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ECONG011 Public Microeconomics Ian Preston

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ECONG011 Public Microeconomics Ian Preston ECONG011 Public Microeconomics Ian Preston 1 Introduction 2 Individuals We consider as starting point a competitive economy without government. Suppose that there are m di®erent consumption goods n di®erent types of labour There are H individuals, h = 1;:::;H, who have endowments of goods !h and consume quantities qh each have an endowment of time, normalised to 1, from which they supply labour Lh Individual preferences are captured in utility functions uh(qh;Lh) 3 Firms There are K ¯rms, k = 1;:::;K, which undertake production plans which involve using labour lk to produce quantities of goods yk according to technological requirements, say Gk(yk; lk) · 0. 4 Trade To simplify, we assume that each ¯rm produces only one type of good each individual supplies only one type of labour Furthermore the only types of trade that occur are sales of labour from individuals to ¯rms and sales of goods from ¯rms to individuals In particular this avoids complications concerned with the tax treatment of trades in goods or labour between ¯rms and ¯rms or between individuals and individuals. 5 Prices We begin without any government. Suppose both ¯rms and consumers behave as price takers. Let the pretax price vector for goods be p0 the pretax wage vector be w 6 Competitive behaviour Firms maximise pro¯ts given technology max ¼k = p0kyk ¡ w0lk s:t:Gk(yk; lk) · 0: lk;yk Pro¯ts are then shared among individuals according to ownership shares ±hk Individuals choose goods demands and labour supplies to maximise utility given their budget X h h h 00 ¡ h h¢ k h h max u (q ;L ) s:t: p q ¡ ! ¡ ±hk¼ ¡ w L · 0: qh;Lh k If we assume constant returns to scale then pro¯ts are zero in equilibrium. 7 Competitive equilibrium A competitive equilibrium consists in prices and wages that lead to a feasible allocation of goods and labour X ¡ ¢ X qh ¡ !h ¡ yk · 0 h X Xk Lh ¡ lk ¸ 0: h k Existence of an equilibrium is guaranteed given convexity of preferences and technology. 8 Welfare theorems By the First Fundamental Theorem any such equilibrium is Pareto e±cient By the Second Fundamental Theorem, any Pareto e±cient allocation can be sustained in such an economy as a competitive equilibrium given an appropriate redistribution of endowments. These are standard results of earlier microeconomics courses. 9 Minimal role for government Trade between agents in a competitive economy needs the protection of a legal system de¯ning property rights and enforcing their recognition. This itself requires a form of government with expenses which need to be covered by the raising of public resources. The security o®ered by a functioning judicial system can be considered as a foundational example of a public good. 10 Public goods and externalities The incorporation into the model of the existence of other public goods raises further issues about the economic role of government. Public goods can be privately provided but there are strong economic reasons to think it may be more e±cient for government to act as provider. The existence of externalities associated with private goods raises related is- sues. 11 Equity The particular competitive outcome associated with a speci¯c initial distri- bution of endowments and abilities may well be considered unacceptably in- equitable compared to others that might follow from a redistribution of re- sources. Government may arise as the agent e®ecting such a redistribution through taxation and disbursement of public funds. To do so e®ectively the government needs to collect information The manner in which it implements taxation should not be such as to dis- courage individuals from revealing that information where it is needed. 12 Other roles for government The assumption of price-taking behaviour may be inappropriate and the ex- istence of monopoly power raises a case for government regulation. The assumption that the economy settles naturally into equilibrium may also be unwarranted and point towards a case for macroeconomic intervention. These are important issues concerned with the role of government but dealt with in other courses. 13 Social welfare, inequality and poverty 14 Social choice 15 Social choice Before proceeding to discussion of the design of schemes for taxation and public provision, we need to establish a criterion to judge the outcomes of gov- ernment intervention. Suppose then that the government has to choose a social state x drawn from a choice set X: These could be thought of as de¯ning points in an Edgeworth box in a purely competitive economy with private goods distinguished by things such as tax schedules levels of public provision of some good 16 Social choice relation Individuals have preferences %h; h = 1;:::;H over those states as captured in utility functions ¡ ¢ U = u1; u2; : : : ; uH What we want is to determine a social choice relation %¤ over X as a function of the individual utilities U. 17 Welfarism The view that only satisfaction of preferences matters to social evaluation