Problem of Allocation of Resources: Public & Private Mechanisms

6 months ago

Atiqur Rahman

15 minutes

Introduction

In Public Economics theory, goods or commodities are broadly divided into two categories.

Private goods
Public Goods are also known as social goods or collective goods.

A good is called a private good if it is allocated under a market mechanism, and a public or social good cannot be provided by a market mechanism. Another interesting phenomenon connected to the concept of Public good is free ridership, which means taking a ride without paying for it.

Given the complication of free ridership, public goods may not be provided efficiently through market mechanisms. In such a situation, Lindahl Equilibrium may be used.

The private mechanism for resource allocation depends on market demand and market supply curve for the private good. Moreover, the mechanism of provision of a private good is not applicable to a public good as, by definition of a public good, they are equally available to all, and even if individual demand curves are different, individuals cannot consume different amounts of a public good.

Concept of Private and Public Good

To understand the allocation of a good, it is extremely important to understand the inherent characteristics of a good, which make it public or private.

A good is called a private good if it is allocated under a market mechanism. A market is a place where buyers and sellers come together. In the case of private goods, buyers reveal their demand curve.

A market demand curve is based on the marginal benefit they derive after consuming successive units of the good and is found by horizontally adding the individual demand curves for the private good under consideration.

For a demand curve, conventionally, ‘price’ is taken on the Y-axis and the quantity demanded is taken on the X-axis. Here, we take horizontal addition because the price is the main determinant of demand in the case of a private good.

Similarly, sellers determine the supply based on the marginal cost of providing the good. Equilibrium is established at the point of intersection between demand and supply curves.

It also represents a situation where the marginal benefit to the private consumers is equal to the marginal cost of providing the good. In an equilibrium condition, every consumer gets to consume the quantity s/he wants to consume at an equilibrium price and according to his individual demand curve. The good can be consumed only by the person who pays the price. All others are excluded from the consumption.

Similarly, a private good is also called as rival or subtractable because if one person is consuming it, others cannot consume the same good simultaneously.

At the other end, a public or social good cannot be provided by market mechanism. The main reason for this is the non-rivalry and non-excludability of the good. By definition, a public good is non-rival because even if one person is consuming it, the consumption does not affect the availability of the good for anyone else.

The theory of public goods was developed by Paul A. Samuelson (1954). He defines a public good as “…[goods] which all enjoy in common in the sense that each individual’s consumption of such a good leads to no subtractions from any other individual’s consumption of that good.”

Examples of public goods are national defence, fresh air, street lights, etc.

Though theoretically, while defining a public good, we take the case of non-rivalry and non-excludability, in practice, very few goods fall in the category of pure public goods. A road, public parking, a playground, etc., can be called as public goods, but they don’t fall into the category of pure public goods.

For example:

A road or public park may be equally available to everyone, but overcrowding will make the consumption rival.
A streetlight in Kolkata, given its non-rival nature, though equally available for a user in Delhi, geographical distance between two cities will make the consumption excludable.
There are goods which can be classified as both private as well as public. For example, law and order and protection of property come in the public domain and hence will be called as public goods. But, if an individual decides to hire a private guard to protect his property, protection can be called a private good.
There are goods which, by characteristic, are non-rival in nature. For example, cable TV connection. Your TV transmission will not be affected by the transmission of your neighbour, and hence, the consumption is non-rival in nature. But the good is excludable as only those people get the good, which are willing to pay for it.
Other related goods are common-pool resources (CPR’s). Common pool resources are shared resources whose consumption is rival but non-excludable. An example of a common pool resource is a village pasture where cattle of everyone is allowed to graze or a village pond where everyone is allowed to catch fish.
A good like cigarettes or alcohol may be a private good, but owing to negative externalities on others, it may not be called as pure private. Similarly, health or education can be purchased in the private market, but these goods generate positive externalities for society.

