Journal of Public Economics 89 (2005) 1045 – 1074
www.elsevier.com/locate/econbase
Second-best optimal taxation of capital and labor
in a developing economy
Cecilia Garcı´a Pen˜alosaa, Stephen J. Turnovskyb,*
aCNRS and GREQAM, France
bDepartment of Economics, University of Washington, P.O. Box 353330, Seattle, WA, 98195-3330, United States
Received 2 February 2004; received in revised form 22 April 2004; accepted 7 June 2004
Available online 25 August 2004
Abstract
As commercial integration reduces the reliance on foreign trade taxation, raising tax revenue has
become a major concern for the governments of developing economies. This paper examines how
the tax burden in a developing economy should be distributed between capital income and labor
income. We study a two-sector model, where the traditional sector is binformalQ and consequently
cannot be taxed by the government. In this setup, we find that the optimal (second-best) tax structure
in order to raise a certain amount of revenue requires to tax capital income at least as much as labor
income, and possibly more.
D 2004 Elsevier B.V. All rights reserved.
JEL classification: E62; O17; O23
Keywords: Endogenous growth; Optimal taxation; Informal sector; Developing economies
1. Introduction
Raising tax revenue is an important concern for the governments of developing
economies. Not only are tax revenues small, but the structures of the tax systems differ
substantially from what we observe in industrial countries. For developing countries,
* Corresponding author. Tel.: +1 206 685 8028; fax: +1 206 685 7477.
E-mail address: sturn@u.washington.edu (S.J. Turnovsky).
0047-2727/$ - see front matter D 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.jpubeco.2004.06.002

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C. Garcı´a Pen˜alosa, S.J. Turnovsky / Journal of Public Economics 89 (2005) 1045–1074
indirect taxation is the main source of government revenue, representing in some cases up
to 80% of total tax receipts, while personal and corporate taxes never account for more
than 25%. By contrast, in OECD economies, personal and corporate income taxation
provide over 40% of tax revenues, while indirect taxation is only 27%; see Tanzi (1987)
and Messere and Owens (1989). As developing countries grow, they need to generate
larger tax revenues to finance the enhanced public services concomitant with a developed
economy. Since indirect taxes are already at a high level, comparable to that in industrial
countries, increasing tax revenue will require higher personal income tax rates, thus raising
the question of the form that this increase in taxation should take.1 This paper examines
how the tax burden in a developing economy should be distributed between capital income
and labor income.
An extensive literature on the optimal taxation of factor incomes in a dynamic setting
has evolved. The main message to emerge from this is that in the long run, capital income
should not be taxed, thus shifting the burden from factor income taxation toward labor; see
Chamley (1985, 1986), Judd (1985, 1999), and Lucas (1990). Indeed, in many developing
countries interest income, if taxed at all, is taxed at a rate below the tax rate on labor
income.2 The standard optimal taxation result would imply that this is an efficient tax
structure, although, being strongly regressive, it may not be desirable once equity
considerations are taken into account.3 In this paper we show that in contrast to the
conventional view, taxing labor income more heavily than capital income may also be
inefficient from a growth and welfare standpoint.
We study a two-sector economy with a modern and a traditional sector, in which agents
allocate their endowment of time and capital between the two sectors. Both sectors use
private capital and labor, with the modern sector having a more capital-intensive
technology. In addition, the aggregate capital stock provides an externality that is
consistent with an equilibrium of ongoing growth, as in Romer (1986). Consumers are
infinitely lived and identical in all respects except for their initial endowment of capital.
We derive a macroeconomic equilibrium in which the economy’s growth rate, the sectoral
allocation of resources and thus the relative size of the two sectors, and the distribution of
income, all become jointly determined.
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 activities are informal, and consequently non-taxable by the government.
Depending on the country, estimates of the proportion of the male non-agricultural labor
force that work in the informal sector range between 15% and 90%, and while the average
1 The importance of increasing direct taxation has been stressed by a number of studies on tax reform in
developing countries, such as Ahmad and Stern (1991). This is particularly important since not only do indirect
taxes account for a large fraction of total revenue, but also value added tax rates in developing countries are
already at a level comparable to those in industrial countries; see Tait (1988).
2 See Tanzi and Zee (2000).
3 Jiminez (1986) documents that in most developing countries, the tax system is highly regressive.

