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Knowledge goods, ordinary goods, and the effects of trade between leading and lagging regions
Research Policy 44 (2015) 1537–1542
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Knowledge goods, ordinary goods, and the effects of trade between leading and lagging regions Amitrajeet A. Batabyal a,∗ , Hamid Beladi b a b
Department of Economics, Rochester Institute of Technology, 92 Lomb Memorial Drive, Rochester, NY 14623-5604,USA Department of Economics, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX 78249-0631, USA
a r t i c l e
i n f o
Article history: Received 3 November 2014 Received in revised form 14 April 2015 Accepted 20 April 2015 Available online 19 June 2015 JEL classification: R11 R13 F12
a b s t r a c t We study the effects of trade in knowledge and ordinary goods on the income and welfare gap between a leading and a lagging region. Knowledge goods are invented and produced in the leading region only. In contrast, ordinary goods can be produced in both regions. Our analysis sheds light on four salient questions. First, we determine the equilibrium wage ratio between the leading and the lagging regions. Second, we show that increasing the rate at which the lagging region copies the technology for producing knowledge goods narrows the income and welfare gap between the leading and the lagging regions. Third, we find the steady state level of welfare in the leading region. Finally, we note that an increase in the rate at which the lagging region copies the technology for producing knowledge goods may make the leading region worse off. © 2015 Elsevier B.V. All rights reserved.
Keywords: Interregional trade Lagging region Leading region Technology Welfare
1. Introduction In a developed nation such as the United States, the economic performance of dynamic California is very different from the economic performance of the less dynamic Mississippi. Similarly, in a developing nation such as India, the economic performance of rapidly growing Gujarat is very different from the economic performance of slowly growing Mizoram. Since many more examples of this sort exist, economists and regional scientists now understand that regardless of whether one considers a developed or a developing nation, there are inequalities of various sorts between the regions that comprise the nation under consideration. This understanding has given rise to considerable interest in studying the attributes of so called leading and lagging regions. As noted in Batabyal and Nijkamp (2014a,b), leading regions are generally dynamic, frequently urban, they display relatively rapid rates of economic growth, and they are technologically more advanced. In contrast, lagging regions are typically less dynamic, they are often
∗ Corresponding author. Tel.: +1 5854752805. E-mail addresses: [email protected] (A.A. Batabyal), [email protected] (H. Beladi). http://dx.doi.org/10.1016/j.respol.2015.04.008 0048-7333/© 2015 Elsevier B.V. All rights reserved.
rural or peripheral, they display slow economic growth rates, and they are technologically stagnant.1 The fascinating subject of leading and lagging regions is actually part of a broader literature on spatial disparities.2 In this regard, the variability in regional economic performance has given rise to much theoretical and empirical research.3 This research has emphasized the causal mechanisms that are responsible for lingering inequality between regions and on the policy levers for dealing with the concomitant equity-efficiency tradeoffs. Clearly, differential access to technology and productivity differences are key factors in explaining and dealing with regional differences but the existence of such differences calls for a deeper analysis of the various factors such as initial conditions, the availability of public services, the mobility of human capital, and technological spillovers.
1 In this paper, we are thinking of both leading and lagging regions as geographic entities that are smaller than nations. However, it should be noted that the word “region” has not always been used in the sense just mentioned. The word “region” has been used to refer to nations and, occasionally, to geographic entities—such as the European Union and North America—that are larger than nations. 2 See Baumol (1986), Lucas (1988), Kochendorfer-Lucius and Pleskovic (2009), Alexiades (2013), and Batabyal and Nijkamp (2014a,b) for more on this literature. 3 See Armstrong and Taylor (2000), Fujita and Thisse (2002), and Nijkamp (2003) for additional details on this literature.
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Researchers now recognize that technology is a major determinant of economic growth within a region. In addition, in the context of trading regions, access to new technology is a key determinant of a region’s income and welfare. Given this recognition, in our paper, we pay particular attention to technological interactions and to goods trade in a spatial-economic system characterized by the existence of a leading and a lagging region. However, before we move to the specifics of our paper, let us briefly review the apposite literature. Ghosh and De (2000, p. 391) concentrate on the metric of income and point out that there are obvious disparities in incomes between the leading and the lagging states in India. Their empirical analysis suggests that these income disparities can be addressed by the government “undertaking large infrastructure projects in lagging regions”. Kalirajan (2004) also concentrates on India and notes that if one is to further economic growth and promote growth spillovers from the leading to the lagging states, then it is important to pay attention to the quality of human capital in the various states. Rahman and Hossain (2009) use annual data from 1977–2000 to analyze per capita income convergence across six regions in Bangladesh. Their empirical study shows that if the lagging regions are to advance, then infrastructural, technological, and financial support to the lagging regions will need to be intensified. Interregional trade between the lagging western and some of the leading regions of China is the focus of He and Duchin (2009). These researchers point out that the planned increase in transport infrastructure in the lagging western region will be cost effective, beneficial to the western region, and conserve overall energy at given levels of demand. Skoufias and Katayama (2011) first note that Brazil’s inequalities in welfare and poverty between and within regions can be explained by differences in household attributes and in the returns to these attributes. They then go on to show that the differences in the welfare gains from the above mentioned attributes largely explain the differences between the lagging Northeast region and the leading Southeast region. Finally, in two papers that are similar in orientation to our paper, Batabyal and Nijkamp (2014a,b) have analyzed models of the technology gap between stylized leading and lagging regions. The first paper studies the implications of the lagging region learning the technology of the leading region for economic growth in both the regions under study. Finally, the second paper analyzes the properties of the temporal gap with which the lagging region utilizes the technology available in the leading region. The various studies discussed thus far in this section have advanced aspects of our understanding of the working of leading and lagging regions in different parts of the world. Specifically, Batabyal and Nijkamp (2014a,b) have pointed to the importance of technology and human capital in enhancing the economic growth prospects of the lagging regions being studied. Even so, as best as we can tell, there are very few studies that have theoretically studied the effects of trade in knowledge and ordinary goods (on which more below in Section 2) on the income and welfare gap between a leading and a lagging region. The objective of our paper is to use a dynamic model to analyze the income and welfare effects of trade between a stylized leading and a lagging region. The remainder of this paper is organized as follows. Section 2 first delineates our theoretical model of a leading and a lagging region that is adapted from Krugman (1979) and Acemoglu (2009, pp. 674–678). Next, this section focuses on the case in which the number of knowledge and ordinary goods is given. Section 3 first studies the case in which the number of knowledge and ordinary goods is endogenously determined in the model and then determines the equilibrium wage ratio between the leading and the lagging regions. Section 4 shows that increasing the rate at which the lagging region copies the technology for producing knowledge goods narrows the income and welfare gap between