All the examples cited above make it clear that pure private or pure public are two extreme definitions for goods, and given the extent of rivalry and excludability, goods can be classified as private or public.

Free-ridership and Pseudo-demand Curves

Another interesting phenomenon connected to the concept of Public good is free ridership. As the name only suggests, ‘it implies taking a ride without paying for it’. As, by definition, a public good is non-excludable and non-rival in nature, people will avoid paying for it voluntarily. They will be aware that once the good is available, it will be equally available to all, even if they have not paid for it. Each of the consumers will have an incentive to not reveal his willingness to pay by his demand curve because he expects that the good will be financed by those who will reveal their willingness to pay. And once the good is available, it will be equally available to all.

This phenomenon makes the allocation of a public good extremely difficult because, in this case, there is no revealed demand curve. How the good should be priced and how much quantity of the good should be produced becomes an extremely challenging question.

Given the incentive to act as a free rider, it is unrealistic to assume that consumers will reveal their true demand for a public good. In this type of situation, theoretically, pseudo-demand curves are used.

Pseudo-demand curves are similar to demand curves for public goods but are not exactly that. We may say that these are the demand curves which we unrealistically expect consumers to reveal. While explaining the Problem of allocating Resources for the public in Partial Equilibrium analysis, these demand curves will be used.

Problem of Allocating Resources: Private Mechanism for Allocating Resources in Partial Equilibrium Analysis

As explained earlier, a private mechanism for resource allocation depends on market demand and market supply curve for the private good. Assuming that there are only two individuals living in the economy, Mr. A and Mr. B, the total market demand curve for the private good under consideration can be found by horizontally adding the private demand curve of Mr. A and that of Mr. B.

The point of intersection between demand and supply curves will give us market equilibrium (as depicted by ‘e’). In this case, Mr. A, as well as Mr. and B, will pay the market price. If we notice the individual demand curves of A and B, we will find that at a price corresponding to equilibrium point e, Mr. A will consume corresponding to the point where his individual demand curve (i.e., his marginal benefit curve) is equal to the prevailing market price.

The same will hold true for Mr. B also. As in the diagram, we have taken Mr. A’s demand curve to be lower than that of Mr. B; A will consume less at the given price compared to B.

Total output produced will be equal to:

Total Output = {Output being consumed by Mr. A} + {Output being consumed by Mr. B}

Private Mechanism for Allocating Resources in Partial Equilibrium Analysis

The mechanism of provision of a private good is not applicable to a public good as, by definition, once provided, goods are equally available to all, and even if individual demand curves are different, individuals cannot consume different amounts of a public good.

In this case, rather than horizontal addition, vertical addition of individual pseudo-demand curves of Mr. A and Mr. B is done. The vertical addition of demand curves for a public good was provided by Howard R. Bowen (1948) and used by Samuelson.

By vertically adding the individual pseudo-demand curves of Mr. A and Mr. B, the total demand curve for the social good can be estimated. In this case, also, we are assuming a normal upward-sloping supply curve. The demand curve intersects the supply curve at e.

Total output produced will be equal to:

Total Output = {Output being consumed by Mr. A} = {Output being consumed by Mr. B}

Point e will not only show us the total quantity of public goods to be produced (which would be consumed by everyone), but it will also give us the total price of the public good.

Then, the Price of Public goods = the Price paid by Mr. A and the price paid by Mr. B.

Using the individual demand curves of Mr. A and Mr. B, one can conclude about the contribution of each person towards the total cost of supplying the social good.

But as stated earlier, the demand curves are ‘pseudo-demand’ curves. One must not forget that social good is not sold in the market, so open demand will not be revealed and very little information is available on the slope as well as the position of such demand curves.

Private Mechanism for Allocating Resources in Partial Equilibrium Analysis 2

Voluntary Solutions for Public Goods

Given the complication of free ridership, public goods may not be provided efficiently through market mechanisms. In such a situation, Erik Lindahl in 1919 presented a solution called as Lindahl Equilibrium, shown in the figure. According to his solution, people will voluntarily come forth to provide for the cost of public goods, given their demand curves and their knowledge of others’ demand curves.

