Public Economics

Public Economics

Study of economic efficiency, distribution and government economic policy.

Developed out of the original political economy of JS Mill and David Ricardo. It is a very important branch of economics because of the foundation it provides for practical policy analysis.

Method of use of models: Models are used for analysis because the possibilities for experimentation are limited and past experience cannot always be relied on to provide a guide to the consequences of new policies.


Efficiency of competition: When utility is maximized, the efficient outcome has been achieved. When there are multiple decision-makers, efficiency is to be defined with respect to a set of aggregate preferences.


First and second best outcomes: A first-best outcome is achieved when only the production technology and the limited endowments restrict the choice of the decision-maker. The first-best is essentially what would be chosen by an omniscient planner with complete command over resources. A second-best outcome arises whenever constraints other than technology and resources are placed on what the planner can do. Such constraints could be limits on income redistribution, an inability to remove monopoly power, or a lack of information.



Theories of public sector


Justification for the public sector


Two basic lines of argument: equity and efficiency


  1. The minimal state: Entirely unregulated economy cannot operate in a very sophisticated way. No proper function without property rights(no trust – Hobbes) and contract laws. These laws and rights need to be policed and upheld in law as well. Costs are involved in this enforcement. A source of income to pay for this must be found hence. Therefore, there is a requirement for a coordination of the collection of revenue and the provision of services.
  2. Market versus government: There are situations where intervention in the economy can potentially increase welfare. Two such situations: those involving market failure and those do not.
  3. Equity: Inequality of income, opportunity and wealth
  4. Efficiency and Equity: The challenge for policy design is to reach the correct trade-off between equity and efficiency.


Public Sector Growth


Listed below are some theories to explain the substantial growth of the public sector in the past century:


  1. Development Models: Economy experiences changes in its structure and needs as it develops.
    • Early stage of development: Indstrialization; migration from rural to urban areas; this leads to a demand for infrastructure; public sector needed to provide this infrastructure
    • Middle stages of development: infrastructure expenditure of the public sector becomes increasingly complementary with expenditure from the private sector; with growth of urbanization, a range of externalities such as pollution and crime develop. This leads to diversion of public spending from infrastructure to control of these externalities.
    • Developed phase: public expenditure driven by the desire to reach to issues of equity.

Criticism: This is a description of the public sector and not an explanation. It does not have a behavioural basis and is essentially mechanistic. Changes in expenditure not related with the changes in preferences


  1. Wagner’s law: Adolph Wagner analyzed data on public expenditure and concluded that the sector had been growing over time. There are three distinct components of his theory:
    • First: Growth in economy results in an increase in complexity. New laws and legal structures imply continuing increase in public sector expenditure.
    • Second: There was a process of urbanization and the increased externalities associated with it.
    • Third: Goods supplied by the public sector have high income elasticity (eg. Education, recreation and healthcare). As economic growth increases income, there will be an increase in the demand of these products. Hence public expenditure will rise.

Criticism: The problem in empirical verification of Wagner’s law is that it is difficult to disentangle the causality between public expenditure and the level of income. Secondly, it concentrates solely on the demand for public sector services. Supply side is neglected.


  1. Baumol’s law: Starts with the hypothesis that the technology of the public sector is labor-intensive relative to that of the private sector. Due to the nature of activities undertaken, it is difficult to substitute capital for labour. Since the public sector cannot substitute capital for labor, the wage increases in the private sector feed through into cost increases in the public sector. Maintaining a constant level of public sector output must therefore result in public sector expenditure increasing. If public sector output/private sector output remain in the same proportion, public sector expenditure rises as a proportion of total expenditure. This is Baumol’s law, which asserts the increasing proportional size of the public sector.

Criticism: Entirely technology driven; does not consider aspects of supply and demand or political processes. Also, it is possible that substitution can take place in the public sector.


  1. Political Model: Capture the conflict in public preferences between those who want higher public expenditure and those who want to limit the burden of tax. The main point is that the equilibrium level of public spending can be related to the income distribution, and more precisely that the growth of government is closely related to the rise of income inequality. (Refer Hendrik and Myles for details).