the leading and the lagging regions. Section 5 ascertains the steady state level of welfare in the leading region. Section 6 notes that an increase in the rate at which the lagging region copies the technology for producing knowledge goods may make the leading region worse off. Finally, Section 7 concludes and then discusses potential extensions of the research delineated in this paper. 2. The theoretical framework 2.1. Preliminaries Consider an aggregate economy made up of a leading and a lagging region. We index these two regions with the subscript i where i = L,F. The subscript L denotes the leading region and the subscript F denotes the lagging or following region. There is free trade between these two regions without any trade costs. The relevant households in the two regions have identical constant elasticity of substitution (CES) preferences which display a love for variety that is defined over a consumption index. At any time t, the consumption index for region i, i = L,F is given by
˛/˛−1
N(t)
Ci (t) =
ci (v, t)
˛−1/␣
dy
,
(1)
0
where ci (v,t) is the consumption of the yth good in region i at time t, N(t) is the total number of goods in the aggregate economy at time t that are traded freely, and ˛ > 1 is the elasticity of substitution between these different goods. There is a representative household in the leading and in the lagging regions with intertemporal preferences defined over the consumption index Ci (t) described in Eq. (1). The goods that may be traded between the leading and the lagging regions are of two possible types. Knowledge goods are first invented and then produced in the leading region exclusively. In contrast, ordinary goods are those that have been invented in the past and whose production technology has been copied by the lagging region. Therefore, ordinary goods can be produced in the leading and in the lagging regions. The basic factor of production (input) in each of the two regions at any time t is human capital Hi (t). One human capital unit produces one unit of any good to which this human capital unit’s region has access. This means that the various human capital units in the leading region have access to both knowledge and ordinary goods but the human capital units in the lagging region have access only to ordinary goods. Note that from a technological standpoint, the only difference between the two regions is that the human capital units in the leading region have access to a larger set of goods. In other words, the human capital units in the leading region have no productive advantage over human capital units in the lagging region. The fixed endowments of human capital in the leading and in the lagging regions are denoted by ˆH L and ˆH F and this available human capital is supplied inelastically in each of the two regions under study.4 In this setting, two kinds of equilibria are possible and, to use Acemoglu’s (2009, p. 675) terminology, these two are an equalization equilibrium and a specialization equilibrium. In the equalization equilibrium, the leading and the lagging regions both produce some ordinary goods. In particular, in this equilibrium,
4 Assumptions very similar to those we make in this paper have been made routinely by other researchers analyzing dynamic models of technology and trade. In other words, our assumptions are standard and they are not extremely restrictive. See chapter 19 in Acemoglu (2009)—a standard textbook—for a mode detailed corroboration of this claim. In particular, our assumption that the knowledge good is invented and produced only in the leading region is analogous to similar assumptions made by Krugman (1979) and Saggi (2004).
A.A. Batabyal, H. Beladi / Research Policy 44 (2015) 1537–1542
the prices of the knowledge and the ordinary goods are identical and incomes in the two regions are also the same. In contrast, in the specialization equilibrium, the leading (lagging) region produces knowledge (ordinary) goods exclusively. We now focus on a given number of knowledge and ordinary goods in our aggregate economy.
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inequality does not hold then a specialization equilibrium does not exist. We would then have an equalization equilibrium in which wages in the leading and the lagging regions are identical and the leading region produces both knowledge and ordinary goods. Let us now proceed to the case where the number of knowledge and ordinary goods in the two regions under study is endogenously determined.
2.2. Given number of knowledge and ordinary goods 3. Endogenous determination of goods and wages Suppose that the total number of goods in our two-region aggregate economy at any time t is N (t) = N k (t) + N o (t), where N k (t) (N o (t)) denotes the given number of knowledge (ordinary) goods. Note that both categories of goods are accessible in the leading region but only ordinary goods are accessible in the lagging region.5 Let us begin the analysis by supposing that our aggregate economy is in a specialization equilibrium. In such an equilibrium, the prices of all the knowledge and the ordinary goods are equal. Let these two sets of prices be denoted by pk (t) and po (t), respectively. In addition, let the return to human capital or the wage in the leading and the lagging regions be wL (t) and wF (t), respectively. To keep the subsequent mathematical analysis straightforward, we suppose that one human capital unit can produce one unit of a good and that the market for goods production is competitive. This means that, in equilibrium, we have k
o
p (t) = wL (t) and p (t) = wF (t) .
(2)
Also, note that as far as the two wages are concerned, we need the inequality wF (t) ≤ wL (t) to hold because if this inequality does not hold then the human capital in the leading region would prefer to produce ordinary goods. Put differently, in a specialization equilibrium, all ordinary goods are produced in the lagging region and the equilibrium wage in the lagging region is (weakly) lower than the corresponding wage in the leading region. Maximizing the utility of the representative household in the leading and the lagging regions—see Eq. (1)—gives us the ratio of the consumption of knowledge goods to ordinary goods. That ratio is c k (t) = c o (t)
pk (t) po (t)
−˛
.
(3)
In addition, because we are in a specialization equilibrium, all of the available human capital in the lagging (leading) region produces ordinary (knowledge) goods only. Mathematically, this means that consumption in the leading and the lagging regions is given by the following two ratios and c k (t) =
ˆH L Nk
(t)
and c o (t) =
ˆH F . N o (t)
(4)
Now combining Eqs. (2)–(4), we get a mathematical relationship between relative wages, the supply of human capital, and technology for our two regions. That relationship is
ˆF N k (t) H o ˆL N (t) H
1/˛ =
wL (t) . wF (t)
(5)
Because the ratio on the left-hand-side (LHS) of Eq. (5) contains variables that are either exogenous or constant, this ratio describes a unique relative wage between the leading and the lagging regions. Note that the specialization equilibrium that we have been discussing thus far exists if and only if wL (t) /wF (t) ≥ 1. If this
5 Consistent with the analysis in Batabyal and Nijkamp (2014b), the ratio N(t)/No (t) can be viewed as a measure of the technology gap between the leading and the lagging regions.
3.1. Endogenous number of knowledge and ordinary goods We begin by supposing that the process for producing new goods over time in the leading region is given by the following ordinary differential equation dN (t) = N˙ (t) = ˇN (t) , dt
(6)
where ˇ > 0 is an innovation parameter and the initial number of new goods N(0) > 0 is given. Goods created in the leading region can be copied by the lagging region. We suppose that this copying process can also be described by an ordinary differential equation given by dN o (t) = N˙ o (t) = N k (t) , dt
(7)
where > 0 is a parameter which describes the rate at which the lagging region copies the goods that are created in the leading region. Combining Eqs. (6) and (7) with the condition N(t) = Nk (t) + No (t) gives us the steady state ratio of knowledge to ordinary goods and that ratio is N k (t) ˇ = . N o (t)
(8)
Eq. (8) tells us that, inter alia, the ratio of knowledge to ordinary goods is high when the innovation rate ˇ in the leading region is high relative to the goods copying rate in the lagging region. 3.2. Equilibrium wage ratio Now combining Eqs. (5) and (8), we can express the equilibrium wage rate between the leading and the lagging regions as wL (t) = max wF (t)
ˆF ˇH H ˆL
1/˛ ,1
.
