8. Collective choice and public sector behaviour. (2016)Apunte Inglés
Notes about the behaviour of the public firms and how to choose collectively efficiently.
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8 . C O L L E C T I V E C H O I C E A N D P U B L I C S E C TO R
B E H AV I O U R
Collective consumption of private goods
For example education or health services. They are rival, so they are private goods, but and
consume collectively, and in the same amount.
∑Hh=1 Zh = Z Z1 = … = Zh = ZH => Zmine· H = Z MV1 (X1) = … = MVH (XH) = MC (X1 + … + XH) (Private) MV1 (Y) + … + MVH (Y) = MC (Y) => ∑MVh(Y) = MC (Y) (Public) K/N is the optimal. N/2 is inclusive in K/N? The optimal inclusivity will be the one that minimize the cost in the voting procedure. If unanimity is required, the cost of the voting procedure could be infinite. So, we have to decide what is the optimal inclusivity point.
We have to take into account the decision-making (CD-M) costs and the inefficiency costs (CI).
Buchan + Tullock (The Calculus of Consent) –> “Public Choice” –> an economic theory of politics.
min C (N) = CDM (N) + CI (N) K* => MCDM (K*) = - MCI (K*) Social choice “a (mathematical) economic theory of voting results.” Public choice (Buchanan + Tullock) “an economic theory of Politics.” Individuals are not political eunuchs.
Arrow’s theorem Individual preferences (U1, …, UH) => (constitution) => A social preference (W (U1, …, UH).
Social rationality: Completeness, reflexivity, transitivity.
Pareto principle: If everyone prefers a to b, society will also do it.
No dictatorship: Pref. of individual h (FF) are not automatically social pref.
IV. Unrestricted domain: Universality of preferences.
Independence of irrelevant alternative: If an alternative if not feasible now, it is irrelevant.
Arrow’s (im)possibility theorem There is no mechanism with which we can go from individual to social preferences without violating at least one of this conditions.
- Pareto efficiency: graphic.
- Majority voting: no transitivity (seen before) –> no social rationality.
(Private goods collectively consumed) => ∑ MVh (Zmine) = H· MC (Zmine) = 1/H ∑ MVh (Zmine) = MC (Zmine) Is N/2 optimal? - Social Welfare Function: Modifying just the social function, from strictly concave through concave, the social outcome will be completely difference. This violate the independence of irrelevant alternatives criteria.
- The market mechanism: Violates the independence of irrelevant alternatives (no explanation, too difficult).
So, there is no a perfect constitution who leads to a social preference. Buchanan and Tullock said early they don’t expect social rationality.
• Single-peakedness: Unidimensional issues.
Economic Theory of Bureaucracy A preliminary analysis. - Monopoly.
Relation between the - Non-for-profit.
bureau and the citizen.
- Limp-sum grant or appropiation.
- A reflection concerning basic microeconomics.
- Niskanen’s model.
- Migué + Bélanger’s model.
- Monopoly QM.
- Non-for-profit QN. (an NGO) - Public bureau QB.
(all-or-nothing demand) The level of output provided by the monopolist will be inefficiently low, and the level of output provided by the bureau will be inefficiently high.
Niskanen Max profits min costs π=R - C ownership=management - Competitive firm Q · p max π = pQ - C(Q) Ownership ≠ management - “Large firms” The manager have a small percentage of profits. If he increases the revenue, his value as manager will increase.
max U[R(Q)] “managerial theories of the firm” s.t. R(Q) - C(Q) = π(Q) ≥ πmin (Parliament being happy) Sending troops to Afghanistan.
B(Q) - C(Q) => B=budget max B(Q) s.t. B(Q) ≥ C(Q) (parliament being happy) B(Q) B’>0 B’’<0 At Qniskanen B(Qnisk)=C(Qnisk) Migué + Bélanger The bureaucrat doesn’t minimize costs, because he doesn’t have external competition pressure. The bureaucrat can increase the costs in an inefficient way (buying a Picasso for the office).
R(Q) = B(Q) - C(Q) =>managerial discretionary budget.
The bureaucrat can appropriate a part of the revenues, not directly but indirectly, buffing the costs.
To achieve this extra amount of money, you put the Qm-b of the 3rd figure, the one that maximize your utility level, in the first figure and you push your costs until the function equals the maximum amount society is willing to pay.
So, we continue to have allocative inefficiency (Qmb>Q*) but close to the efficient point, but now we have production inefficiency (Cnon-min(Qmb)>Cmin(Qmb).
So, Q* requires allocative efficiency and production efficiency.
(General) Second Best Theorem If one on the conditions for efficiency is not fulfilled, maybe is in my interest to create another distortion.