  1. Ratchet Effect: Assumptions: preference of the government is to spend money; public do not want to pay taxes. These two competing objectives are moderated by the fact that governments desire re-election. Equilibrium level of public spending is determined by the balance between these competing forces.
  • In the absence of exogenous changes in preferences, the level of expenditure will remain relatively constant.
  • Occassionally, economies go through upheaval (such as wartime) where the government raises expenditure with the consent of the taxpayer.
  • However, the level of expenditure does not fall after the period of upheaval. This is because a) high expenditure is seen as the norm, b) debts incurred during this period have to be paid off c) promises made by the government during the upheavals to taxpayers have to be met. These are jointly termed as ratchet effects. Finally, there can be inspection effect after the upheaval where the agents reconsider their positions and priorities.
  • The prediction of the ratchet effect model is that spending remains relatively constant unless disturbed by some significant external event.


Excessive government


Listed below are the theories that assess whether the level of public expenditure is optimal or a burden on the economy.


  1. Bureaucracy: In this theory, the analysis of bureaucracy starts with the assumption that bureaucrats are motivated by maximization of their private utilities. The bureaucrat can therefore be modelled as aiming to maximize the size of his bureau in order to obtain the greatest non-pecuniary benefits. It is as a result of this behaviour that the size of government becomes excessive.


  1. Monopoly power: Through the goods it provides, the public sector can behave as a monopolist and extend its monopoly power into market capture. In a monopoly, a good is generally underprovided. However, unlike a monopolist, the objective of the government is not profit maximization. The government may use its monopoly power to oversupply its output. Market capture occurs because the level of goods supplied by the government isnt decided through the market process of demand and supply but exogenously sent by a specialist (eg. Doctor for a healthcare policy). These specialists would try to maximize their power by the expansion of their profession. At the same time they wouldn’t want to decrease their income by expanding too much. It is this balance that determines the level of public expenditure.


  1. Corruption: Consequence of government official using their power for personal gain. Distorts allocation of resources towards rent-seeking occupations. It has enormous efficiency costs. By discouraging entrepreneurs, it can stunt economic growth. Most common form of corruption is predatory regulation. In this process, the government intentionally created regulations that entrepreneurs have to pay bribes to get around. Some people agrue that bribery is a form of auction mechanism that directs resources to their best possible use. However, the following counter-arguments can be given. Firstly, allowing bribery affects the goodwill of the government. Secondly, honest government officials suffer due to bribery. Thirdly, it is impossible to optimize or manage bribery.


  1. Government Agency: The imperfect information of voters enables the government to grow larger by increasing the tax burden.


  1. Cost diffusion: The last explanation we present for the possibility of excessively large government is the common resource The idea is that spending authorities are dispersed while the treasury has the responsibility of collecting enough revenue to balance the overall budget. Each of the spending authorities has its own spending priorities, with little consideration for others’ priorities, that it can be better met by raiding the overall budget.






Include: taxation system in India, sources of revenue for the Indian government, committees on taxation


Commodity Taxation (Indirect tax)


Definition: Commodity taxes are levied on transactions involving the purchase of goods.

Such taxes generally cause distortion in consumer preferences. Eg. Window tax in England between 1696 and 1851.


Deadweight loss


Tax induced distortions are due to the substitution effect. DWL of the tax is the extent to which the reduction in welfare exceeds the revenue raised.



DWL = ½*t*dX, where dX is the changes in consumption due to the tax. Since this change cannot be a priori determined (for policy making), it is useful to reduce this equation to another form. We know,

Elasticity of demand E= (P/X)*(dX/dP)

From above, dX = E*(X/P)*dP

Hence, DWL = ½*E*(X/P)*t2, since the change in price dP = t.

Points to note: DWL is proportional to the square of the taxes. Hence, DWL will rise rapidly with increase in tax rate. Secondly, for a given tax change, the DWL will be larger the more elastic is demand for the commodity.