(9)
Two points about Eq. (9) are worth emphasizing. First, we see that when the maximum operator on the right-hand-side (RHS)
1/˛
picks 1 ˇ/ ˆH F /ˆH L as the equilibrium wage ratio, the equalization {specialization} equilibrium applies. Second, since the equilibrium wage ratio can be interpreted as a ratio of incomes between the leading and the lagging regions, we see that a high rate of innovation—high ˇ—in the leading region makes the leading region better off and the lagging region worse off in relative terms. In contrast, a high rate of copying—high —by the lagging region makes the lagging region better off and the leading region worse off, once again, in relative terms. The policy implications of our findings in the preceding paragraph are straightforward. In this regard, consider the leading region first. We have seen that increasing the rate of innovation ˇ in this region makes this region better off and the lagging region worse off. Therefore, to make this region relatively better off, policy makers ought to put in place policies that stimulate innovation. Examples of such policies include R&D subsidies, R&D tax credits, and other tax benefits such as the deductibility of research
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expenses. In contrast, to make the lagging region relatively better off, policy makers in this region ought to put in place policies that hasten the rate of copying in this region. Examples of policies that are likely to accomplish this objective include the subsidization of educational training and the provision of specialized equipment and services designed to reduce the cost of copying goods produced in the leading region. Note that for each of the two regions under study, the unilateral implementation of the above policy measures by either the leading or the lagging region can make the other region worse off. Our next task is to analyze the effect of increasing the rate at which the lagging region copies the goods produced by the leading region on the income and welfare gap between the leading and the lagging regions. While undertaking this exercise, we shall adapt some results in Peters and Simsek (2009, pp. 427–428) to our aggregate economy consisting of a leading and a lagging region.
region has no impact whatsoever on either relative wages or on relative prices and therefore there is no impact on human capital in the leading region. Given this state of affairs, we now disregard this uninteresting case and focus on the steady state equilibrium that is of the specialization sort. Some thought tells us that in the specialization equilibrium in our model, the number of knowledge and ordinary goods is given by N k (t) =
When the copying rate ␥ in the lagging region increases, from Eq. (9) it follows that the equilibrium wage ratio wL (t) /wF (t) decreases. Because there are no costs to trading goods between the leading and the lagging regions, we can think of the ratio wL (t) /wF (t) as a measure of income and welfare in our model. This means that an increase in results in a narrowing of the relative income and welfare gap between the leading and the lagging regions. An implication of this finding is that a policy maker in the lagging region who would like to reduce the income and welfare gap between the two regions under study ought to institute the kinds of policies suggested in the penultimate paragraph in Section 3.2. However, since the institution of such policies will tend to have an adverse impact on the leading region, it would be desirable for policy makers in both the regions under study to coordinate their innovation and copying policies so as to increase the welfare of the aggregate economy under consideration. Intuitively, when increases, there is an increase in the demand for human capital in the lagging region since more goods are now copied and then produced in this region. Because the supply of human capital in the lagging region is fixed, from Eqs. (3) and (4), it follows that each good produced in the lagging region is now produced at a lower scale and a higher relative price in our aggregate economy. This leads to an increase in the relative wage of human capital—see Eq. (2)—in the lagging region. What is the effect of an increase in the copying rate on income and welfare in the leading region? To answer this question, we will need to derive an expression for the steady state level of welfare in the leading region and it is to this task that we now turn. 5. Welfare in the leading region Before deriving the pertinent expression, let us first discuss the underlying issues intuitively. When the copying rate increases, there are two effects to contend with in the leading region. The first (positive) effect is that more goods are now copied by the lagging region and this reduces the price of these goods and hence increases the purchasing power of human capital in the leading region. The second (negative) effect is that the relative wage ratio in the leading region declines and this reduces income and welfare in the leading region. To see which of these two effects dominates, let us compute the steady state welfare of a human capital unit in the leading region, assuming a given total number of goods N(t). If the steady state equilibrium is of the equalization sort then we know that wages in the leading and in the lagging regions will be the same. As such, increasing the goods copying rate in the lagging
(10)
Now, to state and solve the optimization problem of a human capital unit in the leading region, we use the methodology described in Acemoglu (2009, pp. 425–426). Adapting this methodology to our problem, the human capital unit in the leading region solves6
max[c(v,
4. An increase in the copying rate and the income and welfare gap
ˇ N (t) and N o (t) = N (t) . ˇ+ ˇ+
˛/(˛−1)
N(t)
c(v, t)(˛−1)/˛ dv
t)]∀v
,
(11)
0
subject to the constraint
N(t)
c (v, t) p (v, t) dv ≤ wL (t) .
(12)
0
With the help of the so called Dixit–Stiglitz aggregator, we can write the optimal value of the above problem as wL (t)/I where I is the ideal price index that is given by reformulating Eq. 12.11 in Acemoglu (2009, p. 423). This reformulation gives I=
N(t) 0
p(v, t)1−˛ dv
1/(1−˛)
. We are now in a position to explic-
itly answer whether an increase in the copying rate lowers or raises welfare in the leading region. 6. Change in welfare in the leading region We know that there exists a relationship between the prices of knowledge and ordinary goods and wages in the leading and the lagging regions. Specifically, we have wL (t) = pk (t) > po (t) = wF (t). Knowing this relationship, the optimal value wL (t)/I can be rewritten as
N(t) 0
wL (t) p(v, t)1−˛ dv
1/(1−˛)
⎡
⎤1/(1−˛)
=⎣ N (t)
ˇ ˇ+
−1
wL (t)1−˛
wL (t)1−˛ + ˇ +
−1
wF (t)1−˛
⎦
(13).
With the help of Eq. (5), the RHS of Eq. (13) can be further simplified. This simplification gives us
N(t) 0
wL (t)
1/(1−˛)
p(v, t)1−˛ dv
= N (t)1/(˛−1) ˇ ˇ+
−1
+ ˇ+
−1
ˇˆH F ˆH L
(˛−1)/˛ 1/(˛−1) . (14)
Inspecting the RHS of Eq. (14), it is clear that N(t)1/(˛−1) > 0. Therefore, to determine the impact of increasing the rate —at
6 In this and the following section, our focus is exclusively on the leading region. Hence, when there is no possibility of confusion, we shall drop the subscript i = L on some of the leading region variables.
