Income Taxation when Markets are Incomplete



Income taxation when markets are incomplete

103


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

0to     ^ hhji ^ h,ʌʌ

ts + ts      θj Rs +    θj ys   = 0

hH        j J1       j J2

for all ts0,ts1 = ts 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 , ts1 is
controlled by the central government,
ts0 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 ts1 < 0 is imposed on the return Rsj 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,) Rjsθj (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 (θjh, 0)RS + Σj j2 j = O.

Let T R2S be the set of taxes, with typical element t = t0 ,t1 .
Hereafter, to ease the exposition, we denote by
tI 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 θh .
Further, since in our simple economy ownership implies control, we assume
no-short sales,
θjh0. The market price of a stock j in J2 is qj . When h
purchases θjh stocks in firm j, she pays qjθjh and participates in the firm’s



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