In this figure, a lump sum tax only shifts the equilibrium from a to b. A commodity tax on good 1, on the other hand, increases the price of good 1 relative to good 2. Hence, budget constraint becomes steeper. New equilibrium is at c, where the revenue raised by the lump-sum and commodity tax are equal. However, due to commodity tax, the optimal indifference curve gives a lower utility than U1. This difference between U1 and U2 is the DWL.


Income effect: shift from a to d.

Substitution effect: shift from d to c.


The substitution effect is responsible for DWL.


Optimal Taxation


The purpose of optimal tax analysis is to find the set of taxes that gives the highest level of welfare while raising the revenue required by the government. The set of taxes that do this are termed optimal.


Commodity taxes are second best compared to lump-sum taxes. However, the observability of transactions makes commodity taxes feasible whereas optimal lump-sum taxes are generally not.

The optimal commodity tax is determined at the highest point of the offer curve in the production set.


Production Efficiency


Diamond-Mirrlees Production Efficiency Lemma states that the optimal commodity tax system should not disrupt production efficiency. Production efficiency occurs when an economy is maximizing the output attainable from its given set of resources.

The Diamond-Mirrlees Production E‰ciency Lemma provides a persuasive argument for the nontaxation of intermediate goods and the nondi¤erentiation of input taxes among firms. These are results of immediate practical importance, since they provide a basic property that an optimal tax system must possess.


The result arises from the independence of the consumption side of the economy from the production side. The commodity tax should affect the consumption side but should not distort the production side. Hence, production efficiency must be maintained.


Tax Rules

Issue: How is the burden of tax allocated across different commodities?

Problem: To set the taxes on commodities to maximize social welfare subject to raising a required level of revenue.


  1. The inverse elasticity rule: This rule considers the question whether all goods should have same or differentiated tax rates. An assumption of independence of demand of different goods is made for deriving this rule. The rule states that the proportional rate of tax on a good should be inversely related to its price elasticity of demand. Further, the constant of proportionality is the same for all goods. This clearly implies that the necessities should be highly taxed.

Criticism: This rule provides an efficient way to tax commodities but not an equitable one. Lower income consumers will bear more tax burden than high-income consumers.


  1. Ramsey rule: In order to arrive at this rule, we relax the assumption that prices are independent and allow for substitution effects due to taxation. Compensated demand is the change in demand due to substitution with utility held constant. The rule says that the optimal tax system should be such that the compensated demand for each good is reduced in the same proportion relative to the before-tax position. The Ramsey rule can be looked at as a generalized version of the inverse elasticity rule. The unique feature of this rule is that it says that it is the distortion in terms of quantities, rather than prices, that should be minimized. Since it is the level of consumption that actually determines utility, what happens to quantities is primary.

Since the rule argues for same percentage change in quantity of each good, the goods that are inelastic will have to be taxed higher to achieve this reduction. Hence, this tax structure would lead to low-income consumers paying larger fraction of their incomes as taxes. Again, it reflects only efficiency not equity. The major reason why equity is neglected in this model is because it is based on a single consumer preference.


  1. Equity consideration: Through modelling and optimization, multiple consumers can be introduced in the model which will take care of equity considerations. It is found that in this model, the proportional reduction in the compensated demand for a good will be smaller if it is consumed primarily by the poor consumer. This is the natural reflection of equity considerations.




Two basic pieces of information are needed to calculate the tax rate:

Firstly, knowledge of the demand function of the consumer. Secondly, social marginal utilities of income.


Public Sector Pricing


There are close connections between the theory of commodity taxation and that of choosing optimal public sector prices. In the context of public sector pricing, the optimal prices.



Income Taxation (Direct Tax)


Major source of government revenue. Two views: first, discourages industries; second, effective way of redistribution.


Equity and Efficiency


Two major issues involved income taxation:

  1. Effect on supply of labour
  2. Determination of the optimal level of taxation


Taxation and labour supply


The effect can be discerned through the standard model of consumer choice.

