Journal of Development Economics 76 (2005) 175 – 208
www.elsevier.com/locate/econbase
Production risk and the functional distribution
of income in a developing economy:
tradeoffs and policy responses
Cecilia Garcı´a-Pen˜alosaa, Stephen J. Turnovskyb,*
aGREQAM and CNRS, France
bDepartment of Economics, University of Washington, PO Box 353330 Seattle, WA 98195 3330, United States
Received 1 May 2002; accepted 1 October 2003
Abstract
We develop a stochastic endogenous growth model to examine the relationship between the
volatility of growth and the factor distribution of income. Our framework incorporates two important
features of developing economies: the co-existence of a modern and a traditional sector and the fact
that the income generated in the traditional sector can escape taxation. The relationship between
volatility and factor distribution is complex, depending upon the source of risk and the elasticity of
substitution between capital and labor in the formal sector. The policy options available to the
government for counteracting changes in volatility are analyzed. The second best optimal tax
structure is also characterized.
D 2004 Elsevier B.V. All rights reserved.
JEL classification: E25; O17; O41
Keywords: Production risk; Factor distribution of income; Stochastic growth
1. Introduction
This paper addresses an important, but neglected, question, namely, the relationship
between the volatility of growth and the distribution of factor income. The importance of
* Corresponding author. Tel.: +1 206 685 8028; fax: +1 206 685 7477.
E-mail address: sturn@u.washington.edu (S.J. Turnovsky).
0304-3878/$ - see front matter D 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.jdeveco.2003.10.004

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this issue stems from the fact that who bears the cost of the volatility is likely to have
important consequences for the overall performance of the economy, particularly in a
developing economy where opportunities for insurance may be limited. The empirical
evidence on the relationship between volatility and the distribution of factor income is
sparse. Breen and Garcı´a-Pen˜alosa (2004) obtain a positive relationship between a
country’s volatility (measured by the standard deviation of the rate of GDP growth) and
income inequality. To the extent that greater inequality is likely to be associated with a
higher share of income to capital, these findings suggest that more volatility will be
associated with a smaller share of income being earned by labor.
A simple regression equation shows that this is indeed the case. Using a sample of 83
developed and developing countries, we measure volatility by the standard deviation of the
annual growth rate of per capita GDP over the period 1960–1990 and compute the average
labor share over the same period. Regressing labor share on volatility, we find that a 1
percentage point increase in volatility reduces labor share by 2.36 percentage points.1 This
is a sizable effect, with an increase of one standard deviation of volatility reducing the
labor share by a third of its standard deviation, and raises the question of how risk affects
the shares of output commanded by capital and labor.
In general, the distribution of factor income and growth volatility are endogenously
determined and thus need to be analyzed within an integrated intertemporal general
equilibrium framework. We employ an extension of the stochastic growth model
developed by Grinols and Turnovsky (1993, 1998), Smith (1996), Corsetti (1997) and
Turnovsky (2000). This is a one-sector growth model, in which aggregate equilibrium
output evolves in accordance with a stochastic AK technology. Previous studies have
been incapable of analyzing the impact of volatility on income distribution. This is
because either they abstract from labor (Grinols and Turnovsky, 1993, 1998, Smith,
1996) or alternatively, are based on a Cobb–Douglas production function (Corsetti,
1997, Turnovsky, 2000), in which case the factor distribution of income remains
fixed.
To allow volatility to influence distribution we need both endogenous employment
levels and a production structure that allows for non-constant factor shares. One of the
more striking facts when we examine the evidence on output volatility is that developing
economies are subject to much greater fluctuations in their growth rates than are industrial
countries. We therefore study a two-sector economy with a modern and a traditional sector,
in which agents allocate their labor between the two sectors and where the overall factor
shares depend, among other things, on the endogenous sizes of the two sectors. Adopting
this framework, the equilibrium growth rate, its volatility and the distribution of income
become jointly determined. The relationship between growth and its volatility has been
subject to both theoretical and empirical investigation. The simplest stochastic growth
model yields a negative tradeoff (as some of the more recent empirical evidence suggests)
1 The labor share is defined as compensation of employees paid by resident producers, divided by GDP, both
from the U.N. National Accounts. The data on volatility is from the Penn World Table. The sample contains 83
developed and developing economies for which both data where available. Regressing, LS, on volatility, S.D., we
find LS=57.54À2.36S.D., with a t-statistic for the coefficient on S.D. of À3.40, and R2=0.125. Regressing the
labor share in 1990 on volatility over the period 1960–1990 yields an even stronger negative relationship,
although the sample is smaller.