A.A. Batabyal, H. Beladi / Research Policy 44 (2015) 1537–1542
which the lagging region copies the goods produced by the leading region—on income and welfare in the leading region, we differentiate the expression inside the box brackets [·]1/(˛−1) on the RHS of Eq. (14) with respect to the copying parameter . This gives us d ˇ [·]1/(˛−1) = −
2 + d ˇ+
ˇ/ + 1 − ˛
˛ ˇ+
2
1/␣
ˇˆH F ˆH L
.
Inspecting Eq. (15), it is clear that the change in the steady state level of welfare in the leading region depends on the sign of the term on the RHS of this equation. In particular, steady state welfare in the leading region decreases (increases) in response to an increase in the copying rate if and only if the expression on the RHS of Eq. (15) is negative (positive). Assuming that we are still in a specialization equilibrium and manipulating the RHS of Eq. (15), we see that a sufficient condition for an increase in to lower the steady state level of welfare in the leading region is that ˛ > 1+ˇ/. Interpreting the above sufficient condition, we see that the higher the substitutability between the various goods ˛, the lower the level of innovation in the leading region ˇ, and the higher the level of copying by the lagging region , the more likely it is that the sufficient condition will hold and the leading region will, in fact, be worse off when the copying rate in the lagging region increases. However, this is clearly not the only possibility. Inspecting the RHS of Eq. (15), we see that it is possible that an increase in the copying rate will actually make the leading region better off. Therefore, we conclude this discussion with two observations. First, an increase in the copying—or alternately, the technology adoption—rate definitely reduces the income and welfare gap between the leading and the lagging regions. Second, depending on the parameters of the model, this same increase in may or may not make the leading region worse off. The discussion in the preceding paragraph gives rise to two salient policy implications. First, speaking in terms of elasticity and parameter magnitudes, we have just seen that the combination of a high ˛, low ˇ, and high is likely to make the leading region worse off. In contrast, the combination of a low ˛, high ˇ, and low is likely to make the leading region better off. A policy maker in the leading region is unlikely to have any control over either the elasticity of substitution ˛ or the lagging region copying parameter . Therefore, consistent with the policy implications discussed in the penultimate paragraph in Section 3.2, this policy maker can make the leading region better off by putting in place innovation inducing policies such as R&D subsidies, R&D tax credits, and other tax benefits such as the deductibility of research expenses. Second, the model we have been analyzing thus far describes an aggregate economy consisting of two regions where the two regions are geographic entities that are smaller than nations.7 However, intellectual property rights are typically assigned at the level of nations. With this caveat in mind, note that we can think of 1/ as a measure of the protection of intellectual property rights in our aggregate economy. With this interpretation, our analysis thus far tells us that circumstances exist where weakening intellectual property rights protection in our aggregate economy, i.e., raising and hence lowering 1/ makes the lagging region better off and also narrows the income and welfare gap between the leading and the lagging regions. This result highlights the contrasting incentives facing policy makers in the two regions. Policy makers in the leading (lagging) region will favor strong (weak) intellectual property rights protection. This result is consistent with our statement in the first paragraph in Section 4 that it would be best for policy mak-
Also see footnote 1.
ers in the two regions under study to coordinate their innovation and copying policies. This completes our discussion of knowledge goods, ordinary goods, and the effects of trade between leading and lagging regions.
˛−1/˛
(15)
7
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7. Conclusions Lall et al. (2009) have pointed out that in Brazil, there is a clear difference in the economic performance of the lagging northeast region relative to the leading southeast region. As noted in Section 1, economic disparities of this sort have also been documented in other parts of the world. Therefore, in this paper, we used a dynamic model to study the effects of trade in knowledge and ordinary goods on the income and welfare gap between a leading and a lagging region. Knowledge goods were invented and produced exclusively in the leading region. In contrast, ordinary goods were invented in the past and their production technology was copied by the lagging region. Therefore, ordinary goods could be produced in both regions. Our analysis shed light on five significant questions. First, we determined the equilibrium wage ratio between the leading and the lagging regions. Second, we showed that increasing the rate at which the lagging region copied the technology for producing knowledge goods narrowed the income and welfare gap between the leading and the lagging regions. Third, we ascertained the stationary or steady state level of welfare in the leading region. Fourth, we demonstrated that an increase in the rate at which the lagging region copied the technology for producing knowledge goods could make the leading region worse off. Finally, a policy maker in the leading region could make this region better off by putting in place innovation stimulating policies such as R&D subsidies, R&D tax credits, and other tax benefits such as the deductibility of research expenses. Similarly, we showed that a policy maker in the lagging region would want to, for instance, institute policies that reduced the cost of copying goods and thereby expedited the copying rate in this region. The analysis in this paper can be extended in a number of different directions. In what follows, we suggest two possible extensions. First, it would be interesting to model the interaction between a leading and a lagging region as a dynamic game in which the control variables in the two regions are the innovation rate ˇ in the leading region and the copying rate in the lagging region. Second, it would be useful to endogenize the innovation decision in the leading region and then study the equilibrium rate of technological change and the economic growth rate in the aggregate economy consisting of a leading and a lagging region. Studies that incorporate these aspects of the problem into the analysis will increase our understanding of the nexuses between innovation, technology, copying, and the economic growth and development of leading and lagging regions. Acknowledgments We thank the Editor, two anonymous reviewers, and seminar participants in Monash University, Malaysia, for their helpful comments on a previous version of this paper. In addition, Batabyal acknowledges financial support from the Gosnell Endowment at RIT. The usual disclaimer applies. References Acemoglu, D., 2009. Introduction to Modern Economic Growth. Princeton University Press, Princeton, NJ. Alexiades, S., 2013. Club Convergence: Geography, Externalities, and Technology. Springer, Berlin, Germany. Armstrong, H.W., Taylor, J., 2000. Regional Economics and Policy. Blackwell, Oxford, UK.
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Batabyal, A.A., Nijkamp, P., 2014a. Technology, learning, and long run economic growth in leading and lagging regions. Econ. Polit. Weekly 49, 92–96. Batabyal, A.A., Nijkamp, P., 2014b. Some properties of the technology gap between leading and lagging regions. Theor. Econ. Lett. 4, 1–6. Baumol, W.J., 1986. Productivity growth, convergence, and welfare: what the long run data show. Am. Econ. Rev. 76, 1072–1085. Fujita, M., Thisse, J.-F., 2002. The Economics of Agglomeration. Cambridge University Press, Cambridge, UK. Ghosh, B., De, P., 2000. Linkage between infrastructure and income among Indian states: a tale of rising disparity since independence. Indian J. Appl. Econ. 8, 391–431. He, L., Duchin, F., 2009. Regional development in China: interregional transportation infrastructure and regional comparative advantage. Econ. Syst. Res. 21, 3–22. Kalirajan, K., 2004. Economic reform and the transmission of growth impulses across Indian states. Int. J. Soc. Econ. 31, 623–636. Kochendorfer-Lucius, G., Pleskovic, B. (Eds.), 2009. World Bank, Washington, DC.
