User:Arbraxan/Advanced Public Economics

''This subpage is based on the course "Advanced Public Economics" given by Bas Jacobs at the Erasmus University Rotterdam in 2013. It is intended to gather content for substantial work on the article public economics and potential derivatives of that article.''

Advanced public economics visits a range of of topics related to public economics, including welfare economics, the deadweight loss of taxation, optimal linear and non-linear income taxation, optimal indirect taxation and the debate on indirect and direct taxes, the optimal taxation of capital income and human capital, the optimal provision of public goods and the marginal cost of public funds, and optimal corrective/environmental taxation.

Welfare economics, deadweight loss and optimal linear taxation
In most industrialized countries the state plays a major role as evidenced by taxation as a percentage of economic output, which ranges among OECD countries from 48% in Denmark to 18% in Mexico. This taxation is composed of taxes on income and profits, property, goods and services, payroll taxes, social security contributions and other items, in which regard countries are often widely diverging. Countries are also different with regard to the share of government spending in of total economic activity (GDP), spanning from 58% in Denmark to 23% in Mexico. This diversity pattern is also maintained concerning the composition of government spending: Whereas Germany, Denmark or Luxembourg spend most public revenues on social protection, South Korea, the United States or Canada spend more on public order and defense or health Last, countries as well differ widely with respect to the marginal tax burden they impose on labor income and the corresponding tax wedges due to income and/or consumption taxes, e.g. 66% marginal tax burden in Belgium and 7% in Chile, and a 59% combined tax wedge in Belgium compared to 22% in Mexico in the OECD.

First Theorem of Welfare Economics
The first theorem of welfare economics states that if markets are competitive as well as complete and information asymmetries, externalities and transaction costs absent, then any (general) equilibrium in competitive markets is Pareto-efficient. In this context, Pareto efficiency implies that no exchange improving the situation of one economic agent is possible without deteriorating the situation of another. This means that voluntary trade exhausts all possible gains from trade, and trade continues until the relative benefits of consuming a good (MRS) are equal to the relative costs of producing a good (Marginal rate of transformation|MRT]]).

However, the first theorem of welfare economics fails in practice because of the wedge between social (relative) costs or benefits and private (relative) costs or benefits in production or consumption. This wedge can be attributed to economic phenomena such as market power ((monopoly or oligopoly), asymmetric information distribution, transaction costs or externalities.

Second Theorem of Welfare Economics
The second theorem of welfare economics states that if markets are competitive as well as complete and in the absence of information asymmetries, externalities and transaction costs, every Pareto-efficient market allocation can be achieved by appropriate individualized lump-sum transfers (i.e. the redistribution of endowments such as individual resources, earning abilities, etc.).

The second welfare theorem fails due to the government's inability to observe individuals' earnings capacity and consequently its inability to implement non-distortionary individualized lump-sum taxes. Instead, government uses distorting instruments such as taxes on what are assumed to be results of individuals' earnings capacity, e.g. (observed) income, which is taken to be largely a product of effort and ability. However, while taxing income reduces inequality due to differences in ability, it also distorts individuals' incentives to provide effort. Therefore, there is no possibility to redistribute income without deteriorating efficiency, a theoretical result known as the equity-efficiency trade-off One exception to the equity-efficiency trade-off is a non-individualized lump-sum tax (i.e. head tax) as it is not based on his work effort.

Assumptions of welfare economics
Modern welfare economics make several assumptions, chief among which are:
 * Rational individuals with individualistic preferences;
 * A well-defined social welfare function and cardinal utility allowing for interpersonal welfare comparison;
 * Only individuals' earnings capacity or initial endowments differ;
 * No market failure (this assumption can be relaxed if explicitly stated, e.g. for failures in labor, capital, and insurance markets);
 * No behavioral effects such as bounded rationality, Keeping up with the Joneses or hyperbolic discounting;
 * Perfect respect of individual preferences by social objectives based on the assumption of rational and individualistic agents gifted with perfect will-power.

Welfare economics and consumer theory
Much of modern welfare economics relies on the standard neoclassical labor supply model. Therein, households derive utility from consumption and leisure and maximize this utility, which is taken as a welfare criterion. Underlying this are the assumptions that both consumption and leisure are normal goods with positive and diminishing marginal utility. Furthermore, an individual's time is spent on labor and leisure.

In this model, household budget constraints (HBC) limit the amount of consumption possible and define consumption as corresponding to the sum of labor and non-labor income, labor income being the after-tax product of the hourly wage rate and the labor input. Then, individuals maximize their utility from consumption and labor (i.e. leisure) under their household budget constraints. Econometrically, this maximization problem can be solved using the Lagrange function, with the Lagrange multiplier featuring as an exchange rate between monetary and utility values (utils). It is further assumed that the problem's second-order conditions hold based on the utility function's second derivatives.

Solving the utility maximization's first-order conditions shows equalities between the marginal benefits and costs of consumption as well as between the marginal benefits and costs of leisure. Mathematical substitution then results in the marginal rate of substitution between consumption and leisure, i.e. the marginal cost of one unit of leisure in terms of consumption. The indirect utility function of the net wage rate and transfer then corresponds to the utility function at optimal levels of consumption and labor. This indirect utility function can then be differentiated with respect to its policy variables, yielding Roy's lemma. Roy's lemma stats that the change in utility resulting from a change in one of the parameters equals the product of the change in income attributable to the change in the parameter and the marginal utility of income. Therein, a change in one of the exogenous variables (i.e. the indirect utility function's variables) does affect the optimal choices for consumption and labor (i.e. the endogenous variables), but this impact won't have any effect on overall utility since otherwise these variables would not have been optimally chosen by the household, as given by the Envelope theorem.