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C. Garcı´a-Pen˜alosa, S.J. Turnovsky / Journal of Development Economics 76 (2005) 175–208
177
if and only if the coefficient of relative risk aversion is less than unity, inconsistent with the
evidence. Other more complex models, involving portfolio adjustments, are capable of
generating a negative tradeoff under more plausible assumptions on preferences. The
implications for income distribution provide a further dimension to this relationship, and
indeed, the elasticity of substitution between the capital and labor is an important
determinant of the growth-volatility tradeoff.
Our analysis has two aspects. First, we derive the equilibrium balanced growth path.
The economy we consider has a modern sector, in which output is produced by a constant
elasticity of substitution (CES) production function, using both private capital and labor,
and a traditional sector in which individuals are self-employed and output is produced
using only labor. In both sectors, the aggregate capital stock provides an externality that is
consistent with an equilibrium of ongoing growth, as in Romer (1986).
The equilibrium we derive provides a framework for considering the options available
to the policy maker to offset the effects of volatility. In doing so, we make the crucial
assumption that the government cannot tax the traditional sector. Given our interest in the
effects of risk in a developing economy, this seems a natural assumption. In such
economies, the bulk of self-employment is found within what is often called the binformal
sectorQ, and estimates of the proportion of the male non-agricultural labor force in that
sector range between 15% and 90%, depending on the country.2 It is often argued that the
production structure of the economy and, in particular, the degree to which certain
activities are commercialized as opposed to black-market or subsistence-oriented is a
major determinant of the capacity of governments to raise tax revenue. To capture this
feature of developing economies, we simply assume that all traditional sector employment
is informal, taking place outside the formal labor market and consequently is non-taxable
by the government.
This policy constraint allows us to address two questions. First, it makes the tax on
labor income a tool that can be used to counteract the impact of increased volatility.
Because only one of the sectors is taxed, changing the wage tax affects the allocation of
labor across sectors and, consequently, partially offsets the impact of increased volatility
on employment. Second, the policy constraint allows us to consider the effect of
redistributing the tax burden from labor to capital on growth and welfare. This is an
important question. In many developing countries, interest income, if taxed at all, is taxed
at a rate below the labor income tax rate (see Tanzi and Zee, 2000). This not only implies a
regressive tax structure3 but may also be inefficient in a representative agent framework.
Moreover, as developing countries attempt to become fully integrated in the world
economy, they need both a higher tax level and a reduction of their reliance on foreign
trade taxation. This will require higher personal income tax rates and raises the question of
the form that this increase in taxation should take.
Formal analysis is intractable and the second phase of our analysis is to calibrate the
model to a developing economy. In this respect, the model is capable of replicating the
equilibria of a range of such economies with relative ease. In general, we find that the
2 See United Nations (2000) and Thomas (1992).
3 It is well documented that in many developing countries the tax structure is far from progressive. See
Jimenez (1986).