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C. Garcı´a Pen˜alosa, S.J. Turnovsky / Journal of Public Economics 89 (2005) 1045–1074
1047
for the OECD is 17%, it rises to 60% for less developed economies.4 These figures
indicate the importance of the black market economy in developing countries and hence of
the fiscal constraints that it imposes on their governments.
A number of authors, such as Todaro (1989), have emphasized the bbuffer functionQ of
the informal sector, which absorbs the hours of work that individuals choose not to spend
in the formal production sector. Hence, we model labor supply decisions not as a tradeoff
between work and leisure, but as the allocation of a fixed amount of time between formal
sector employment and an informal productive activity. Empirical evidence on the
elasticity of labor supply in developing countries is scarce due to the difficulty of having
data on formal plus informal hours of work. But once the amount of time the individual
devotes to informal/domestic production is taken into account in calculating total hours
worked, existing evidence seems to support the hypothesis of a total fixed labor supply,
see Skoufias (1996).
We assume that the only feasible fiscal instruments are proportional taxes on the capital
and labor incomes generated in the formal sector. We also assume that the government
fixes the amount of revenue that it wants to raise and obtain the (second-best) optimal tax
structures under two possible scenarios. First, we suppose that the government
redistributes the revenue raised from the capital-rich to the capital-poor, so that all
revenue is rebated to consumers in lump-sum transfers. Our results are striking. On the one
hand, we find that to maximize the growth rate, subject to the fixed revenue objective,
requires capital and labor incomes to be taxed at the same rate. To understand this result
note that both taxes are distortionary, as they shift capital and labor toward the informal
sector. In fact, they generate two types of distortions: they affect both the allocation of
factors across sectors and within sectors. Equalizing the tax rates eliminates the distortion
within sectors. The capital-labor ratio in the formal sector adjusts to offset exactly the tax
distortion, so that factor prices are those that would prevail in the absence of taxes, and
growth is maximized. On the other hand, under the sectoral capital intensity assumption
being made, maximizing welfare requires the capital income tax to exceed the tax on labor
income. In addition to the above growth effect, taxes also have a level effect on welfare
since too little capital and labor are employed in the formal sector, thus reducing the
aggregate level of output. Now consider any given tax rate,s. The distortion arising from
taxing capital income at rate s is equivalent to that of taxing labor income at the same rate.
However, since the formal sector is capital-intensive, the capital income tax raises more
revenue than does the labor income tax. It is therefore optimal to tax capital income more
heavily in order to raise a given amount.
As an alternative scenario, we consider the case in which the government purchases
some of the final good in order to provide the infrastructure required to operate the formal
sector technology. The idea that the use of a modern technology requires the provision of
public infrastructure—and consequently, the raising of taxes—has been suggested to
explain the existence of a large, low-productivity, informal sector in developing countries.5
4 See Thomas (1992), United Nations (2000), Irhig and Moe (2000).
5 See Dessy and Pallage (2003). See also Fortin et al. (1997) for alternative explanations of the existence of
an informal sector.