Krugman, P.R., 1979. A model of innovation, technology transfer, and the world distribution of income. J. Polit. Econ. 87, 253–266. Lall, S.V., Timmins, C., Yu, S., 2009. Connecting lagging and leading regions: the role of labor mobility. In: Policy Research Working Paper 4843. World Bank, Washington, DC. Lucas, R.E., 1988. On the mechanics of economic development. J. Monetary Econ. 22, 3–42. Nijkamp, P., 2003. Entrepreneurship in a modern network economy. Reg. Stud. 37, 395–405. Peters, M., Simsek, A., 2009. Solutions Manual for Introduction to Modern Economic Growth. Princeton University Press, Princeton, NJ. Rahman, M.H., Hossain, M.S., 2009. Convergence in per capita income across regions in Bangladesh. Bangladesh Dev. Stud. 32, 45–60. Saggi, K., 2004. International Technology Transfer to Developing Countries. Commonwealth Secretariat, London, UK. Skoufias, E., Katayama, R.S., 2011. Sources of welfare disparities between and within regions of Brazil: evidence from the 2002–2003 household budget survey (POF). J. Econ. Geogr. 11, 897–918.
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Research Policy journal homepage: www.elsevier.com/locate/respol
Short communication
Knowledge goods, ordinary goods, and the effects of trade between leading and lagging regions Amitrajeet A. Batabyal a,∗ , Hamid Beladi b a b
Department of Economics, Rochester Institute of Technology, 92 Lomb Memorial Drive, Rochester, NY 14623-5604,USA Department of Economics, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX 78249-0631, USA
a r t i c l e
i n f o
Article history: Received 3 November 2014 Received in revised form 14 April 2015 Accepted 20 April 2015 Available online 19 June 2015 JEL classification: R11 R13 F12
a b s t r a c t We study the effects of trade in knowledge and ordinary goods on the income and welfare gap between a leading and a lagging region. Knowledge goods are invented and produced in the leading region only. In contrast, ordinary goods can be produced in both regions. Our analysis sheds light on four salient questions. First, we determine the equilibrium wage ratio between the leading and the lagging regions. Second, we show that increasing the rate at which the lagging region copies the technology for producing knowledge goods narrows the income and welfare gap between the leading and the lagging regions. Third, we find the steady state level of welfare in the leading region. Finally, we note that an increase in the rate at which the lagging region copies the technology for producing knowledge goods may make the leading region worse off. © 2015 Elsevier B.V. All rights reserved.
Keywords: Interregional trade Lagging region Leading region Technology Welfare
1. Introduction In a developed nation such as the United States, the economic performance of dynamic California is very different from the economic performance of the less dynamic Mississippi. Similarly, in a developing nation such as India, the economic performance of rapidly growing Gujarat is very different from the economic performance of slowly growing Mizoram. Since many more examples of this sort exist, economists and regional scientists now understand that regardless of whether one considers a developed or a developing nation, there are inequalities of various sorts between the regions that comprise the nation under consideration. This understanding has given rise to considerable interest in studying the attributes of so called leading and lagging regions. As noted in Batabyal and Nijkamp (2014a,b), leading regions are generally dynamic, frequently urban, they display relatively rapid rates of economic growth, and they are technologically more advanced. In contrast, lagging regions are typically less dynamic, they are often
∗ Corresponding author. Tel.: +1 5854752805. E-mail addresses: [email protected] (A.A. Batabyal), [email protected] (H. Beladi). http://dx.doi.org/10.1016/j.respol.2015.04.008 0048-7333/© 2015 Elsevier B.V. All rights reserved.
rural or peripheral, they display slow economic growth rates, and they are technologically stagnant.1 The fascinating subject of leading and lagging regions is actually part of a broader literature on spatial disparities.2 In this regard, the variability in regional economic performance has given rise to much theoretical and empirical research.3 This research has emphasized the causal mechanisms that are responsible for lingering inequality between regions and on the policy levers for dealing with the concomitant equity-efficiency tradeoffs. Clearly, differential access to technology and productivity differences are key factors in explaining and dealing with regional differences but the existence of such differences calls for a deeper analysis of the various factors such as initial conditions, the availability of public services, the mobility of human capital, and technological spillovers.
1 In this paper, we are thinking of both leading and lagging regions as geographic entities that are smaller than nations. However, it should be noted that the word “region” has not always been used in the sense just mentioned. The word “region” has been used to refer to nations and, occasionally, to geographic entities—such as the European Union and North America—that are larger than nations. 2 See Baumol (1986), Lucas (1988), Kochendorfer-Lucius and Pleskovic (2009), Alexiades (2013), and Batabyal and Nijkamp (2014a,b) for more on this literature. 3 See Armstrong and Taylor (2000), Fujita and Thisse (2002), and Nijkamp (2003) for additional details on this literature.