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relationship between volatility and factor shares is complex, depending upon both the
sectoral source of the productive risk and the elasticity of substitution in production. Two
main policy conclusions are obtained. First, attempting to stabilize aggregate volatility at
its original level following an increase in risk is infeasible requiring a wage tax well in
excess of 100%. The welfare loss can, however, be fully eliminated, and by a suitable
adjustment of the tax rates on both labor and capital income, it is possible to maintain both
factor shares and welfare at their original levels. Second, we find that the second best
optimal tax policy response is to set the wage tax below the capital income tax. In other
words, when the government is constrained in its capacity to tax all labor incomes, the
standard first best result that taxing labor is preferable to taxing capital income no longer
holds.4 Moreover, optimal policy exhibits a tradeoff between growth and welfare
maximization.
The literature on this topic is sparse. The study of distribution in developing
countries has been concerned mainly with examining Kuznets’ hypothesis that as an
economy grows, migration from agriculture to industry entails changes in the personal
distribution of income. Recent work on this dual-economy model has shown the
complexity of the relationship between development and inequality, but even when
unemployment is introduced the assumption of risk neutrality has meant that risk and
uncertainty has played no role.5 Our approach departs from this literature in various
>respects. First, our setup is not strictly a dual-economy model, as we do not
consider migration, but rather the way in which individuals (or households) divide
their time between two types of activities. Second, instead of examining how growth
affects inequality, we argue that both distribution and the growth rate are
endogenously determined by a number of factors, including the riskiness of the
economy.6 Lastly, we focus on the factor rather than the personal distribution of
income.
The paper closest to our work, at least in spirit, is Aghion et al. (1999), who find that
greater inequality is associated with more volatility. They show how combining capital
market imperfections with inequality in a two-sector model can generate endogenous
fluctuations in output and investment. In their model, it is unequal access to investment
opportunities and the gap between the returns to investment in the modern and the
traditional sectors that cause fluctuations. We reverse the focus, examining how exogenous
production uncertainty determines output volatility and distribution.
The remainder of the paper proceeds as follows. Section 2 sets out the components of
the model, while Section 3 summarizes the implied macroeconomic equilibrium. We then
provide some initial analytical results in Section 4. Section 5 undertakes the calibration,
4 See Stokey and Rebelo (1995) and the work they discuss for an analysis of the effects of shifting the tax
burden in an endogenous growth model.
5 See, e.g., Fields (1980), Bourguignon (1990), and Anand and Kanbur (1993), for analyses of the Kuznets
hypothesis where either inequality within sectors or relative prices change along the development path. Temple
(1999) examined the evolution of inequality as an economy grows in a dual-economy model with unemployment
in the modern sector.
6 Eicher and Garcı´a-Pen˜alosa (2001) also address the question of how growth and distribution are
simultaneously determined in developing economies, but the focus of that paper is innovation and the
accumulation of human capital.

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179
first computing the numerical impacts of increases in the exogenous risk on the key
economic variables and then computing the appropriate policy responses. The next section
considers second best optimal policy, obtaining the tax rates that maximize growth and
welfare. Section 7 concludes, while the technical solution to the problem—itself quite a
challenging exercise—is relegated to Appendix A.
2. Elements of the economy
This section describes the analytical framework and the behavior of the relevant agents.
In developing the model, we distinguish between quantities that pertain to and are chosen
by the representative agent and corresponding economywide average quantities, denoted
by bars, that the individual takes as given, but which in equilibrium are endogenously
determined.
2.1. Technology and returns
We assume that the representative agent supplies a unit of labor inelastically. A fraction,
1Àl, may be allocated to employment in a formal or modern sector, with the remainder, l,
being spent in an informally organized sector. Output in the formal sector is produced by
the CES production function:
 ÁÀq
ÃÀ1=q
dY ¼ B a ð1 À lÞ ¯
K
þ ð1 À aÞKÀq
ðdt þ duÞ
ð1aÞ
uZðdt þ duÞ
0bab1;
À 1bqbl
where K denotes the individual firm’s stock of capital, K
¯ is the average economywide
stock of capital, so that (1Àl)K
¯ measures individual labor in efficiency units. This is a
generalization of the stochastic Cobb–Douglas production function employed by
Corsetti (1997) and Turnovsky (2000), with the elasticity of substitution defined by
eu1/(1+q). The stochastic variable, du, is temporally independent and normally
distributed with mean zero and variance r 2
u dt
over the instant dt. This stochastic
production function exhibits constant returns to scale in the private decisions, the
fraction of time devoted to employment in the formal sector, and the private capital
stock. In addition, the average stock of capital yields an externality such that in
equilibrium, when K=K
¯ , the production function is linear in the accumulating stock of
capital, as in Romer (1986). Letting
À Á h À
Á
i
Àq
À1=q
X ¯l u a 1 À ¯l
þ ð1 À aÞ
Aggregate (average) output, dY¯, is thus represented by:
h À
Á
i
Àq
À1=q
À Á
d ¯
Y ¼ B a 1 À ¯l
þ ð1 À aÞ
¯
K ðdt þ duÞ
¯
uBX ¯l K ðdt þ duÞ
ð1bÞ