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We use a simple version of this setup to highlight the differences between the
previous case, in which public expenditure does not involve the purchase of
goods, and the case in which it does. Public provision of infrastructure changes
the aggregate budget constraint, and this has important implications. If the only
use of government revenue is the provision of infrastructure, then taxing both
capital and labor incomes at a rate equal to the infrastructure requirement equalizes
the (static) private and social rates of return. In this case, the level of output is
optimal, implying that both growth and welfare are maximized when the tax rates
on capital and labor income are the same and equal to the infrastructure
requirement. But if some of the revenue is used for transfers, the resulting
divergence between private and social rates of return would generate a level effect and
requires taxing capital income more heavily than labor income in order to maximize
welfare.
A number of recent works have examined the circumstances under which optimal
factor taxation may involve a non-zero tax rate on capital income. This literature has
focused on two issues. First, the desirability of taxing capital can stem from
suboptimal capital accumulation in a growing economy caused by a technological
externality associated with capital accumulation as in Turnovsky (1996), or by
excessive savings when agents are credit rationed, as in Chamley (2001). The second
reason is associated with restrictions on the taxation of factors. Correia (1996) shows
that when a production factor is non-optimally taxed, a positive or negative tax on
capital will be required, depending on whether the untaxed factors are complements or
substitutes to capital. Jones et al. (1997) find that the impossibility for the government
to tax human capital and workers’ time separately implies that the tax rates on both
capital and labor incomes should be positive. Turnovsky (2000a) examines a setup
with an elastic supply of labor and productive government expenditure. He shows that,
if all other fiscal instruments are optimally chosen, the tax rate on capital income
should be zero. But if government expenditures are not set optimally, then positive
capital income taxation may be required. Cremer et al. (2003) develop an overlapping-
generations model with altruistic individuals. Under the assumption that inherited
wealth cannot be taxed, it is optimal to tax or subsidize capital, in order to indirectly
affect inherited wealth. All these papers can be seen as examples of the argument in
Judd (1999) that it is the presence of constraints (for the government or the
individual) or suboptimal expenditure choices that makes capital income taxation
desirable. Hence, they are second-best results.
Our contribution to this literature is threefold. First, we explore an alternative
scenario in which capital income taxation is desirable, one that is particularly relevant
for developing countries, namely the impossibility to tax a sector rather than a factor.
Second, we illustrate that the use of tax revenue is crucial in determining the structure
of taxes. Most of the literature assumes that all revenue is rebated in lump-sum
transfers to consumers; see, for example, Chamley (2001). Our analysis shows that
optimal tax rates depend on whether it is consumers or the government that spend the
revenue, implying that the assumption of how the revenue is used is not innocuous.
Third, although previous work has found that a non-zero tax rate on capital income
may be desirable, in almost all cases the optimal rate remained well below that for

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C. Garcı´a Pen˜alosa, S.J. Turnovsky / Journal of Public Economics 89 (2005) 1045–1074
1049
labor income.6 Our analysis provides a rationale for taxing capital income at least as much
as, and possibly more heavily than, labor income.
The paper is structured as follows. Section 2 briefly sets out a basic one-sector model to
serve as a benchmark against which we may compare our results. Section 3 then describes
the two-sector economy, with the optimal tax structure being derived in Section 4. Section
5 supplements the analytical results with some numerical simulations, while Section 6
concludes, noting some caveats. Technical details are minimized throughout the text and
relegated to an Appendix.
2. The basic one-sector model
We begin by considering a conventional one-sector economy with a representative
agent who we assume supplies a unit of labor inelastically. We shall derive the first-best
and second-best optimal tax structures, which we will then compare to those of the two-
sector economy.
2.1. Technology and returns
There is a mass 1 of firms, indexed by j. A representative firm produces output
according to
À
Á
Yj ¼ F ALj; Kj ;
where Kj denotes the individual firm’s stock of capital, ALj are the efficiency units of labor
employed by the firm, and F(.) is assumed to have constant returns to capital and labor. All
firms are identical and hence in equilibrium they will all choose the same level of
employment and capital stock. That is, Kj=K and Lj=L for all j.
We further assume that there is an externality associated with the stock of capital, so
that the efficiency of labor depends on the average stock of capital in the economy, K. In
particular, A=K, such that aggregate output Y is linear in the stock of capital. That is,
Y ¼ FðLK; KÞuKf ðLÞ:
ð1VÞ
There is perfect competition in factor markets, so that wages and rates of return on capital
are determined by the usual marginal productivity conditions,
BF
BF
r ¼ B ¼ f ðLÞ À Lf VðLÞ
w ¼
¼ f VðLÞK:
ð2Þ
Kj
BLj
6 One exception is Fuest and Huber (2001), who using a static model, find that for some agents the optimal
marginal tax rate on capital income is higher than that on labor income. Another is Koskela and Scho¨b (2002)
who study optimal factor taxation in the presence of unemployment, resulting from union-firm bargaining when
capital is internationally mobile but labor is immobile. Assuming that the government in setting taxes behaves as a
Stackelberg leader toward the private sector, they also find that in the presence of unemployment capital should
generally be taxed at a higher rate than labor. To the extent that unemployment is important in developing
economies, these results are particularly relevant in the present context.