is known as welfarism Often taken for granted in economic discussion but it is restrictive Rules out consideration of certain things sometimes considered important such as rights, duties, etc High rates of tax on alcohol may be motivated by moral disapproval of drinking Taxation of labour may be influenced by views on the virtue of work Certain libertarian perspectives take a view of property rights that makes them regard redistributive taxation as theft 18 Impossibility of a Paretian liberal Problems arise if preferences can have regard to activities of others As an example, we can take Sen's proof of the impossibility of a Paretian liberal. Suppose there are two individuals, a puritan P and a libertine L. There is a salacious novel and we consider social choice over three states the novel is read by noone x0 the novel is read by the puritan alone xP the novel is read by the libertine alone xL 19 Impossibility of a Paretian liberal: Preferences The puritan would rather noone read the novel but if anyone is going to read it then he would rather it were him than the libertine: x0 ÂP xP ÂP xL The libertine would least prefer that the book be unread but he also prefers that the puritan read it than that he himself does: xP ÂL xL ÂL x0 20 Impossibility of a Paretian liberal: Social choice ¤ By the (welfarist) Pareto principle xP Â xL since everyone shares that pref- erence. But this is inconsistent with the liberal view that it is a matter only for the individual concerned to choose whether or not to read the book if the alternative is that noone do so: ¤ ¤ xL Â x0 x0 Â xP since these views together generate a cycle in social preferences: ¤ ¤ ¤ x0 Â xP Â xL Â x0 21 Invariance The options for aggregation of individual preferences depends upon the infor- mation assumed to be contained in the individual utilities A convenient way of capturing this is by de¯ning classes of transformations under which the social choice relation is invariant We specify the information content of utilities by requiring ¡ ¡ ¢ ¡ ¢ ¢ ¡ ¢ %¤ Á1 U 1 ;Á2 U 2 ;:::;U H; X =%¤ U i;U 2;:::;U H; X for all Á1;Á2; ¢ ¢ ¢ 2 © where © is some class of transformations. 22 Ordinal comparability assumptions Ordinal Noncomparability, ONC: © contains all increasing Ái Individual preference orderings are known but no interpersonal com- parisons of preference intensity are permitted Corresponds to the assumption that we know no more than we can identify from individual choice behaviour Ordinal Level Comparability, OLC: © contains all common increasing Ái Restriction that transformations must be common means that we can say whether one individual is better o® or worse o® than another 23 Cardinal comparability assumptions Cardinal Noncomparability CNC: © contains all increasing Ái = ai + biU A±ne transformations are permitted but since parameters can be individual speci¯c this is not very di®erent from ONC Cardinal Unit Comparability CUC: © contains all Ái = ai + bU Cardinal Full Comparability CFC: © contains all increasing Ái = a + bU Cardinal Ratio Scale Comparability CRS: © contains all increasing Ái = bU Requiring common parameters in admissible a±ne transformations strengthens comparability 24 Arrow's Theorem Arrow's General Possibility Theorem shows that ONC severely restricts the possibility for social choice Arrow proved that no social choice relation can satisfy all of the following: ² Universal Domain ² Pareto Principle ² Independence of irrelevant alternatives ² Nondictatorship 25 Arrow's requirements I ² Universal Domain: The social choice relation should be complete and tran- sitive for any choice set X. ¤ ¤ For all xA; xB in any X, either xA % xB or xB % xA ¤ ¤ ¤ For all xA; xB; xC in any X, if xA % xB and xB % xC then xA % xC ² Pareto Principle: The social choice relation should respect unanimous pref- erence. ¤ xA % xB if xA %h xB for all h = 1;:::;H 26 Arrow's requirements II ² Independence of irrelevant alternatives: The restriction of the social choice relation to any pair of outcomes should be independent of the wider choice set X. ¤ ¤ If xA % xB when X = fxA; xBg then xA % xB whenever X ¶ fxA; xBg ² Nondictatorship: No one individual should decide the social choice relation. ¤ There is no h such that xA % xB if and only if xA %h xB 27 Interpreting Arrow Sen interprets the result as arising from "informational famine": Firstly, welfarism demands that you allow only utility information to enter into social choice decisions Secondly, assumptions are made so that that utility information is utterly impoverished 28 Outline of a proof The proof of the theorem can be loosely summarised as follows: ² Take two outcomes and suppose opinion di®ers between two groups which exhaust the population ² Social preference has to follow the opinion of one or other group ² Their opinion is decisive over this pair and over any choice where opinion is similarly split ² It cannot matter to their decisiveness that their opinion is opposed by the others ² Within the group there must be a decisive subgroup ² It is possible to keep dividing until you arrive at an eventual dictatorship.
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