Income Taxation when Markets are Incomplete

Income taxation when markets are incomplete

(for any finite B). The asset market clearing condition, together with the
no-short sell conditions, imply that θ^r → |θ*| < ∞ is a subsequence
of (θ^r). Then, Assumption 2(2), and the spot market clearing conditions,
imply that individual demands have subsequences (x^r) → |x*| < ∞ such
that (2) holds. Since the utility function is twice continuously differentiable,
Du (x^r) → |Du (x*) | (for any finite A). This also implies that (λ^r) →
|λ*| < ∞, and thus (1) is satisfied. The last condition - together with the
fact that θ^r is bounded - implies that β^r also converges to a finite bounded
entity. Then, note that, by definition of T', (t^{1 r}) is always bounded. The
above facts imply that for every firm the Lagrange multiplier υ^r is such that
υ^r → |υ*| < ∞ and (4) holds. Moreover, the above facts, and (3) and (7)
respectively, also imply that there exist subsequences q^r → |q^*| < ∞, and
(t0^r) → 110| < ∞. This completes the proof. □

References

Balasko, Y., Cass, D. (1989): The structure of financial equilibrium with exogenous yields:
the case of incomplete markets. Econometrica 57, 135-162

Cass, D., Citanna, A. (1998): Pareto improving financial innovation in incomplete markets.
Economic Theory 11, 467-494

Citanna, A., Kajii, A., Villanacci, A. (1998): Constrained suboptimality in incomplete mar-
kets: a general approach and two applications. Economic Theory 11, 495-521

Citanna, A., Polemarchakis, H.M., Tirelli, M. (2001): The taxation of trades in assets. Work-
ing Paper No. 01-21. Department of Economics, Brown University, Providence, RI

De Marzo, P. (1988): An extension of the Modigliani-Miller theorem to stochastic economies
with incomplete markets and independent securities. Journal of Economic Theory 45,
353-369

Diamond, P.A. (1967): The role of a stock market in a general equilibrium model with
technological uncertainty. American Economic Review 57, 759-776

Diamond, P.A., Mirrlees, J.A. (1992): Optimal taxation of identical consumers when markets
are incomplete. In: Dasgupta, P. et al. (eds.): Economic analysis of markets and games:
essays in honor of Frank Hahn. MIT Press, Cambridge, MA, pp. 561-581

Dierker, E., Dierker, H., Grodal, B. (1999): Incomplete markets and the firm. Paper 9902.
Department of Economics, University of Vienna, Vienna

Drèze, J.H. (1987): Investmentunderprivateownership: optimality, equilibrium and stability.
In: Dreze, J.H.: Essays on economic decisions under uncertainty. Cambridge University
Press, Cambridge, pp. 261-297

Elul, R. (1995): Welfare effects of financial innovation in incomplete markets economies
with several consumption goods. Journal of Economic Theory 65, 43-78

Elul, R. (1999): Welfare-improving financial innovation with a single good. Economic Theory
13, 25-40

Feldstein, M. (1976): On the theory of tax reform. Journal of Public Economics 6, 77-104

<<   29   30   31   32   33   >>

More intriguing information