ECON41115 PUBLIC ECONOMICS 2020
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ECON41115
PUBLIC ECONOMICS
2020
1. Assume a representative consumer with indirect utility
V(q1, q2, ... , qn, w, I) = U(..., xi ( q1, q2, ... , qn, 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. Furthermore, producer prices: p1, p2, ... , pn are assumed to be fixed, and the commodity tax rate of good i is ti, so that
qi = pi+ ti, i=1,...,n.
Furthermore, good n as well as labour cannot be taxed:
qn = pn , i.e. tn, = 0
a) Assuming an exogenously fixed revenue requirement for the government, derive
the Inverse Elasticity rule for optimal commodity taxation. (Hint: Make use of
Roy's Identity ∂V/∂qk = -(∂V/∂I)xk = -αxk ).
b) Interpret the rule you obtained in a).
(70 marks)
(15 marks)
c) To what extent does the optimal tax structure in a) differ from a situation when all
n commodities can be taxed?
(15 marks)
2. Consider the Mirrlees (1971) model of optimal income taxation
a) Explain the ‘no-distortion at the top’ and ‘no-distortion at the bottom’ results.
(40 marks)
b) Why can the optimal tax schedule generate voluntary unemployment?
(25 marks)
c) What insight does the model give on the desirability of progressive tax schedules?
(35 marks)
3. A government announcing a future optimal capital-income tax of zero may change its mind when implementation is due. Discuss why. (100 marks)
4. If there are multiple firms causing pollution, to what extent can a uniform Pigou tax
solve the externality problem?
(100 marks)
5. Assume that there are three individuals, A, B, and C. Consider four (two-dimensional) policy proposals: a, b, c, and d. The preference orderings (>) are as follows:
Individual A: a > d > c > b
Individual B: b > d > c > a
Individual C: c > b > a > d
a) Show that there is no Condorcet winner. (40 marks)
b) Limit the number of proposals to be the set of ideal points (i.e. each individual's most preferred alternative). Show that there is a Condorcet winning proposal.
(40 marks)
c) Draw a graph in two-dimensional space that gives the preference ordering above.
(20 marks)
6. Consider a public-good economy with two households, each with a utility function of the following form: Uh = ln(x ) 
ln(G)h , where xh is private consumption of household h={1,2}, G is public consumption, and η 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) Assuming interior solutions for both households, solve for the Nash-equilibrium contribution levels. (55 marks)
b) Suppose household 2 is wealthier than household 1, i.e. ω2 > ω 1 . Solve for the threshold level of ω 1 at which household 1 contributes 0. What happens if the wealth level of household 1 is lower than this threshold level? (45 marks)
2022-04-22