ECON41115 Public Economics 2021
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ECON41115
Public Economics
2021
1. Consider an economy with three consumption goods and labour where a representative consumer has the indirect utility function
V(q1 , q2 , q3 , w, I) = U(..., xi ( q1 , q2 , q3 , w, I), ...),
where qi is the consumer price of good i, w is the wage rate (fixed and untaxed) and I is lump-sum income. As a simplification, assume producer prices are constant and equal to
unity: p1 =p2= p3=1. The commodity tax-rate of good i is ti, so that
qi = pi+ ti = 1+ ti, i=1,2,3.
Assume an exogenously fixed revenue requirement for the government.
a) Derive the Inverse Elasticity rule for optimal commodity taxation for the tax of good 1. (Hint: Make use of Roy's Identity ∂V/∂qk = -(∂V/∂I)xk = -αxk, and the assumption of zero cross price effects ∂xi /∂qk = 0, i≠k).
(40 marks)
b) Suppose the government is forced to tax good 2 and 3 at the same rates (uniform ad valorem taxes) so that ti/pi is the same for i=2,3. Since by assumption p2= p3=1, consumer prices and unit taxes are also the same across these two goods, implying that the consumer price of good 3 is a function of the tax of good 2 as follows
q3 = 1+ t2.
Derive the Inverse Elasticity rule for tax 2 (taking into account that the tax affects both consumer price 2 and consumer price 3).
(50marks)
c) Discuss how the rule you derived in b) compares to the rule in a).
(10 marks)
2. One of the important results of the Mirrlees (1971) model of optimal income taxation is the so called ‘no-distortion at the top’ result. Explain this result and discuss why this maximises social welfare. To what extent does the actual tax system in the UK conform to the Mirrlees result?
3. In the context of a two-period model, explore the zero capital-income tax theorem. To what extent are assumptions of a steady state and homogenous households crucial?
4. Compare mechanisms for solving externality problems, including corrective taxation and compensation to victims.
5. Discuss the role of income distribution in determining the level of taxation, when the decision on the tax is taken through a series of binary elections.
6. Consider a public-good economy with two households, each with a utility function of the following form:
U = x 
ln( G )
where xh is private consumption of household h={1,2}, G is public consumption, and ηh is a preference parameter. Total public consumption is the sum of the households' private provision: G = g1 + g2 . Each individual is facing the budget constraint xh + gh = ωh , where ωh is the endowment of individual h.
a) Solve for the First-Best level of the public good (the Pareto problem).
(45 marks)
b) Suppose household 2 has a stronger preference for the public good, i.e. η2 > η 1 . Solve for the Nash-equilibrium to the game where household make voluntary contributions to the public good.
(45 marks)
c) Compare the result in b) to that of a). To what extent are they different and what is the role of the wealth distribution (ω2 , ω 1)?
(10 marks)
2022-04-22