Utility function

U = U(x,l)

X – consumption, l – labour supplied (inversely related), L – total time available



The effect of wage increase is shown in figure 15.2. There is a substitution effect (a to b) and an income effect (b to c)


If there is a tax threshold, people below a certain income level wouldn’t be required to pay tax. This will create a kink in the aggregate budget constraint as shown in the figure 15.3



There will be a bunch of consumers at the kink. In practice, income tax systems generally have a number of thresholds at which the marginal tax rate rises.


Optimal Income Taxation


Mirrlees’ model:

  1. There is an unequal distribution of income, so there are equity motivations for taxation.
  2. Income tax affects the labour supply decisions of the consumers so that it has efficiency consequences.
  3. Due to the above the income tax structure should be flexible enough so that no prior restrictions are placed on the optimal tax functions that may arise.


The income tax function is chosen to maximize social welfare subject to it raising enough revenue to meets the government’s requirements.


Due to the property of agent monotonicity, a high-skill consumer will never earn less income than low skill consumer. It arises because at the point where the indifference curve of the low-skill consumer is tangential to the consumption function (and so determines the optimal choice for that consumer), the indifference curve of the high-skill consumer is flatter and so cannot be at a tangency.


The first property of optimal taxation is that it should be less than 100 percent. Secondly, marginal tax rate should be non-negative. This however, does not mean that average rate of tax cannot be negative. The average rate of tax is negative whenever the consumption function is above the 45 degree line. Finally, the optimal tax rule must have zero marginal rate of taxation for the consumer with the highest skill. This leaves with us with an important conclusion that the optimal tax system cannot be a fully (marginal rate) progressive one.


Criticism: This result is different from the one observed in practice. The result is valid only for the highest skill consumer, and says nothing about the tax rate faced by the consumer with the second highest skill. It is possible that for them the optimal tax rate may be significantly different from zero. If this is the case, the observed tax systems may be wrong only at the very top and hence there wouldn’t be much difference from the optimal point.

The result also relies on the fact that the highest skill person and be identified and the system adjusted around his needs. Putting this into practice is an impossible task.


Two specializations

We will now consider special cases of the model to gain further insights.


  1. Quasi-Linearity

Here we consider a special form of the utility function. We assume that utility is quasi-linear with respect to labour income.

<This is some pseud shit!!>


  1. Rawlsian Taxation

Use the Rawlsian welfare function that is concerned with the utility of the worst off individual. The tax collected is entirely redistributed in the form of lump-sum grant. Consequently, the optimal income tax is simply which maximizes the lump-sum grant, or, equally, that which maximizes the revenue extracted from taxpayers.

<This is pseuder shit!>


Tax Mix: Separation Principle

The central question is whether there should be differential commodity taxation

in combination with a nonlinear income tax. There is a sense in which commodity

taxation can usefully supplement income taxation by reducing the distortion in

the labor-consumption choice induced by income tax. If we tax commodities that

are substitutes for work and subsidize those that are complements, we can encourage

people to work more and thus reduce the work-discouraging effect of the income





Government Debt


When a government spends more than it collects in taxes, it borrows from the private sector to finance the budget deficit. The accumulation of past borrowing is the government debt.


A tax cut stimulates consumer spending and reduces national saving. The reduction in saving raises the interest rate, which crowds out investment. As per Solow’s model, lower investment leads to a lower steady-state capital stock and a lower level of output.


The Ricardian View of Government Debt


The traditional view of government debt suggests that when the government cuts taxes and runs a budget-deficit, consumers respond to their higher after-tax income by spending more. However, according to the Ricardian view, consumers are forward looking and base their spending not only on their current income but also on their expected future income.

The forward-looking consumer understands that government borrowing today

means higher taxes in the future. A tax cut financed by government debt does

not reduce the tax burden; it merely reschedules it. It therefore should not encourage

the consumer to spend more.


The general principle is that government debt is equivalent to future taxes,

and if consumers are sufficiently forward-looking, future taxes are equivalent to

current taxes. Hence, financing the government by debt is equivalent to financing

it by taxes. This view is called Ricardian equivalence.

The implication of Ricardian equivalence is that a debt-financed tax cut

leaves consumption unaffected.






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