Applied Public Economics: Samuelson Model and Public Goods

Formally derive the Samuelson condition from the Lagrangian, showing all steps, and explicitly state what assumptions are necessary for its validity. Explain the economic interpretation of the condition in terms of marginal rates of substitution and transformation.

Consider an economy with $H$ households and $m$ firms, where the production function of each firm $j$ is given by $y^j = f^j(l^j, G)$, where $l^j$ is labor and $G$ is a public input. If $G = \theta^{-1}(l^G)$, derive the condition for the optimal provision of the public input, demonstrating how the marginal products in all firms equate to opportunity costs. Further, discuss how this condition is affected by the productivity of labor, $\theta$.

Suppose a public good is financed through majority voting with cost shared equally among households. Outline the conditions under which the median voter outcome aligns with the efficient Samuelson condition. Discuss potential scenarios where this alignment fails and explain how income inequality might influence the voting outcome.

Elaborate on the concept of distortionary financing of public goods following Atkinson and Stern (1974). Write the Lagrangian, incorporating the effects of distortionary taxes. Explain in detail how the conditions for optimal public good provision differ from the standard Samuelson rule under lump-sum taxation. What are the key implications for public policy?

Consider the distortions introduced when using commodity taxes to finance public goods. Derive an expression for $\alpha / \lambda$, where $\alpha$ is the private marginal utility of income and $\lambda$ is the shadow price of public funds, under the conditions of taxation. Evaluate how deviations from the basic rule (α/λ = 1) affect the optimal public good supply. What are the policy implications for the level of public good provision?

In the context of personalized prices (Lindahl pricing), explain how Lindahl equilibrium leads to a Pareto-efficient allocation of public goods. Discuss the practical challenges associated with implementing Lindahl pricing in a real-world economy and how preference revelation mechanisms attempt to address these challenges.

Critically evaluate the experimental evidence on free-riding in public goods games. What behavioral factors, such as altruism and warm-glow giving, are not captured in standard economic models? How do these factors influence the provision of public goods in laboratory settings versus real-world contexts?

Discuss the concept of crowding out in the context of private contributions to public goods. Differentiate between the theoretical predictions of complete crowd-out and the empirical evidence. How do studies by Andreoni and Payne (2003) contribute to understanding the relationship between government spending and private charitable giving, and what are the implications for policymakers?

Analyze randomized field experiments that test the role of reciprocity and social pressure in charitable giving, citing Falk (2007) and Dellavigna-List-Malmendier (2012). Explain how these psychological effects differ from traditional economic incentives and their implications for designing effective fundraising campaigns.

Explain the Tiebout model and the conditions required for its successful operation. How does the Tiebout mechanism promote efficiency in the provision of local public goods, and what are the major limitations and criticisms of this model in real-world settings?

In the context of the Tiebout model, explain how local governments can effectively implement tax-benefit linkages to mitigate issues related to redistribution and migration. Detail specific strategies that balance the provision of public goods with the tax burden to prevent adverse selection.

Assume that the economy has $H$ identical households. Each household h has a utility function $U^h(x^h, G)$, where $x^h$* represents quantity of unit of private good consumed by household h, and G quantity of public good. Let aggregate production be given by $F(X, G) = 0$. Derive and interpret the first-order conditions for the Pareto-efficient level of public good provision.

Analyze the conditions under which majority voting leads to the efficient provision of a public good. Assume households have single-peaked preferences. How does the median voter theorem apply, and what assumptions must hold for the median voter’s preferred level of the public good to coincide with the Pareto-efficient level?

Formulate a Lagrangian for the optimal provision of public inputs, considering that public inputs increase firms' productivity. Assume $m$ firms, where the production function of each firm j is given by $y^j=f^j(l^j, G)$, where $l^j$ is labor, $G$ is a public input. Households' utility is $U^h(x^h, l^h)$, where $x^h$ is the private good and $l^h$ is labor. Derive the first-order conditions and interpret the optimal rule. How does the rule change if labor supply is endogenous?

In the context of Lindahl pricing and personalized prices, specify the conditions under which a Lindahl equilibrium is achieved. How does each consumer’s personalized price relate to their marginal willingness to pay for the public good? Further, detail the informational and practical challenges associated with implementing Lindahl pricing.