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Since the labor supply, L, is constant, the interest rate, r, and factor shares, sWuf V(L)L/
f(L) and sKu1Àf V(L)L/f(L), are all constant, while the wage rate grows at the same rate as
does capital.
2.2. Consumer optimization
The representative agent maximizes lifetime utility, taken to depend upon consumption,
C(t), as represented by the isoelastic utility function
Z l 1 CceÀqtdt Àlbcb1
ð3aÞ
0
c
subject to the flow budget constraint
˙
K ¼ rð1 À sKÞK þ wð1 À sWÞL À C;
ð3bÞ
where sK and sW are, respectively, the capital income and wage income taxes. The solution
to this problem yields the equilibrium growth rate, w, together with the consumption–
capital ratio cuC/K
ð1 À s Þð f ðLÞ À Lf VðLÞÞ À q
w ¼
K
ð4aÞ
1 À c
c ¼ f ðLÞ À w
ð4bÞ
Substituting Eqs. (4a) and (4b) into Eq. (3a), the welfare of the representative individual
along the equilibrium path can be expressed as
Z l 1
1
cc
W ¼
CceÀqtdt ¼
Kc;
ð5Þ
0
0
c
c q À cw
where qNcw by the transversality condition, and cW N0.7
2.3. First- and second-best optimal taxation
It is well known (see, for example, Romer, 1986) that because of the presence of the
externality associated with capital, the competitive economy will not yield the socially
optimal rate of growth. The socially optimal equilibrium takes into account the effect of the
capital externality on the productivity of labor, which leads to the equilibrium growth rate
f ðLÞ À q
w4 ¼
;
ð4aVÞ
1 À c
and the corresponding consumption–capital ratio still given by Eq. (4b). Comparing Eq.
(4aV) to Eq. (4a), we see that the socially optimal growth rate can be achieved in the
competitive economy by subsidizing the return to capital at the rate capital s*
K=ÀsW/
7 The transversality condition is limkKeÀqt ¼ 0, where k denotes the shadow value of capital.
tYl

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C. Garcı´a Pen˜alosa, S.J. Turnovsky / Journal of Public Economics 89 (2005) 1045–1074
1051
(1ÀsW). In the absence of any lump-sum taxation, the government’s tax choices are
restricted by its budget constraint s
*
WwL+sKrK=0. Substituting for sK and the factor
returns, w, r, this implies s *
W=1, so that the subsidy to capital must be financed by fully
taxing labor income.
Suppose now that at each point in time the policy maker wants to raise a fixed fraction
of output, h, as revenue using the capital income and labor income taxes only. We are not
concerned with how this revenue is spent. The government budget constraint is then
hY=sWwL+sKrK, which can be expressed as sWsW+sKsK=h. We can now determine the
second-best tax rates that would maximize the growth rate and welfare, given the target
government revenue, h. Differentiating the expression (4a) for w, and since L, and
therefore the return to capital, is constant, we obtain
Bw
f ðLÞsK
B
¼ À
sK
1 À c b0:
The growth rate is maximized by setting the lowest possible capital income tax, that is, by
setting the highest possible wage income tax. Since sW is bounded above, the optimal
policy is to set
h À s
ˆs
W
W ¼ 1
and
ˆsK ¼
;
ð6Þ
1 À sW
which implies
ˆ
f ðLÞð1 À hÞ À q
w ¼
:
1 À c
Note that sˆK can be positive or negative (i.e. a tax or a subsidy), depending on the size
of the required government revenue. However, even when capital income is subsidized,
the first-best growth rate cannot be obtained as long as hN0.
Consider now the welfare-maximizing tax policy. Differentiating Eq. (5), we can show
that
dW =dsK
s
ð
Þs
¼ À
W þ 1 À sW
K
f ðLÞ2ð1 À s Þ
:
c
W
W
cð1 À cÞðq À cwÞ
Welfare is then maximized when capital is subsidized at the first-best tax rate s*
K=ÀsW/
(1ÀsW). However, this implies a wage tax of sW=(sW+u)/sW, which exceeds 1 and
hence is infeasible. The second-best policy is then to set the wage tax as high as
possible, i.e., to chose sˆW and sˆK in accordance with Eq. (6). Such taxes will
simultaneously maximize growth and welfare. These results can be summarized in the
following proposition.
Proposition 1. (A) The first best optimum in the one-sector economy can be replicated by
subsidizing capital at the rate: ˆsK=ÀsW /(1ÀsW), financed by fully taxing labor income.
(B) Consider the second-best optimum, where the objective is to raise a fraction, h, of