We are retaining the assumption of having two individuals, Mr. A and Mr. B and one social good. Demand curve DaDa shows Mr. A’s demand for a particular public good. The vertical axis measures the share of the public good’s cost that he will have to pay. DbDb is Mr. B’s demand curve. OE is the equilibrium level of output, whose cost will be shared by A and B according to their demand schedules. For output levels greater than OE, people are not willing to pay the total cost of the good. Output level OE is a Lindahl equilibrium, which is a balance between people’s demand for public goods and the tax shares that each must pay for them.

Problem of Allocating Resources: Private and Public Mechanism for Allocating Resources in General Equilibrium Analysis (Samuelson’s General Equilibrium Model)

Samuelson’s General Equilibrium Model is based on two goods (a public and a private good) and two people, Mr. A and Mr. B. As we are now studying the allocation in the general equilibrium framework, first of all, it is extremely important to understand the difference between partial equilibrium and general equilibrium.

Partial equilibrium analysis focuses only on the part of the market, assuming other things to remain the same. Compared to partial equilibrium, general equilibrium is a detailed framework where the focus is on the entire economy.

The present analysis is based on the assumptions given below:

There are two goods in the economy: one private good P, and one social good S.
The production possibility curve for two goods P and S is given. The production possibility curve (PPC), also called as the transformation function or production frontier, shows the possibilities open for increasing the output of one good by reducing the output of another.
Tastes of the consumers are given, i.e., we have a utility map of Mr. A as well as Mr. B.

To show the efficient allocation of social goods in a general equilibrium framework, first, we select a given level of utility for individual A, which is depicted by his indifference curve ICA. Subtracting it vertically from the transformation curve, we get another curve known as the residual curve or consumption curve for B. This consumption curve will reveal the maximum private good available for B, given A’s utility level.

Out of various options of private goods available for B, B will choose that point where the residual curve touches its highest Indifference curve. In Figure ICB2 is that indifference curve, and E is the equilibrium for B. Corresponding to E, Mr. A will choose a point like K on his Indifference curve as a point of consumption, K being exactly vertical to E.

It is important to note here that both A as well as B will be consuming the same amount of public good, which can be found. In the case of private good, it will not be so.

Two Approaches: Partial Equilibrium and General Equilibrium

In the partial equilibrium approach, the existence of other good(s) is ignored, and the good’s price is seen in terms of money. The characteristic of a partial equilibrium approach is the assumption that some things – like other prices -that conceivably could change do not change.

Partial equilibrium analysis, therefore, tends to ignore some of the interrelationships among prices and markets. By contrast, in a general equilibrium analysis, all goods and prices are considered variable, and the analysis focuses on the simultaneous determination of equilibrium in all markets.

Problem of Allocation of Resources: Public & Private Mechanisms

Introduction

Concept of Private and Public Good

Free-ridership and Pseudo-demand Curves

Problem of Allocating Resources: Private Mechanism for Allocating Resources in Partial Equilibrium Analysis

Voluntary Solutions for Public Goods

Problem of Allocating Resources: Private and Public Mechanism for Allocating Resources in General Equilibrium Analysis (Samuelson’s General Equilibrium Model)

Two Approaches: Partial Equilibrium and General Equilibrium

Read More in: Theory of Public Finance

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Introduction

Concept of Private and Public Good

Free-ridership and Pseudo-demand Curves

Problem of Allocating Resources: Private Mechanism for Allocating Resources in Partial Equilibrium Analysis

Voluntary Solutions for Public Goods

Problem of Allocating Resources: Private and Public Mechanism for Allocating Resources in General Equilibrium Analysis (Samuelson’s General Equilibrium Model)

Two Approaches: Partial Equilibrium and General Equilibrium

Read More in: Theory of Public Finance

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