Book cover for Intermediate Microeconomics: A Modern Approach

Intermediate Microeconomics: A Modern Approach

Hal R. Varian

ISBN #9780393927023

7th Edition

224 Questions

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7,544 Students Helped

Homework Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This chapter on public goods elucidates the complexities in providing goods that are inherently non-excludable and non-rivalrous. It highlights key challenges such as the free rider problem and explores economic strategies, including quasilinear preferences, the Clarke tax, and agenda manipulation, to improve public decision-making and efficient resource allocation. Understanding these mechanisms is essential for addressing the inefficiencies in public goods provision and ensuring fair distribution of resources.

Learning Objectives

1

Explain the concept of public goods and distinguish them from private goods.

2

Describe the challenges in providing public goods, particularly the free rider problem.

3

Analyze the role of quasilinear preferences in demand revelation for public goods.

4

Evaluate innovative mechanisms such as the Clarke tax and agenda manipulation in addressing public goods provision.

Key Concepts

CONCEPT

DEFINITION

Public Goods

Goods that are non-excludable and non-rivalrous in consumption, meaning everyone can benefit from them without diminishing their availability to others.

Private Provision

The supply of goods by private entities, typically characterized by excludability and rivalry in consumption.

Free Rider Problem

A situation in which individuals benefit from resources or services without paying for the cost of the benefit, leading to under-provision of public goods.

Quasilinear Preferences

A specification of preferences in economic models that simplifies analysis of consumer choice by assuming linearity in one argument, facilitating demand revelation for public goods.

Clarke Tax

An incentive-compatible mechanism designed to reveal true preferences in the provision of public goods by penalizing individuals who misrepresent their valuation.

Agenda Manipulation

A strategy or mechanism that involves altering the set of alternatives or the order of decision-making to influence outcomes in public goods provision.

Example Problems

Example 1

Consider an auction in which people will bid in turn, where each bid has to be at least a dollar higher than the previous bid, and the item is sold to the person who bids the highest. If the value of the good to person $i$ is $v_{i}$ what will be the winning bid? Which person will get the good?

Example 2

Consider a sealed bid auction among $n$ people for some good. Let $v_{i}$ be the value of the good to person $i .$ Prove that if the good is sold to the highest bidder at the second highest price bid, it will be in each player's interest to tell the truth.

Example 3

Suppose that 10 people live on a street and that each of them is willing to pay $\$ 2$ for each extra streetlight, regardless of the number of streetlights provided. If the cost of providing $x$ streetlights is given by $c(x)=x^{2}$, what is the Pareto efficient number of streetlights to provide?
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Step-by-Step Explanations

QUESTION

How does the free rider problem affect the provision of public goods?

STEP-BY-STEP ANSWER:

Step 1: Recognize that public goods are non-excludable, meaning individuals cannot be prevented from using them.
Step 2: Understand that because consumers can benefit without paying, there is an incentive to rely on others for the provision.
Step 3: Explain that this reliance leads to the free rider problem, where too few people may contribute voluntarily to fund the provision of the public good.
Step 4: Conclude that the free rider problem can result in the under-provision of the good compared to the socially optimal level.
Final Answer: The free rider problem undermines efficient public goods provision by reducing the incentive for individuals to contribute voluntarily, leading to potential market failure.

Free Rider Problem

QUESTION

What is the purpose of the Clarke tax in the provision of public goods?

STEP-BY-STEP ANSWER:

Step 1: Identify that the Clarke tax is a mechanism designed to encourage truthful revelation of preferences in public goods provision.
Step 2: Understand that by imposing a tax on misrepresentation, it aligns individuals' incentives with the socially optimal decision-making process.
Step 3: Note that this reduces the free rider problem by making it less beneficial to hide preferences.
Step 4: Recognize that through this mechanism, the collected funds can help achieve efficient resource allocation for public goods.
Final Answer: The Clarke tax enforces truthful reporting of individual valuations for public goods, thereby improving allocation efficiency and addressing the free rider problem.

Clarke Tax

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Common Mistakes

  • Confusing public goods with private goods, ignoring the non-excludable and non-rivalrous nature of public goods.
  • Underestimating the impact of the free rider problem on public goods provision.
  • Assuming that traditional market mechanisms suffice for funding public goods without innovative solutions like the Clarke tax.
  • Misinterpreting quasilinear preferences as implying linearity in all aspects of consumer choice rather than in a specific argument for analysis simplification.