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Factor returns over the period (t,t+dt) are generated as follows. The wage rate (return
to labor) is described by the stochastic process
dA ¼ aðdt þ duÞ
ð2aÞ
where
À Á1þqÀ
ÁÀ 1ðþqÞ
À Á
a
¯
¯
uðBZ=Bð1 À lÞÞ
¼ BaX ¯l
1 À ¯l
K
K
l¼¯l;K¼ ¯
K
ud ¯l
Likewise, the private rate of return on capital, dRK, over the period (t,t+dt) is specified
by:
dRK ¼ rKðdt þ duÞ
ð2bÞ
where
h À
Á
i
Àq
À1þq
q
À Á1þq
rKuðBZ=BKÞ
¼ B 1
ð À aÞ a 1 À ¯l
þ ð1 À aÞ
ð
ÞX ¯l
l¼¯l;K¼ ¯
K
uB 1 À a
Eqs. (2a) and (2b) assume that the returns to capital and labor are represented by their
respective aggregate stochastic marginal physical products. Eqs. (2a) and (2b) imply
that the rate of return to capital is stationary, while over time, the wage rate grows with
the aggregate capital stock.7 The stochastic shock in the formal sector is reflected
proportionately in both factor returns.
Output in the informal sector depends upon labor in accordance with the production
function
dQ ¼ ql ¯
K ðdt þ dvÞ
ð3aÞ
where the aggregate capital stock serves as a proxy for knowledge that conditions the
productivity of individual labor. For simplicity, we assume that labor has constant
productivity, parameterized by q.8 The production function also includes the assumption
that unlike labor, individual capital cannot move between the two sectors. This is a
reasonable first approximation for a developing economy in which banks are unlikely to
lend to finance investment in the informal sector, as well as because the btypesQ or
bvintagesQ of capital are different. The stochastic disturbance in the informal sector, dv, is
temporally independent and normally distributed with mean zero and variance r 2
v dt over
the instant dt. The correlation between the two shocks is ruvdt. Aggregate output in the
informal sector is
d ¯
Q ¼ q¯l ¯
K ðdt þ dvÞ
ð3bÞ
In addition to holding capital, the agent may hold government bonds, b, the before-tax real
rate of return on which is postulated to be
dRBurBdt þ duB
ð4Þ
where rB and duB will be determined endogenously in macroeconomic equilibrium. The
bonds we shall consider have an endogenously determined variable price, P, but beyond
7 Together, Eqs. (2a) and (2b) imply (1Àl¯)dA+K¯dRK=BX(l¯)K¯(dt+du)=dY¯.
8 It is straightforward and changes little if we assume that labor interacts with a fixed factor land, T, say, in
accordance with the production function dQ=qlhT1ÀhK
¯ (dt+dv).

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C. Garcı´a-Pen˜alosa, S.J. Turnovsky / Journal of Development Economics 76 (2005) 175–208
181
that, their precise nature is unimportant. Equilibrium asset-pricing considerations will
determine rB and duB in terms of the real shocks, du, dv to the economy, with P adjusting
to support this equilibrium.
2.2. Consumer optimization
The representative consumer’s asset holdings are subject to the wealth constraint
W ¼ Pb þ K
ð5Þ
where W denotes real wealth. In addition, the agent is assumed to purchase output over the
instant dt at the non-stochastic rate C(t)dt out of income generated by these asset holdings.
His objective is to select his portfolio of assets and the rate of consumption to maximize
expected lifetime utility, taken to depend upon consumption, C(t), as represented by the
isoelastic utility function
Z l 1
E0
CceÀbtdt
À lbcb1
ð6Þ
0
c
subject to the wealth constraint, Eq. (5), and the stochastic wealth accumulation equation:
dW ¼ W ½nBdRB þ nKdRKŠ þ ð1 À lÞdA À Cdt À dT
ð7Þ
where nBuPb/W is the share of portfolio held in government bonds, nkuPb/W the share
of portfolio held in capital, and dT taxes paid.
The government is assumed to tax income from capital and labor generating the
aggregate flow of tax revenues
À
Á
À
Á À
Á
dT ¼ r ¯
V
¯
V
K K sK dt þ sK du
þ d 1 À ¯l K sW dt þ sWdu
ð8Þ
where we assume that only the formal sector is taxed. This specification allows for
different tax rates on capital and wage income, as well as on the deterministic and
stochastic components of each. Different values for sK, sV
K
and sW, sV
W reflect the
possibility that taxes might include offset provisions having the effect of reducing the
degree of after-tax randomness of real returns. Without loss of generality, interest income
is untaxed, the before-tax return adjusting to satisfy the equilibrium arbitrage conditions.
Substituting for ni into Eq. (5) and for Eqs. (2a), (2b), (4) and (8) into Eq. (7), the
stochastic optimization problem can be expressed as choosing the consumption–wealth
ratio, C/W, and the portfolio shares, ni to maximize expected intertemporal utility Eq. (6)
subject to
&
!
'
C
dW ¼
n
¯
BrB þ nK ð1 À sK ÞrK À
W þ ½ð1 À sW Þð1 À lÞd þ qlŠ¯nKW dt
W
þW dw
ð9aÞ
nB þ nK ¼ 1
ð9bÞ