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Researchers now recognize that technology is a major determinant of economic growth within a region. In addition, in the context of trading regions, access to new technology is a key determinant of a region’s income and welfare. Given this recognition, in our paper, we pay particular attention to technological interactions and to goods trade in a spatial-economic system characterized by the existence of a leading and a lagging region. However, before we move to the specifics of our paper, let us briefly review the apposite literature. Ghosh and De (2000, p. 391) concentrate on the metric of income and point out that there are obvious disparities in incomes between the leading and the lagging states in India. Their empirical analysis suggests that these income disparities can be addressed by the government “undertaking large infrastructure projects in lagging regions”. Kalirajan (2004) also concentrates on India and notes that if one is to further economic growth and promote growth spillovers from the leading to the lagging states, then it is important to pay attention to the quality of human capital in the various states. Rahman and Hossain (2009) use annual data from 1977–2000 to analyze per capita income convergence across six regions in Bangladesh. Their empirical study shows that if the lagging regions are to advance, then infrastructural, technological, and financial support to the lagging regions will need to be intensified. Interregional trade between the lagging western and some of the leading regions of China is the focus of He and Duchin (2009). These researchers point out that the planned increase in transport infrastructure in the lagging western region will be cost effective, beneficial to the western region, and conserve overall energy at given levels of demand. Skoufias and Katayama (2011) first note that Brazil’s inequalities in welfare and poverty between and within regions can be explained by differences in household attributes and in the returns to these attributes. They then go on to show that the differences in the welfare gains from the above mentioned attributes largely explain the differences between the lagging Northeast region and the leading Southeast region. Finally, in two papers that are similar in orientation to our paper, Batabyal and Nijkamp (2014a,b) have analyzed models of the technology gap between stylized leading and lagging regions. The first paper studies the implications of the lagging region learning the technology of the leading region for economic growth in both the regions under study. Finally, the second paper analyzes the properties of the temporal gap with which the lagging region utilizes the technology available in the leading region. The various studies discussed thus far in this section have advanced aspects of our understanding of the working of leading and lagging regions in different parts of the world. Specifically, Batabyal and Nijkamp (2014a,b) have pointed to the importance of technology and human capital in enhancing the economic growth prospects of the lagging regions being studied. Even so, as best as we can tell, there are very few studies that have theoretically studied the effects of trade in knowledge and ordinary goods (on which more below in Section 2) on the income and welfare gap between a leading and a lagging region. The objective of our paper is to use a dynamic model to analyze the income and welfare effects of trade between a stylized leading and a lagging region. The remainder of this paper is organized as follows. Section 2 first delineates our theoretical model of a leading and a lagging region that is adapted from Krugman (1979) and Acemoglu (2009, pp. 674–678). Next, this section focuses on the case in which the number of knowledge and ordinary goods is given. Section 3 first studies the case in which the number of knowledge and ordinary goods is endogenously determined in the model and then determines the equilibrium wage ratio between the leading and the lagging regions. Section 4 shows that increasing the rate at which the lagging region copies the technology for producing knowledge goods narrows the income and welfare gap between
the leading and the lagging regions. Section 5 ascertains the steady state level of welfare in the leading region. Section 6 notes that an increase in the rate at which the lagging region copies the technology for producing knowledge goods may make the leading region worse off. Finally, Section 7 concludes and then discusses potential extensions of the research delineated in this paper. 2. The theoretical framework 2.1. Preliminaries Consider an aggregate economy made up of a leading and a lagging region. We index these two regions with the subscript i where i = L,F. The subscript L denotes the leading region and the subscript F denotes the lagging or following region. There is free trade between these two regions without any trade costs. The relevant households in the two regions have identical constant elasticity of substitution (CES) preferences which display a love for variety that is defined over a consumption index. At any time t, the consumption index for region i, i = L,F is given by
˛/˛−1
N(t)
Ci (t) =
ci (v, t)
˛−1/␣
dy
,
(1)
0
where ci (v,t) is the consumption of the yth good in region i at time t, N(t) is the total number of goods in the aggregate economy at time t that are traded freely, and ˛ > 1 is the elasticity of substitution between these different goods. There is a representative household in the leading and in the lagging regions with intertemporal preferences defined over the consumption index Ci (t) described in Eq. (1). The goods that may be traded between the leading and the lagging regions are of two possible types. Knowledge goods are first invented and then produced in the leading region exclusively. In contrast, ordinary goods are those that have been invented in the past and whose production technology has been copied by the lagging region. Therefore, ordinary goods can be produced in the leading and in the lagging regions. The basic factor of production (input) in each of the two regions at any time t is human capital Hi (t). One human capital unit produces one unit of any good to which this human capital unit’s region has access. This means that the various human capital units in the leading region have access to both knowledge and ordinary goods but the human capital units in the lagging region have access only to ordinary goods. Note that from a technological standpoint, the only difference between the two regions is that the human capital units in the leading region have access to a larger set of goods. In other words, the human capital units in the leading region have no productive advantage over human capital units in the lagging region. The fixed endowments of human capital in the leading and in the lagging regions are denoted by ˆH L and ˆH F and this available human capital is supplied inelastically in each of the two regions under study.4 In this setting, two kinds of equilibria are possible and, to use Acemoglu’s (2009, p. 675) terminology, these two are an equalization equilibrium and a specialization equilibrium. In the equalization equilibrium, the leading and the lagging regions both produce some ordinary goods. In particular, in this equilibrium,
4 Assumptions very similar to those we make in this paper have been made routinely by other researchers analyzing dynamic models of technology and trade. In other words, our assumptions are standard and they are not extremely restrictive. See chapter 19 in Acemoglu (2009)—a standard textbook—for a mode detailed corroboration of this claim. In particular, our assumption that the knowledge good is invented and produced only in the leading region is analogous to similar assumptions made by Krugman (1979) and Saggi (2004).
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the prices of the knowledge and the ordinary goods are identical and incomes in the two regions are also the same. In contrast, in the specialization equilibrium, the leading (lagging) region produces knowledge (ordinary) goods exclusively. We now focus on a given number of knowledge and ordinary goods in our aggregate economy.
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inequality does not hold then a specialization equilibrium does not exist. We would then have an equalization equilibrium in which wages in the leading and the lagging regions are identical and the leading region produces both knowledge and ordinary goods. Let us now proceed to the case where the number of knowledge and ordinary goods in the two regions under study is endogenously determined.
2.2. Given number of knowledge and ordinary goods 3. Endogenous determination of goods and wages Suppose that the total number of goods in our two-region aggregate economy at any time t is N (t) = N k (t) + N o (t), where N k (t) (N o (t)) denotes the given number of knowledge (ordinary) goods. Note that both categories of goods are accessible in the leading region but only ordinary goods are accessible in the lagging region.5 Let us begin the analysis by supposing that our aggregate economy is in a specialization equilibrium. In such an equilibrium, the prices of all the knowledge and the ordinary goods are equal. Let these two sets of prices be denoted by pk (t) and po (t), respectively. In addition, let the return to human capital or the wage in the leading and the lagging regions be wL (t) and wF (t), respectively. To keep the subsequent mathematical analysis straightforward, we suppose that one human capital unit can produce one unit of a good and that the market for goods production is competitive. This means that, in equilibrium, we have k
o
p (t) = wL (t) and p (t) = wF (t) .
(2)
Also, note that as far as the two wages are concerned, we need the inequality wF (t) ≤ wL (t) to hold because if this inequality does not hold then the human capital in the leading region would prefer to produce ordinary goods. Put differently, in a specialization equilibrium, all ordinary goods are produced in the lagging region and the equilibrium wage in the lagging region is (weakly) lower than the corresponding wage in the leading region. Maximizing the utility of the representative household in the leading and the lagging regions—see Eq. (1)—gives us the ratio of the consumption of knowledge goods to ordinary goods. That ratio is c k (t) = c o (t)
pk (t) po (t)
−˛
.
(3)
In addition, because we are in a specialization equilibrium, all of the available human capital in the lagging (leading) region produces ordinary (knowledge) goods only. Mathematically, this means that consumption in the leading and the lagging regions is given by the following two ratios and c k (t) =
ˆH L Nk
(t)
and c o (t) =
ˆH F . N o (t)
(4)
Now combining Eqs. (2)–(4), we get a mathematical relationship between relative wages, the supply of human capital, and technology for our two regions. That relationship is
ˆF N k (t) H o ˆL N (t) H
1/˛ =
wL (t) . wF (t)
(5)
Because the ratio on the left-hand-side (LHS) of Eq. (5) contains variables that are either exogenous or constant, this ratio describes a unique relative wage between the leading and the lagging regions. Note that the specialization equilibrium that we have been discussing thus far exists if and only if wL (t) /wF (t) ≥ 1. If this
5 Consistent with the analysis in Batabyal and Nijkamp (2014b), the ratio N(t)/No (t) can be viewed as a measure of the technology gap between the leading and the lagging regions.
