Download Module 4 Lecture 16 Topics 4.7 Optimal Provision of Private Goods

NPTEL-Economics-Public Economics
Module 4
Lecture 16
Topics
4.7 Optimal Provision of Private Goods
4.8 Optimal Provision of Public Goods
4.9 Samuelson Rule
4.10 Free Rider Problem
4.11Private Provision of Public Goods
4.11.1 Private-Sector Underprovision: a Numerical Example.
4.11.2 The Free Rider Problem in Practice
4.12 Private Provision of Public Goods: Experiments Testing
Free Rider Behavior
4.12.1 Marwell and Ames 1981
4.7 OPTIMAL PROVISION OF PRIVATE GOODS
In the case of private goods, equilibrium is determined by the interplay of supply
and demand
As prices adjust, each person changes his quantity consumed according to own
preferences.
For a private good, consumers demand different quantities at the same market
price.
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Indian Institute Of Technology, Kanpur
NPTEL-Economics-Public Economics
Figure 16.1
Consider a private good B and the market for it.
The alternative use of money is buying the numeraire
are individual
curves for A &B respectively coming from private
preferences of A & B.
Adding up
for good Y we get
, which is same as the demand
curve.
Market supply is S.
Competitive equilibrium price PE.
is the market clearing quantity, But A & B
derive their demand from the individual demand curve.
.
The private market equilibrium in this case is socially efficient.
The MRS for any quantity of Y equals the SMB of that quantity–the marginal
value to society equals the marginal value to any individual in the perfectly
competitive market.
4.8 OPTIMAL PROVISION OF PUBLIC GOODS
Now consider the market for military spending as opposed to Food spending.
Demand for a public good is determined by the Willingness To Pay
That is, holding quantity fixed, what is each person‟s willingness to pay?
2
Indian Institute Of Technology, Kanpur
NPTEL-Economics-Public Economics
Figure 16.2
Demand for a public Good
for Missiles
demand curve for Missiles
We want to know if individuals are willing to pay for missiles.
Suppose we need 1 missile
A is willing to pass
for 1 missile
B is willing to pass
for 1 missile
Adding the two willingness to pay we get,
For the 5th missile , A is willing to pay
For the 5th missile, B is willing to pay
For the 5th missile Total
Adding A & B‟s WTP for each quantity of the public good we get, society‟s
Demand curve or society‟s WTP.
is the market supply curve
Competitive equilibrium =5 missiles, B & A consume 5 missiles each.
Unlike the case of private goods, where aggregate demand is found by summing the
individual demands horizontally, with public goods, aggregate demand is found by
summing individual demand curve vertically.
4.9 SAMUELSON RULE: Optimal Provision of Public Goods
Private Goods: social efficiency is maximized when the marginal costs are set
equal to the marginal rate of substitution for each individual
3
Indian Institute Of Technology, Kanpur
NPTEL-Economics-Public Economics
Public Goods: social efficiency is maximized when the marginal costs are set
equal to the sum of the marginal rates of substitution (rather than each
individual‟s MRS).
Two goods P and G
Two individuals A&B
To A: The marginal public good is worth
To B:
Now
= Marginal benefit derived from consumption of G.
The social marginal benefit from the next unit of public good G is
The social MC is the same as before: derived from the production function of G.
.
Efficiency requires
Samuelson Rule (1954)}
as opposed
to private good case when
This is because the good is nonrival:
– Since a unit can be consumed by all consumers, society would like the
producer to take into account all consumers‟ preferences.
– This is because the good is non-rival.
– Excludability plays no role in the analysis. Only relevant for determining
feasible provision mechanisms
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Indian Institute Of Technology, Kanpur
NPTEL-Economics-Public Economics
4.10 FREE RIDER PROBLEM
All of the individual members of a group can benefit from the efforts of each
member and all can benefit substantially from collective action.
For example, if each of us pollutes less, we all benefit from the reduction of
harmful gases in the air we breathe.
If all of us prefer the state of less pollution over the state of pollution, then the
provision of cleaner air is a collective good for us.
Unfortunately, my polluting less does not matter enough for anyone -- especially
me -- to notice. Therefore, I may not contribute my share toward not polluting.
I may be a free ride on the beneficial actions of others.
4.11 PRIVATE PROVISION OF PUBLIC GOODS
In general, the private sector under-provides public goods because of the free rider
problem.
4.11.1 PRIVATE-SECTOR UNDERPROVISION: A NUMERICAL
EXAMPLE
Consider two people, A and B, with identical preferences
Two consumption goods – private and public, Roads and Cars.
Set the prices of each good at 1.
A and B benefit equally from Road that is provided by either of them since road is
a public good.
Each person chooses combinations of Car and Roads in which his own MRS
equals the ratio of price.
Recall that marginal utilities diminish with increasing consumption of a good.
In this example, optimal provision would require that Roads are consumed until
their utility equals half the marginal utility of Cars.
Thus, each individually buys too much Car privately & provides too few roads
privately.
Strong positive externality in private provision of roads leads to underprovision
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Indian Institute Of Technology, Kanpur
NPTEL-Economics-Public Economics
4.11.2 THE FREE RIDER PROBLEM IN PRACTICE
There are some interesting examples of the free-rider problem in practice.
– Many users of file sharing services, like youtube, never contribute
uploaded files; they only download files.
– To overcome this problem some of these services though give download
priority to those who contribute.
4.12 PRIVATE PROVISION OF PUBLIC GOODS:
EXPERIMENTS TESTING FREE RIDER BEHAVIOR
4.12.1 MARWELL AND AMES 1981
Groups of 5 subjects, each given 10 tokens.
Can invest tokens in either an individual or group account.
Money deposited in own account returned 1-1. Money deposited in the public
account was first pooled, then multiplied by some factor greater than one, and
then distributed equally among all subjects.
Thus tokens given to group account paid out money at higher rate but the group
sum was divided equally between all contributors irrespective of their donation to
the fund
Nash equilibrium is 100% individual contribution but Pareto efficient outcome is
100% group contribution.
Rationality implies that all subjects will follow the individual strategy.
For empirical evidence: Compute fraction invested in group account under
various treatments.
Experiment run on various groups of high school and college students &
economics PhD students.
Finding: 40 to 60% of tokens were still invested in the public good.
Only one group free-rode a lot: 1st year econ graduate students (20% donation
rate).
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Indian Institute Of Technology, Kanpur
NPTEL-Economics-Public Economics
Stephen Marglin, The Dismal Science: Thinking like an economist undermines
community
Two follow up questions:
– What is a “fair” investment in the public good?
75 percent of the noneconomists answered “1/2 or more”, 25 percent
answered “all.”
– Are you concerned about “fairness” in making your investment decision?
Almost all noneconomists answered “yes.”
More than one-third of the economists either refused to answer the question
regarding what is fair.
Those who did respond were much more likely to say that little or no contribution
was „fair.‟
They were about half as likely as other subjects to indicate „concerned with
fairness‟ in making their decisions.
Criticism
– Difference in age
– Difference in gender composition of their group of economics graduate
students
These experiments may be of limited applicability or fail external validity:
– Individuals may behave differently in a contrived laboratory setting.
– The stakes are often small, so the cost of being altruistic is low.
– College undergraduates may not be representative of the population more
generally.
7
Indian Institute Of Technology, Kanpur