Describe the complexities introduced to the Samuelson condition when public goods are financed via distortionary taxes. Illustrate how the shadow price of public funds ($\lambda$) influences the provision rule. Assuming a utility function where consumers consume both private and public goods, explain how public goods are over or under provided?

Explain the Tiebout model and the assumptions required for its perfect functioning, including mobility, information, and number of towns. Further, explain how the model promotes efficiency and what are the main limitations.

Describe findings from either Andreoni or Falk. How can this inform how local public goods are funded or provided?

Suppose there are N families and 2 towns, explain the Tiebout sorting mechanism. How do the rich and poor tend to gather in different cities?

Assume that the production possibility frontier is given by $F(X, G) = 0$, where $X$ is the aggregate quantity of the private good and $G$ is the quantity of the public good. Let the individual households' utility functions be represented as $U^h(x^h, G)$, where $x^h$ is the individual consumption of the private good and $G$ is the level of the public good. Suppose the government finances $G$ with distortion of $\Tau$ where $G(q)=H \sum_{i=1}^n t_i x_i$. Derive the modified Samuelson rule under this condition and explain its implications.

Within the framework of the Tiebout model, analyze the impact of inter-community externalities on the efficient provision of local public goods. Consider a scenario where pollution generated in one town affects the environmental quality in neighboring communities. How does this externality affect the Tiebout sorting mechanism, and what policy interventions can restore efficiency?

Suppose an economy consists of perfectly altruistic individuals. Discuss the implications for the provision of public goods compared to an economy made up of purely self-interested agents, and how these two contrasting behavioral assumptions affect the equilibrium level of public goods.

A public good is provided by a monopolist. Suppose that the monopolist can impose personalized prices for the good. Will the outcome be more or less efficient than if the government were providing the same good. Justify your answer.

Briefly describe the warm-glow model of giving, and list a scenario where the model is more reasonable versus a scenario that is more appropriate for pure altruism.

You are tasked with maximizing the effectiveness of a door-to-door fundraising campaign. How would you use the result s of Dellavigna, Li, and Malmendier to set policy rules? Why would this improve outcomes on average?

In an economy with heterogeneous agents, how can the government determine who values a public good the most to optimize revenue collection when using personalized prices?

Define the free rider problem with the example of a public park. Elaborate on three mechanisms that private firms can use to overcome it.

In the Tiebout model, governments may wish to redistribute resources to the poor within their jurisdiction. What is a problem with this? What implications does this have?

A country is debating whether they should subsidize the wealthy or middle-to-lower class for the creation of a public good. Argue for each sides by pointing out both pros and cons.

The Tiebout model supposes there is no externalities, and all utility is derived in local jurisdictions. How does an externality in the provision of a local public good change the outcome?

Why do all models of publicly provided goods require government.

Lindhal prices provide an elegant theoretical solution to provision of public goods, however they hardly ever exist in reality. Explain a circumstance where these are seen in practice.

A government provides a public good with an amount decided by majority vote. Suppose that some subset of the population could pay the other off to reduce the amount of the public good. Would this improve social welfare.?

A large amount of experiments test how public goods can be privately provided. Summarize some of the main findings that these have produced.

How do governments decide which taxes to rely on to raise revenue given the results from Auerbach and Hines.?

In an analysis of taxes versus revenue, what did Shaviro state were an important consideration when choosing between what type to take.

Briefly explain behavioral economics approach to individuals provision of public goods. In what general way is this different from standard "textbook" provision.

Some have argued that, for a variety of reasonable assumptions, it should be thought of as optimal for a government to completely crowd-out private donations to local charities. What would have to be true for this to improve social welfare?

Briefly describe the results from Falk (2007) in their field experiment and charitable giving. What general lesson should be taken away?

What do Dellavigna, List, and Malmendier conclude that economists should now take into account when considering funding? Is social pressure a net positive for public provision or a costly tax?

In order, list the most basic components that an individual must have and know in order for the Tiebout to be successful.

Briefly explain how the Tiebout result implies that it may be difficult for local level governments in the U.S .to redistribute by listing two reasons.