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output from tax revenue. Fully taxing labor at the maximal rate ˆsW=1 and capital at the
rate ˆsK=(hÀsW)/(1ÀsW) will maximize both the growth rate and welfare.
The clear message from the one-sector model is that for both objectives, the tax burden
should be more heavily borne by the fixed factor, labor.
3. The two-sector economy
We now modify the basic model in two dimensions. First, we assume that agents are
heterogeneous and differ in their initial capital endowments, as in Bertola (1993). Second,
we seek to capture an important feature of developing economies, namely the fact that
much of the production takes place outside the formal sector, in a second sector, termed the
informal sector. The latter, being less organized, is characterized by a lower capital
intensity than is the formal sector. Also, being less structured, economic activities in the
informal sector are less transparent to the government and thus can avoid all taxes.
We continue to maintain the assumption that aggregate labor is fixed, abstracting from
the labor-leisure choice. While this assumption has the advantage of analytical
convenience, it is not implausible for a developing economy. Given the low levels of
consumption in such countries, it is unlikely that much leisure is consumed. Rather, what
happens is that flexibility regarding hours of employment leads to variations in the labor
supplied to the formal sector, with individuals then devoting the remaining time to informal
productive activities, in the way that we model it. But given the importance of this
assumption, in the concluding section, we briefly discuss the modifications to our results
when labor is supplied elastically, arguing how this basically reinforces our key findings.
3.1. Technology and returns
We shall denote the formal and informal sectors by 1 and 2, respectively. Output in each
sector is produced by capital and labor in accordance with the production functions
Y1 ¼ F½L1K; K1Š
ð7aÞ
Y2 ¼ G½L2K; K2Š
ð7bÞ
where K1 and K2 denote the capital stock of a representative firm in sector 1 and sector 2,
respectively; K=K1+K2 is the economy-wide stock of capital, and L1K, L2K measure the
labor supply in each sector in efficiency units. We normalize the stock of labor so that
L1+L2=1.
Both production functions are assumed to exhibit constant returns to scale in the private
factors, employment and the private capital stock. In addition, the aggregate stock of
capital yields an externality such that in equilibrium, the production functions are linear in
the accumulating stock of capital, as in Romer (1986). We further assume that the use of
the formal technology requires the provision of infrastructure. The amount of infra-
structure required is proportional to the level of output of that sector, so that in order for

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C. Garcı´a Pen˜alosa, S.J. Turnovsky / Journal of Public Economics 89 (2005) 1045–1074
1053
the economy to produce Y1 the government must spend an amount /Y1 on infrastructure,
with /b1.
The private returns to capital and labor are represented by their respective marginal
physical products. Letting k1uK1/K and k2uK2/K denote the shares of aggregate
capital employed in the formal and the informal sectors, respectively, and since


 


 
L1K
L1
L2K
L2
Y1 ¼K1F
; 1 uK1f
and
Y2 ¼ K2G
; 1 uK2g
K1
k1
K2
k2
we can write factor payments as
B
 
 
 
Y1
L1
L1
L1
BY1
L1
r1 ¼ B ¼ f
À
f V
;
w1 ¼
¼ Kf V
ð8aÞ
K1
k1
k1
k1
BL1
k1
B
 
 
 
