1. The Economic Analysis
of Public Goods

2. In the Economic analysis of public goods the optimal
allocation of resources for the provision of public goods is
examined.
Pigou analysed the model for the optimal allocation of the
resources for the public and private goods.

3. The pigovian Approach
► Each individual receives utility from the consumption of public good
and has to pay tax which is an opportunity cost of forgone private
good consumption
► The objective is to find the optimal allocation of consumer’s budget
between all private and public goods
► The equilibrium occurs where
► Marginal utility of public good=marginal disutility of tax payment

4. The partial equilibrium analysis for the
optimal provision of the public good
► This is based upon the single commodity equilibrium analysis
► The consumer’s taste, income and price of other goods is assumed to
be constant
► The equilibrium is analysed for both private and public goods one by
one and then their differences are examined

5. The partial equilibrium analysis of pure
private good
► Assumptions
► Markets are competitive
► There are two individuals A and B.
► DA and DB are the individual demand curves.
► DD is the market demand curve DD=DA+DB
► SS= Market Supply curve and OP is the equilibrium price.
► OQ is the equilibrium quantity. OQ=OQA+OQB

6. Figure 3.1

7. The partial equilibrium analysis of pure
public good
► The total willingness to pay for the public good is found by adding individual
demand curves vertically (As the supply of the public good is fixed).
► At the equilibrium level the total revenue received is equal to the total cost
of supplying the good.
► It is further assumed that everyone equally reveals its willingness to pay for
the public good.

8. Figure 3.2

9. Difference in the analysis of public and
private good
Private Good
► Each individual is price taker and
quantity adjuster.
► Equilibrium occurs where
Qd=Qs
The supply curves represent the
marginal cost of supplying additional
units of output
► Efficient prices rule for the private
good
OPA=OPB=OP=MC
Public Good
► Each individual is quantity taker
and price adjuster.
Equilibrium occurs where
Total willingness to pay for the public
good output=price at which producer
is willing to supply
► Efficient prices rule for the private
good
OPA+OPB=OP=MC

10. Demand curve for the public good
► The demand curve for the public good can be derived from Ics.
► The efficient supply of the public good requires sum of the individual
prices=MC

11. Optimal provision of public good-
General Equilibrium Analysis
► This is the case of many public and private goods.
► Assumptions
► Two commodities model.
► Private good=X
► Public Good=G
► The production possibility set and taste is given

12. ► The analysis is similar to usual General Equilibrium Analysis but here one is
good is pure public good.
► In the figure 3.3(A, b and c) there are two individuals assumed A and B
(Graphs are referred to text book page 55).
► The combination of outputs represented by points M in 3.3(a) and N in 3.3 (b)
are pareto optimal combinations of the public and private goods.
► At a pareto optimum slope of production possibility curve=Slope of
B2B2+Slope of A1A1 or
► MRT=MRSA+MRSB
Optimal provision of public good-
General Equilibrium Analysis

13. ► The condition for the optimum supply of public good for economy with public
and private goods and with many individuals is :
► Sum of the marginal rates of substitution=Marginal rate of transformation
► The pareto optimal supply of public good requires a set of individualized
prices for each consumer adding to MC.
► The Samulseon model assumes the existence of omniscient planner who
knows sets of prices of public good. This is the first restrictive assumption.
The second restrictive assumption is that each individual strictly reveals its
preferences.
Optimal provision of public good-
General Equilibrium Analysis

14. “Muhammad Akmal” is discussant of
this topic. He will further discuss this
topic in class.