a) Explain why a state that provides a legal system and guarantees property rights might emerge out of anarchy with everyone’s approval. Use game theory to explore this issue.

b) Discuss the view that welfare benefits are an efficiency-enhancing insurance scheme that insures against income risks. Use relevant diagrams to illustrate your arguments.

Question 2:
Consider an economy consisting of the three citizens Rich, Middle, and Poor. Rich has a gross income of £ 13, Middle of £ 4, and Poor of £ 3. The three citizens vote on whether or not to build a new arts centre. The costs of the new arts centre are £ 6. The project, if approved, is financed through proportional taxes, with individual tax payments of Ti = tyi (i = Rich, Middle, Poor), where t and yi stand for the constant tax rate and the gross income of citizen i, respectively.

The willingness-to-pay of the citizens for this project is as follows: Rich is willing-to-pay £ 4.5; Middle £ 1.5; and Poor £ 0.5. Each citizen aims at maximising her individual net benefit (i.e., individual willingness-to-pay minus individual tax payment). The public budget has to be balanced.
a) Calculate the tax rate t that is necessary to finance the arts centre. Which citizen votes for the project, which citizen votes against the project? Is there a majority in favour of the project?
b) For given aggregate gross income, give an example of an income distribution so that the project will be rejected at the polls. (10 marks)

c) Assume now that the arts centre is financed through a lump-sum tax. Does the project gain a majority? (8 marks)

d) Does voting lead to efficient policies in part a) and part c). Explain the differences between the two cases. (10 marks)

e) Assume now that the citizens vote on their tax system. They can choose either a proportional tax scheme as in part a) or a lump-sum tax as in part c). The vote on the tax system takes place prior to the vote on the arts centre, and the citizens anticipate correctly the implication of the tax system for the ensuing vote on the arts centre. Which tax system gains a majority? Explain your conclusion. (10 marks)

Question 3:

a) Assume that the citizens vote directly on the level of provision of a public good. Further assume that all citizens receive the same marginal benefits from the public good, but that they differ in their income and thus in their tax payments. In this context, explain the median voter theorem, and characterise the voting outcome (Condorcet winner). Use a diagram to support your arguments. (22 marks)

b) Discuss the properties of public goods. Explain the condition for the efficient provision of a public good (Samuelson rule). Again, use a diagram to illustrate your arguments. (16 marks)

c) Discuss whether the voting outcome in part a) is efficient. More precisely, assume that the median income is smaller than the average income. Under these circumstances, does voting lead to overprovision or underprovision of the public good compared to the efficient level? Explain your conclusion. (12 marks)
Question 4: (50 marks)
The city of Plymouth can finance only one out of three public projects. The nine councillors of Plymouth vote on whether they should finance either a new football stadium (proposal F) or a new school building (proposal S) or a new theatre (proposal T). The preferences of the councillors are
C1: F > S > T C4: S > T > F C7: F > T > S
C2: F > S > T C5: T > F > S C8: F > T > S
C3: S > F > T C6: T > F > S C9: S > T > F

Assume that the councillors vote sincerely.
a) What voting outcome would follow from following voting rules?

(i) Condorcet rule (ii) plurality rule (iii) two-round elimination rule (iv) Borda rule
(16 marks)

b) Show that plurality voting does not ensure selection of the Condorcet winner. To this end, modify the preferences of the councillors such that proposal F is the Condorcet winner while either proposal S or T wins if the plurality rule is applied. (10 marks)
c) Show that the system of two-round-elimination voting does not ensure selection of the Condorcet winner. To this end, modify the preferences of the councillors such that proposal F is the Condorcet winner while either proposal S or T wins if the two-round elimination rule is applied. (12 marks)
d.) Show that Borda voting does not ensure selection of the Condorcet winner. To this end, modify the preferences of the councillors such that proposal F is the Condorcet winner while either proposal S or T wins if the Borda rule is applied. (12 marks)
**Remark: Clearly indicate in parts b) – d) which councillor’s, or councillors’, preferences are modified, how these preferences are modified, and how these changes affect the votes each proposal receives under the voting rules to be applied.
**Hint: Try to minimise the number of councillors whose preferences you modify.

 

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