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C. Garcı´a-Pen˜alosa, S.J. Turnovsky / Journal of Development Economics 76 (2005) 175–208
where, for convenience, we denote the stochastic component of dW/W by
À

Á
À
Á
¯ !
W
¯
W
dw
V
V
u
1 À sK nKrK þ 1 À sW dð1 À lÞ¯nK
du þ nBduB þ qlnK
dv
ð9cÞ
W
W
In performing the optimization, the agent takes the rates of return of the assets and the
relevant variances and covariances as given, although these will ultimately be determined
in equilibrium.
Through the equilibrium wage rate, the individual’s rate of wealth accumulation
depends upon aggregate wealth, which accumulates as follows:

 ¯ 
!
C
Â
À
Á
Ã
d ¯
W ¼ ¯
W ¯nBrB þ ¯nKð1 À sKÞrK À
þ ð1 À swÞd 1 À ¯l þ q¯l ¯nK
W
 ¯
W dt þ ¯
W d ¯
w
ð9aVÞ
À
Â
Á
À
Á À
ÁÃ
d ¯
w
V
V
u
1 À sK rK þ 1 À sW d 1 À ¯l ¯nKdu þ ¯nBduB þ ql ¯nKdv
ð9cVÞ
This renders the agent’s optimization a two-state variable problem, the two states being the
agent’s individual wealth, W, which is under his direct control, and the aggregate stock of
wealth, W
¯ , the evolution of which follows Eqs. (9aV) and (9cV), and which the individual
takes as exogenous. However, although from the individual’s point of view, there are two
state variables since all agents are identical, with aggregate and individual shocks being
identical and perfectly correlated, in the macroeconomic equilibrium, the two state
variables evolve proportionately [W
¯ =W]. Thus, along the equilibrium growth path, the
dynamic evolution of the economy can be represented by a single-state variable.9
2.3. Government policy
Government policy is restrictive, its sole purpose being to respond to changes in the
sectoral volatilities. For this purpose, it levies taxes and issues debt subject to its flow
budget constraint:
dðPbÞ ¼ ðPbÞdRB À dT
ð10Þ
It is straightforward to introduce stochastic government expenditure, which may or may
not be productive, as in Turnovsky (1999), but this is unnecessary for present purposes.
2.4. Goods market equilibrium
Finally, the flow of physical goods in the economy to consumption, investment and
government expenditure must satisfy the resource constraint
dY þ dQ ¼ dC þ dK
ð11Þ
9 As we will discuss in Section 3.1 and further in the Appendix A, the equilibrium is the continuous time
analogue to the brecursive competitive equilibriumQ concept defined by Stokey and Lucas (1989).

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C. Garcı´a-Pen˜alosa, S.J. Turnovsky / Journal of Development Economics 76 (2005) 175–208
183
which using Eqs. (1a) (1b), (11) and dC=C(t)dt implies that the equilibrium rate of capital
accumulation (rate of growth) in the economy is

!
dK
À Á
C
À Á
¼ BX ¯l þ q¯l À
dt þ BX ¯l du þ qldvuwdt þ dw:
ð12Þ
K
nKW
3. Macroeconomic equilibrium
The solution of the model is derived in the Appendix A. This is based on the
assumption that the equilibrium is a recurring one, in which risks and returns on assets are
unchanging through time. This implies that the agent chooses the same allocation of
portfolio wealth at each instant of time. Since all agents are identical, we drop the
distinction between individuals and the aggregate by dropping the bars. The equilibrium is
summarized by the stochastic growth path defined below.
3.1. Equilibrium growth path
Definitions of d, X, rK, /
d ¼ BaX1þq 1
ð À lÞÀð1þqÞ
ð13aÞ
X ¼ a
½ ð1 À lÞÀq þ ð1 À aÞŠÀ1q
ð13bÞ
rK ¼ Bð1 À aÞX1þq
ð13cÞ
/ ¼ rB 1
ð À nKÞ þ rKð1 À sKÞnK
ð13dÞ
Equilibrium labor allocation
À
Â
À
Á
À
À
Á
Ã
d 1 À s
V
V
W Þ À q ¼ ð1 À cÞ BXd 1 À sW r2 À
BX À dl 1 À s
qr
u
W
uv À q2lr2
v
ð13eÞ
Equilibrium portfolio allocation &
À
Á
rB ¼ rKð1 À sKÞ þ ð1 À cÞ r2 þ BXr2 þ qlr
w
u
uv

