Income Taxation when Markets are Incomplete



100


M. Tirelli

accounted for in the definition of the state space (e.g., aggregate supply
shocks, financial crises, etc.). Secondly, our model does not endogenously
provide an explanation of why markets are incomplete. Extensions in this di-
rection, although potentially interesting, are beyond the scope of this paper.
Moreover, at this stage, our positive analysis of tax reform does not provide
any specific recipe for policy intervention. Yet, our results do indicate and
analyze interesting effects that income taxes may exhibit in incomplete mar-
ket economies. Finally, our analysis is local. We do not derive an optimal
fiscal policy rule: a mapping from the equilibrium set to the set of feasible
tax rates which a central government should optimally enforce. We instead
trace the direction of (robust) welfare-improving tax reforms.

Our work is organized as follows. In Section 2 we present the benchmark
economy, and give a notion of competitive equilibrium. In Section 3, we state
and discuss our main results (Theorem 1 and Corollary 1). There, we also
discuss and compare our notion of constrained optimality with the standard
ones used in the GEI literature; this is done by mean of a few examples, both
for a pure exchange and for a production economy. The proofs of our results
are in Section 4, which also includes other technical results such as the
(local) existence and regularity of equilibria (Theorem 2 and Corollary 2).

2. The model

2.1. The general framework

2.1.1. Private agents and commodities There are two dates indexed by 0
and 1. At date 1 there is a finite number
S of possible states of the world,
s = 1,... ,S, and S = {1,... ,S}. We also use the convention of labeling
date 0 as
s = 0. There is a single perishable good that can be used both for
consumption and investment at date 0, and for consumption at date 1. We
denote by
N = S + 1 the number of contingent goods in the economy.

There are H2 consumers, H = {1,... ,h,... ,H}. Every consumer
h is endowed with a vector (e0h,e1h) RN++ of contingent goods, where
e1h = e1h, ... ,eSh denotes date 1 endowments. For simplicity, we assume
that each individual consumption set coincides with the nonnegative orthant
of the commodity space,
RN+ , and we denote a typical element by (x0,x1).
The utility function
uh : RN+ → R represents the preference ordering of con-
sumer
h over his consumption set. Lastly, some rather strong, but standard,
assumptions on preferences and endowments are introduced.

Assumption 1. For every h in H:

(1) uh is twice continuously differentiable, and differentiably strictly in-
creasing (
Duh(x) ^ 0 x R+++)1 ;



More intriguing information

1. Eigentumsrechtliche Dezentralisierung und institutioneller Wettbewerb
2. The name is absent
3. The use of formal education in Denmark 1980-1992
4. DISCUSSION: POLICY CONSIDERATIONS OF EMERGING INFORMATION TECHNOLOGIES
5. The growing importance of risk in financial regulation
6. The name is absent
7. Developmental changes in the theta response system: a single sweep analysis
8. The name is absent
9. The Role of Immigration in Sustaining the Social Security System: A Political Economy Approach
10. Place of Work and Place of Residence: Informal Hiring Networks and Labor Market Outcomes
11. Industrial Cores and Peripheries in Brazil
12. Innovation and business performance - a provisional multi-regional analysis
13. The name is absent
14. Pupils’ attitudes towards art teaching in primary school: an evaluation tool
15. The name is absent
16. Human Resource Management Practices and Wage Dispersion in U.S. Establishments
17. The name is absent
18. Rural-Urban Economic Disparities among China’s Elderly
19. The name is absent
20. Imitation in location choice