Income Taxation when Markets are Incomplete

Income taxation when markets are incomplete

Definition 1 (Fiscal budget balance). For every production plan y ∈ Y, and
portfolio θ ∈ R^J₊^H,

∑0t^o     ^ h^hji ^ /ɔh,ʌʌ

t_s + t_s      θ_j R_s +    θ_j y_s   = 0

h∈H        j ∈J1       j ∈J2

for all t_s⁰,t_s¹ = t_s ∈ T1_,s and all s ∈ S.

Our assumption defines the government budget constraint, imposing fis-
cal budget balance state-by-state. This implies that no centralized transfers
across time or states of the world are allowed. Moreover, in every state s ,
one tax variable is not a policy instrument; precisely, if, in state s , t_s¹ is
controlled by the central government, t_s⁰ is endogenously determined by
the fiscal budget constraint. The choice of policy instruments, between t⁰
and t ¹, is completely arbitrary, it may be different across states, and it does
not affect any of the latter results. Finally, two possible tax regimes can be
considered:

(i) one in which interest payments are tax-deductible at the rate t¹;

(ii) a system in which interest earnings are taxed, but interest payments are
not tax deductible.

In the first system, say, a tax rate t_s¹ < 0 is imposed on the return Rs^j θj from
holding a bond portfolio θj , in state s ; then, the net interest paid to the bond
holders by the bond issuer is (1 + t,) R^j_sθj (i.e., bond j interest payments
are tax deductible). This conforms to Definition 1. In a system of type (ii),
with no tax deductible interest payments, the fiscal budget constraint is
HS + ts¹( ∑∈ j, max (θj^h, 0)RS + Σj∈ j2 j = O.

Let T ⊂ R^2S be the set of taxes, with typical element t = t⁰ ,t¹ .
Hereafter, to ease the exposition, we denote by t^I the S-vector of policy
instruments, and by T ^I (⊂ T) its domain.

2.1.3. Spot and security markets There are N (= (S + 1)) spot markets in
the economy. Since the only good produced is perishable, consumers’ saving
can only take place through portfolio holdings (i.e., financial markets fully
specify the available saving technology).

Every consumer, h, holds an initial ownership share (or portfolio en-
dowment) θj ∈ [0, 1] such that ∑_hθj = 1 for all firms j in J2. At date
0, when financial markets open, h can trade for a final portfolio vector θ^h .
Further, since in our simple economy ownership implies control, we assume
no-short sales, θ_j^h ≥ 0. The market price of a stock j in J2 is q^j . When h
purchases θ_j^h stocks in firm j, she pays q^jθ_j^h and participates in the firm’s

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