Y2
L2
L2
L2
BY2
L2
r2 ¼ B ¼ g
À
gV
;
w2 ¼
¼ KgV
ð8bÞ
K2
k2
k2
k2
BL2
k2
3.2. Government policy
The government is assumed to tax income from capital and labor in the formal sector, at
rates sK and sW, respectively. There are two types of government expenditure. First, the
government must finance the infrastructure requirement of the formal sector, /Y1. Second,
the government is assumed to be concerned about the distribution of income. An amount T
is hence rebated as a lump-sum transfer to all agents, and the policy-maker fixes the
fraction of formal-sector output that is to be spent on transfers, so that T=hY1 where h is
given. The government budget constraint is then
sWw1L1 þ sKr1K1 ¼ ðh þ /ÞY1;
ð9Þ
and we will term h the btransfer rateQ and / the binfrastructure requirement.Q8
3.3. Consumer optimization
There is a mass 1 of infinitely lived agents in the economy. Consumers are indexed by i
and are identical in all respects except for their initial stock of capital, Ki0. Since the
economy grows, we will be interested in the share of individual i in the total stock of
capital, ki, defined as kiuKi/K, where K is the aggregate (or average) stock. Aggregating
P
over the individual capital stocks,
iki=1, that is, the distribution of relative capital
endowments has mean 1. In addition, we assume that the variability of the endowments
across agents is given by the standard deviation, rk and the range is k a [0, k¯].
All agents supply a unit of labor inelastically. A fraction, L1i, may be allocated to
employment in the formal sector, with the remainder, L2i, being spent in the informal
8 Other types of public spending that involve the purchase of goods by the government—e.g. if formal sector
production depended on the quality/quantity of infrastructure that the government provides, or if a public
consumption good entered the consumers’ utility function—yield equivalent results. Such formulations, however,
complicate the analysis as the optimal amount of government expenditure is to be endogenously determined.

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1054
C. Garcı´a Pen˜alosa, S.J. Turnovsky / Journal of Public Economics 89 (2005) 1045–1074
P
P
sector, such that L1 ¼
L
L
i
1i; L2 ¼
i
2i and L1i+L2i=1. Similarly, his total stock of
capital, Ki, is allocated between the two sectors. His objective is to select his portfolio of
assets, allocation of labor time, and the rate of consumption to maximize lifetime utility,
taken to depend upon consumption, Ci(t), and represented by an isoelastic utility function.
Formally, the problem is
Z l 1
max
CceÀqtdt;
with
À
i
lbcb1
ð10Þ
0
c
subject to
˙
K i ¼ r1ð1 À sKÞK1i þ w1ð1 À sWÞL1i þ r2K2i þ w2L2i þ T À Ci
ð11aÞ
L1i þ L2i ¼ 1
ð11bÞ
K1i þ K2i ¼ Ki
ð11cÞ
The first-order conditions are
CcÀ1 ¼ k
ð12aÞ
i
y
˙
2
k
¼ À
þ q
ð12bÞ
k
k
y1
w1ð1 À sWÞ ¼
¼ w
k
2
ð12cÞ
y2
r1ð1 À sKÞ ¼
¼ r
k
2
ð12dÞ
where k is the shadow value of capital, and t1, and t2 are the multipliers associated with
the labor and capital allocation constraints, respectively.
Combining Eqs. (8a) and (8b) with Eqs. (12c) and (12d), we obtain the static allocation
conditions for capital and labor,
 
 !
 
 
L
L
L
L
L
L
ð
1
1
1
2
2
2
1 À sKÞ f
À
f V
¼ g
À
gV
ð13aÞ
k1
k1
k1
k2
k2
k2
 
 
L
L
ð
1
2
1 À sWÞf V
¼ gV
ð13bÞ
k1
k2
The first-order conditions (12a) and (12b), together with (12d), imply the rate of growth of
consumption
˙
Ci
ð1 À s Þr ð
Þ À q
¼
K
1 L1=k1
ð14aÞ
Ci
1 À c
Observe that the only difference between agents, namely their initial stock of capital,
does not appear in this equation. Hence, all individuals choose the same consumption
growth rate. This has two implications. First, the aggregate rate of growth, w, is

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Document Outline

• Second-best optimal taxation of capital and labor in a developing economy
  • Introduction
  • The basic one-sector model
    • Technology and returns
    • Consumer optimization
    • First- and second-best optimal taxation
  • The two-sector economy
    • Technology and returns
    • Government policy
    • Consumer optimization
    • Macroeconomic equilibrium
    • The distribution of income
  • First- and second-best optimal taxation
    • The first-best optimum
    • Second-best taxation
      • Redistributive government expenditure
      • Infrastructure and the second-best optimum
    • Factor intensity reversal
  • Some numerical simulations
  • Concluding comments
  • Acknowledgements
    • Comparative static analysis
    • The first-best optimum
    • Redistributive government expenditure and second-best taxation
    • Infrastructure and second-best taxation
  • References

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