3.1. Endogenous number of knowledge and ordinary goods We begin by supposing that the process for producing new goods over time in the leading region is given by the following ordinary differential equation dN (t) = N˙ (t) = ˇN (t) , dt
(6)
where ˇ > 0 is an innovation parameter and the initial number of new goods N(0) > 0 is given. Goods created in the leading region can be copied by the lagging region. We suppose that this copying process can also be described by an ordinary differential equation given by dN o (t) = N˙ o (t) = N k (t) , dt
(7)
where > 0 is a parameter which describes the rate at which the lagging region copies the goods that are created in the leading region. Combining Eqs. (6) and (7) with the condition N(t) = Nk (t) + No (t) gives us the steady state ratio of knowledge to ordinary goods and that ratio is N k (t) ˇ = . N o (t)
(8)
Eq. (8) tells us that, inter alia, the ratio of knowledge to ordinary goods is high when the innovation rate ˇ in the leading region is high relative to the goods copying rate in the lagging region. 3.2. Equilibrium wage ratio Now combining Eqs. (5) and (8), we can express the equilibrium wage rate between the leading and the lagging regions as wL (t) = max wF (t)
ˆF ˇH H ˆL
1/˛ ,1
.
(9)
Two points about Eq. (9) are worth emphasizing. First, we see that when the maximum operator on the right-hand-side (RHS)
1/˛
picks 1 ˇ/ ˆH F /ˆH L as the equilibrium wage ratio, the equalization {specialization} equilibrium applies. Second, since the equilibrium wage ratio can be interpreted as a ratio of incomes between the leading and the lagging regions, we see that a high rate of innovation—high ˇ—in the leading region makes the leading region better off and the lagging region worse off in relative terms. In contrast, a high rate of copying—high —by the lagging region makes the lagging region better off and the leading region worse off, once again, in relative terms. The policy implications of our findings in the preceding paragraph are straightforward. In this regard, consider the leading region first. We have seen that increasing the rate of innovation ˇ in this region makes this region better off and the lagging region worse off. Therefore, to make this region relatively better off, policy makers ought to put in place policies that stimulate innovation. Examples of such policies include R&D subsidies, R&D tax credits, and other tax benefits such as the deductibility of research
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expenses. In contrast, to make the lagging region relatively better off, policy makers in this region ought to put in place policies that hasten the rate of copying in this region. Examples of policies that are likely to accomplish this objective include the subsidization of educational training and the provision of specialized equipment and services designed to reduce the cost of copying goods produced in the leading region. Note that for each of the two regions under study, the unilateral implementation of the above policy measures by either the leading or the lagging region can make the other region worse off. Our next task is to analyze the effect of increasing the rate at which the lagging region copies the goods produced by the leading region on the income and welfare gap between the leading and the lagging regions. While undertaking this exercise, we shall adapt some results in Peters and Simsek (2009, pp. 427–428) to our aggregate economy consisting of a leading and a lagging region.
region has no impact whatsoever on either relative wages or on relative prices and therefore there is no impact on human capital in the leading region. Given this state of affairs, we now disregard this uninteresting case and focus on the steady state equilibrium that is of the specialization sort. Some thought tells us that in the specialization equilibrium in our model, the number of knowledge and ordinary goods is given by N k (t) =
When the copying rate ␥ in the lagging region increases, from Eq. (9) it follows that the equilibrium wage ratio wL (t) /wF (t) decreases. Because there are no costs to trading goods between the leading and the lagging regions, we can think of the ratio wL (t) /wF (t) as a measure of income and welfare in our model. This means that an increase in results in a narrowing of the relative income and welfare gap between the leading and the lagging regions. An implication of this finding is that a policy maker in the lagging region who would like to reduce the income and welfare gap between the two regions under study ought to institute the kinds of policies suggested in the penultimate paragraph in Section 3.2. However, since the institution of such policies will tend to have an adverse impact on the leading region, it would be desirable for policy makers in both the regions under study to coordinate their innovation and copying policies so as to increase the welfare of the aggregate economy under consideration. Intuitively, when increases, there is an increase in the demand for human capital in the lagging region since more goods are now copied and then produced in this region. Because the supply of human capital in the lagging region is fixed, from Eqs. (3) and (4), it follows that each good produced in the lagging region is now produced at a lower scale and a higher relative price in our aggregate economy. This leads to an increase in the relative wage of human capital—see Eq. (2)—in the lagging region. What is the effect of an increase in the copying rate on income and welfare in the leading region? To answer this question, we will need to derive an expression for the steady state level of welfare in the leading region and it is to this task that we now turn. 5. Welfare in the leading region Before deriving the pertinent expression, let us first discuss the underlying issues intuitively. When the copying rate increases, there are two effects to contend with in the leading region. The first (positive) effect is that more goods are now copied by the lagging region and this reduces the price of these goods and hence increases the purchasing power of human capital in the leading region. The second (negative) effect is that the relative wage ratio in the leading region declines and this reduces income and welfare in the leading region. To see which of these two effects dominates, let us compute the steady state welfare of a human capital unit in the leading region, assuming a given total number of goods N(t). If the steady state equilibrium is of the equalization sort then we know that wages in the leading and in the lagging regions will be the same. As such, increasing the goods copying rate in the lagging
(10)
Now, to state and solve the optimization problem of a human capital unit in the leading region, we use the methodology described in Acemoglu (2009, pp. 425–426). Adapting this methodology to our problem, the human capital unit in the leading region solves6
max[c(v,
4. An increase in the copying rate and the income and welfare gap
ˇ N (t) and N o (t) = N (t) . ˇ+ ˇ+
˛/(˛−1)
N(t)
c(v, t)(˛−1)/˛ dv
t)]∀v
,
(11)
0
subject to the constraint
N(t)
c (v, t) p (v, t) dv ≤ wL (t) .
(12)
0
With the help of the so called Dixit–Stiglitz aggregator, we can write the optimal value of the above problem as wL (t)/I where I is the ideal price index that is given by reformulating Eq. 12.11 in Acemoglu (2009, p. 423). This reformulation gives I=
N(t) 0
p(v, t)1−˛ dv
1/(1−˛)
. We are now in a position to explic-
itly answer whether an increase in the copying rate lowers or raises welfare in the leading region. 6. Change in welfare in the leading region We know that there exists a relationship between the prices of knowledge and ordinary goods and wages in the leading and the lagging regions. Specifically, we have wL (t) = pk (t) > po (t) = wF (t). Knowing this relationship, the optimal value wL (t)/I can be rewritten as
N(t) 0
wL (t) p(v, t)1−˛ dv
1/(1−˛)
⎡
⎤1/(1−˛)
=⎣ N (t)
ˇ ˇ+
−1
wL (t)1−˛
wL (t)1−˛ + ˇ +
−1
wF (t)1−˛
⎦
(13).
