Problem of Allocation of Resources: Public & Private Mechanisms

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:

  1. A road or public park may be equally available to everyone, but overcrowding will make the consumption rival.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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
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
Private Mechanism for Allocating Resources in Partial Equilibrium Analysis 2

Voluntary Solutions for Public Goods

Voluntary Solutions for Public Goods 1
Voluntary Solutions for Public Goods 1

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.

Voluntary Solutions for Public Goods 2
Voluntary Solutions for Public Goods 2

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:

  1. There are two goods in the economy: one private good P, and one social good S.
  2. 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.
  3. Tastes of the consumers are given, i.e., we have a utility map of Mr. A as well as Mr. B.
Voluntary Solutions for Public Goods 3
Voluntary Solutions for Public Goods 3
Voluntary Solutions for Public Goods 4
Voluntary Solutions for Public Goods 4

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.

Read More in: Theory of Public Finance

  1. Public Finance: Meaning, Nature & Scope
  2. Role of Government in Economy
  3. Role of Government in Mixed Economy: Public & Private Sector
  4. Role of Government under Cooperation and Competition
  5. Role of Government in Economic Development and Planning
  6. Concept of Public Goods, Private Goods, and Merit Goods
  7. Concept of Market Failure and Functions of Government
  8. Market Failure and Functions of Government: Decreasing Costs
  9. Market Failure and Functions of Government: Externalities
  10. Market Failure and Functions of Government: Public Goods
  11. Future Market: Meaning, Role & Uncertainty
  12. Concept of Information Asymmetry
  13. Theory of Second Best: Concept & Explanation
  14. Problem of Allocation of Resources: Public & Private Mechanisms
  15. Preferences: Meaning, Types & Problems of Preference Revelation
  16. Preference Aggregation & Its Mechanism
  17. Voting Systems, Direct Democracy, Representative Democracy, Leviathan Hypothesis & Arrow’s Impossibility Theorem
  18. Economic Theory of Democracy: Concept & Explanation
  19. Politico Eco Bureaucracy: Concept & Explanation
  20. Rent-Seeking and Directly Unproductive Profit-Seeking Activities
  21. Rationale for Public Goods: Concept & Explanation
  22. Benefit Theory or Voluntary Exchange Theory
  23. Lindahl Model: Concept, Equilibrium & Limitations
  24. Bowen Model: Concept, Advantages & Limitations
  25. Samuelson’s Model of Public Expenditure
  26. Musgrave’s Model of Public Expenditures
  27. Demand Revealing Schemes for Public Goods
  28. Vickery-Clarke-Groves Mechanism
  29. Groves-Ledyard Mechanism
  30. Tiebout Model: Concept, Assumptions Equilibrium & Simple Tiebout Model
  31. Theory of Club Goods
  32. Keynesian Principles of Stabilization Policy
  33. Difference Between Keynesian Economic Thought and Others
  34. Role of Expectations and Uncertainty in Formulating Stabilization Policy
  35. Intertemporal Markets Efficiency & Failure
  36. Liquidity Preference Theory
  37. Diamond-Dybvig Banking Model
  38. Preference Shocks, Adverse Selection & Central Bank
  39. Equilibrium Deposit Contract
  40. Social Goods and Its Effect on Stabilization Policy
  41. Effect of Infrastructural Facilities on Stabilization Policy
  42. Effect of Distributional Inequality on Stabilization Policy
  43. Effect of Regional Imbalances on Stabilization Policy
  44. Wagner’s Law of Increasing State Activities: Explanation, Graph & Criticism
  45. Peacock-Wiseman Hypothesis: Explanation, Graph & Criticism
  46. Public Expenditure: Concept, Objectives, & Public vs Private Expenditure
  47. Pure Theory of Public Expenditure
  48. Structure & Growth of Public Expenditure in India
  49. Trends, Lessons & Priorities in Public Expenditure in India
  50. Social Cost-Benefit Analysis: Project Evaluation, Estimation of Costs & Discount Rate
  51. Performance Based Budgeting and Zero Based Budgeting
  52. Theories of Tax Incidence: Concentration Theory, Diffusion Theory & Modern Theory
  53. Tax System and Its Principles
  54. Equity Principle and Efficiency Principle of Taxation: Meaning, Explanation & Examples
  55. Ability to Pay and Benefits Received Principle of Taxation
  56. Theory of Optimal Taxation: Excess Burden & Distortions of Taxation
  57. Deadweight Loss of Taxation: Causes, Measurement & Example
  58. Concept of Equity & Efficiency in Economics
  59. Trade-Off Between Equity and Efficiency: Meaning & Example
  60. Theory of Measurement of Dead Weight Loss
  61. Double Taxation: Meaning, Desirability, Forms & Solution
  62. Solution to Problem of Double Taxation: Intra-Country & International
  63. Double Taxation Avoidance Agreement (DTAA) and Indian Policy
  64. Classical View on Public Debt
  65. Compensatory Aspect of Public Debt Policy
  66. Public Debt or Borrowings: Concept, Need, Sources & Types
  67. Concept of Public Debt or Public Borrowings
  68. Need for Public Debt or Public Borrowing
  69. Sources of Public Debt
  70. Classification of Public Debt
  71. Burden of Public Debt: Meaning, Types & Explanation
  72. Debt Through Created Money or Deficit Financing
  73. Public Debt (Public Borrowings) and Inflation (Price Level)
  74. Crowding Out of Private Investment and Activity
  75. Principle of Public Debt Management and Debt Repayment

Share Your Thoughts

en English