!'
ð13f Þ
n
À
Á
À
Á
Â
K
s V
V
V
K rK þ sWdð1 À lÞ
À rK 1 À sK
1 À nK
Consumer budget constraint
C
w ¼ / þ ð
½ 1 À swÞdð1 À lÞ þ qlŠnK À
ð13gÞ
W
Goods market equilibrium
 
C
1
w ¼ BX þ ql À
ð13hÞ
W
nK

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184
C. Garcı´a-Pen˜alosa, S.J. Turnovsky / Journal of Development Economics 76 (2005) 175–208
Equilibrium volatility
À
Á0:5
rw ¼ B2X2r2 þ 2BXqlr
ð13iÞ
u
uv þ q2l2r2
v
Equilibrium growth rate
/ À b
hc
À
Á
i
w ¼
À B2X2
À 1 À s V
W
1 À ð1 À aÞXp
½
ŠnK r2
1 À c
2
u
Â
À
Á À
Á
Ã
À BX c À n
V
V
K 2 À sW
þ 1 À sW ð1 À aÞXqnK qlruv

c 
þ nK À
q2l2r2
ð13jÞ
2
v
This system characterizes a recursive competitive equilibrium that holds along a
balanced growth path. In this respect, the solution procedure is the continuous time
analogue to the recursive competitive equilibrium concept defined by Stokey and Lucas
(1989) and others. It is well known that for the constant elasticity utility function and
stochastic labor income, it is, in general, impossible to derive an explicit closed-form
expression for the consumption function.10 Nevertheless, despite this, using the
equilibrium 13a) conditions (13b) conditions (13c) conditions (13d) conditions (13e)
conditions (13f) conditions (13g) conditions (13h) conditions (13i) conditions (13j), one
can determine an equilibrium relationship between consumption and wealth, one that
holds along the balanced growth path.
The equilibrium has the following recursive structure. The first four equations repeat
the definitions of the equilibrium output–capital ratio, the wage rate, the return to capital,
which are all functions of the labor allocation decision, l, and the average return on asset
income, l. The first critical equilibrium equation is the labor allocation condition (13e).
This asserts that labor is allocated such that the risk-adjusted after-tax returns to labor in
the two sectors are equal. Having thus determined l yields d, X, rK and, in turn, the
volatility of the growth rate, rw, along the equilibrium growth path. The consumer budget
constraint, goods market equilibrium, the equilibrium portfolio allocation condition and
the equilibrium growth condition then jointly determine nK, w, C/W, rB. Eq. (13f) further
reveals how the before-tax return on bonds adjusts to yield the equilibrium after-tax rate of
return so that the real growth equilibrium is independent of the tax rates on interest
income.
3.2. Initial prices and wealth effects
The equilibrium growth path (Eqs. (13a)–(13j)) describes a stable rational expectations
equilibrium. As in any such equilibrium, its attainment, or the shift from one equilibrium
to another resulting from a structural change, is brought about by an appropriate initial
jump in the price of bonds, P(0). To the extent that the representative agent holds bonds in
his equilibrium portfolio, these jumps impose initial capital gains or losses, thereby
10 See, e.g., Blanchard and Mankiw (1988).

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Document Outline

• Production risk and the functional distribution of income in a developing economy: tradeoffs and policy responses
  • Introduction
  • Elements of the economy
    • Technology and returns
    • Consumer optimization
    • Government policy
    • Goods market equilibrium
  • Macroeconomic equilibrium
    • Equilibrium growth path
    • Initial prices and wealth effects
    • Feasibility of equilibrium
    • Distributional measures
    • Welfare
  • Some analytical properties
    • Some policy implications
  • Calibration
    • Equilibrium
    • Effects of risk
    • Policy responses
  • Second best optimal policy responses
  • Conclusions
  • Acknowledgement
  • References

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