With the help of Eq. (5), the RHS of Eq. (13) can be further simplified. This simplification gives us
N(t) 0
wL (t)
1/(1−˛)
p(v, t)1−˛ dv
= N (t)1/(˛−1) ˇ ˇ+
−1
+ ˇ+
−1
ˇˆH F ˆH L
(˛−1)/˛ 1/(˛−1) . (14)
Inspecting the RHS of Eq. (14), it is clear that N(t)1/(˛−1) > 0. Therefore, to determine the impact of increasing the rate —at
6 In this and the following section, our focus is exclusively on the leading region. Hence, when there is no possibility of confusion, we shall drop the subscript i = L on some of the leading region variables.
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which the lagging region copies the goods produced by the leading region—on income and welfare in the leading region, we differentiate the expression inside the box brackets [·]1/(˛−1) on the RHS of Eq. (14) with respect to the copying parameter . This gives us d ˇ [·]1/(˛−1) = −
2 + d ˇ+
ˇ/ + 1 − ˛
˛ ˇ+
2
1/␣
ˇˆH F ˆH L
.
Inspecting Eq. (15), it is clear that the change in the steady state level of welfare in the leading region depends on the sign of the term on the RHS of this equation. In particular, steady state welfare in the leading region decreases (increases) in response to an increase in the copying rate if and only if the expression on the RHS of Eq. (15) is negative (positive). Assuming that we are still in a specialization equilibrium and manipulating the RHS of Eq. (15), we see that a sufficient condition for an increase in to lower the steady state level of welfare in the leading region is that ˛ > 1+ˇ/. Interpreting the above sufficient condition, we see that the higher the substitutability between the various goods ˛, the lower the level of innovation in the leading region ˇ, and the higher the level of copying by the lagging region , the more likely it is that the sufficient condition will hold and the leading region will, in fact, be worse off when the copying rate in the lagging region increases. However, this is clearly not the only possibility. Inspecting the RHS of Eq. (15), we see that it is possible that an increase in the copying rate will actually make the leading region better off. Therefore, we conclude this discussion with two observations. First, an increase in the copying—or alternately, the technology adoption—rate definitely reduces the income and welfare gap between the leading and the lagging regions. Second, depending on the parameters of the model, this same increase in may or may not make the leading region worse off. The discussion in the preceding paragraph gives rise to two salient policy implications. First, speaking in terms of elasticity and parameter magnitudes, we have just seen that the combination of a high ˛, low ˇ, and high is likely to make the leading region worse off. In contrast, the combination of a low ˛, high ˇ, and low is likely to make the leading region better off. A policy maker in the leading region is unlikely to have any control over either the elasticity of substitution ˛ or the lagging region copying parameter . Therefore, consistent with the policy implications discussed in the penultimate paragraph in Section 3.2, this policy maker can make the leading region better off by putting in place innovation inducing policies such as R&D subsidies, R&D tax credits, and other tax benefits such as the deductibility of research expenses. Second, the model we have been analyzing thus far describes an aggregate economy consisting of two regions where the two regions are geographic entities that are smaller than nations.7 However, intellectual property rights are typically assigned at the level of nations. With this caveat in mind, note that we can think of 1/ as a measure of the protection of intellectual property rights in our aggregate economy. With this interpretation, our analysis thus far tells us that circumstances exist where weakening intellectual property rights protection in our aggregate economy, i.e., raising and hence lowering 1/ makes the lagging region better off and also narrows the income and welfare gap between the leading and the lagging regions. This result highlights the contrasting incentives facing policy makers in the two regions. Policy makers in the leading (lagging) region will favor strong (weak) intellectual property rights protection. This result is consistent with our statement in the first paragraph in Section 4 that it would be best for policy mak-
Also see footnote 1.
ers in the two regions under study to coordinate their innovation and copying policies. This completes our discussion of knowledge goods, ordinary goods, and the effects of trade between leading and lagging regions.
˛−1/˛
(15)
7
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7. Conclusions Lall et al. (2009) have pointed out that in Brazil, there is a clear difference in the economic performance of the lagging northeast region relative to the leading southeast region. As noted in Section 1, economic disparities of this sort have also been documented in other parts of the world. Therefore, in this paper, we used a dynamic model to study the effects of trade in knowledge and ordinary goods on the income and welfare gap between a leading and a lagging region. Knowledge goods were invented and produced exclusively in the leading region. In contrast, ordinary goods were invented in the past and their production technology was copied by the lagging region. Therefore, ordinary goods could be produced in both regions. Our analysis shed light on five significant questions. First, we determined the equilibrium wage ratio between the leading and the lagging regions. Second, we showed that increasing the rate at which the lagging region copied the technology for producing knowledge goods narrowed the income and welfare gap between the leading and the lagging regions. Third, we ascertained the stationary or steady state level of welfare in the leading region. Fourth, we demonstrated that an increase in the rate at which the lagging region copied the technology for producing knowledge goods could make the leading region worse off. Finally, a policy maker in the leading region could make this region better off by putting in place innovation stimulating policies such as R&D subsidies, R&D tax credits, and other tax benefits such as the deductibility of research expenses. Similarly, we showed that a policy maker in the lagging region would want to, for instance, institute policies that reduced the cost of copying goods and thereby expedited the copying rate in this region. The analysis in this paper can be extended in a number of different directions. In what follows, we suggest two possible extensions. First, it would be interesting to model the interaction between a leading and a lagging region as a dynamic game in which the control variables in the two regions are the innovation rate ˇ in the leading region and the copying rate in the lagging region. Second, it would be useful to endogenize the innovation decision in the leading region and then study the equilibrium rate of technological change and the economic growth rate in the aggregate economy consisting of a leading and a lagging region. Studies that incorporate these aspects of the problem into the analysis will increase our understanding of the nexuses between innovation, technology, copying, and the economic growth and development of leading and lagging regions. Acknowledgments We thank the Editor, two anonymous reviewers, and seminar participants in Monash University, Malaysia, for their helpful comments on a previous version of this paper. In addition, Batabyal acknowledges financial support from the Gosnell Endowment at RIT. The usual disclaimer applies. References Acemoglu, D., 2009. Introduction to Modern Economic Growth. Princeton University Press, Princeton, NJ. Alexiades, S., 2013. Club Convergence: Geography, Externalities, and Technology. Springer, Berlin, Germany. Armstrong, H.W., Taylor, J., 2000. Regional Economics and Policy. Blackwell, Oxford, UK.
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