTP since non-excludable. Avoid a loss by G = 0. Free rider problem –> underprovision of public good.
How do contributions to public good and consumption of public good relate in voluntary contributions model?
Contributions may NOT equal consumption - consumption depends on how much society produces as a whole. i.e. consumption = G = g1 + g2.
Optimisation for voluntary contributions model
Max individual utility st individual BC
In voluntary contributions model, if both good are private what’s the outcome?
PE by 1st welfare theorem
How do we determine equilibrium in voluntary contributions model with public good? Why?
Nash Equilibrium: strategic interaction - how much contribute yourself depends on other’s contribution. Take other’s contribution as given.
Do we need Lagrangian for voluntary contributions? Why/why not?
NO - sub in BC into U = unconstrained optimisation with only one FOC wrt gi
NE in voluntary contributions is where…
Each consumers gi is a BR to the others.
Where reaction functions intersect.
Explain shape of ICs for g1 g2 axis.
Initially slope down: if want to increase g1, g2 must fall to stop utility increasing. G1 = good = IC slopes down.
At some point, unwilling to increase g1 further so if do, g2 must increase as compensation. g1 = bad = IC slops up.
Where is utility highest for consumer 1 in g1 g2 space?
Where g2 highest and g1 lowest.
Individual BC in g1 g2 space.
BC1 is independent of g2 = vertical line.
BC2 is independent of g1 = horizontal line.
How do we find BR/reaction function?
At any g2 bar, 1’s BR where g2 bar tangent to IC. Join all points = BR function.
Is the NE in voluntary model PE? Explain.
NO - there are a set of Pareto improving allocation.s
PE allocation where…
How do we find locus of PE allocations?
IC1 and IC2 tangential = cannot increase U1 without decrease U2. Join up points of tangency = locus.
Why is NE suboptimally low?
Free riding: if one consumer increases their contribution the other’s BR is to decrease theirs. Consumers do not take +VE externality into account.
3 limitations of Samuelson rule.
- Gov needs to know all preferences or have a mechanism to reveal them.
- How aggregate preferences into SWF?
- How to finance public good: need to redistribute, but only distortionary taxes available.
Lindahl pricing =
decentralised pricing, one way to reach optimum Lebel of public good in free market.
What’s the aim of lindahl pricing?
To modify incentives to align private and social benefits.
Mechanim of lindahl pricing =
Personalised prices
What 2 things do personalised prices do?
- align social and private benefits
2. capture WTP of an individual.
In Lindahl, each individual pays how much of public good? What does this mean for individual BC?
A share of the total cost, tiG
t1 + t2 = 1
BC: xi + tiG = Mi
- BC has G, not gi.
Lindahl equilibrium shares are where…
G1 = G2.
Government continues to adjust t1 and t2 until contributions equal.
Do t1 and t2 have to be equal for Lindahl?
NO - as long as G1 and G2 equal.
Lindahl reaction functions show…
X axis = t and Y axis = gi
Loci of vertical points of the IC i.e. where a specific t is tangent to IC then join up points.
ICs for Lindahl graph show MRS between…
Gi and ti
Whats the relationship between ti and gi given by Lindahl reaction functions?
Higher ti = lower gi
Explain shape of ICs for Lindahl graph
Initially: willing to pay increased ti so if gi rises, need ti to rise to stop utility rising.
No longer willing to rise ti so if gi rises, need ti to fall to stop utility falling = backwards bending.
The shape of Lindahl ICs reflect the fact that…
consumers prefer more of the public good but dislike an increased share.
Lindahl equilibrium on graph where
reaction function 1 = reaction function 2
2 properties of Lindahl equilibrium
Consumers demand same level G1=G2
ICs tangential = PE
The Lindahl shares are determined by…
the slope of the reaction functions.
Mathematically, how does Lindahl satisfy Samuelson?
Sub in individual BC into U: FOC wrt G.
MRS = ti for each individual.
Sum MRS = t1 + t2 = 1 since shares add to 1
Samuelson (for MRT=1)
2 pros of Lindahl
- shares reflect WTP
- Corrects for difference between PMB and SMB = PE
3 cons of Lindahl
- Preference revelation problem - incentive to lie to reduce ti.
- Preference knowledge problem - may not know/be unable to quantify WTP.
- Preference aggregation problem - how aggregate into social value?
Does the free rider problem always lead to a complete absence of public good provision?
NO - in some cases the private market provides a public good, but less than the optimal level. e.g. BBC license fee.
For what type of funds and reasons for charitable giving does private provision of a public good work better for?
Types = religious, education, health, arts, environment. Reasons = warm glow, reciprocity, altruism, social pressure.
Charitable giving is a form of what?
private provision of a public good.
What is crowd out? When does it become critical?
When there is some private provision (not zero), such as charitable donations towards a public good, government provision can crowd it out.
Implication of crowd out in terms of gov growth over time
Gov has grown a lot without any net effect on poverty and welfare.
2 charitable donation crowd out channels.
- decrease willingness to donate if already paying through involuntary taxes.
- Charities have less incentive to fundraise if they receive funds from gov.
3 factors affecting extent of free riding.
- preferences: altruism
- contextual setting: social pressure.
- Policy relevant parameters: crowd-out, price elasticity of private contributions to public good.
Empirically, to what extent to we see free riding?
Some free riding, but not to a strong extent.
