Balancing short-run costs and long-run gains: the welfare implications investing in new technologies in developing countries Open Access

Understanding economic growth as a dynamic process is essential for comprehending the varying behaviors that have been exhibited by countries throughout history. Two key elements contributing to the recent success stories of economic catch-up are learning and adoption. More than a quarter of the disparity in GDP per capita among countries may be attributed to the adoption and diffusion of technologies (Comin & Hobijn, 2010). Many economic thinkers, from Schumpeterian and evolutionary economists, such as Nelson and Winter (1982), to more mainstream authors, such as Parente and Prescott (1994) or Parente (1994), have underscored the pivotal role of technology adoption in enabling lagging countries to catch up.

In most cases, countries do not invent new technologies; instead, they have to adopt those that already exist. Introducing these technologies, even those that have become well-established, may bring about a significant impact on the growth of both developing and developed nations, since the adoption process involves costs. One illustrative example of an incentive to reduce the cost of adopting new technologies may be observed in the semiconductor industry, known as the Mead-Conway revolution. In the late 1970s, the development of new chips in company labs was prohibitively expensive. The design and architecture of new chips were inseparable from the assembly of blueprints, thereby necessitating simultaneous execution. This structural limitation posed a significant challenge to the development of the semiconductor industry and its ability to keep pace with Moore’s Law, which aimed to exponentially increase computer capacity. To address this challenge, the Defense Advanced Research Projects Agency (DARPA) initiated the Very Large Scale Integration (VLSI) project, enabling designers to develop new architectures independently from chip production. While a few companies undertook VLSI projects, DARPA identified that the widespread adoption of VLSI across academia and industry, rather than being confined to a few select firms, would significantly reduce the costs associated with developing new chip designs and improve production efficiency. This initiative transformed the semiconductor industry, resulting in a surge in new technologies and architectures, along with the development of software tools for more efficient circuit design.

Although DARPA did not invent VLSI technology, its strategic approach demonstrated how public policy could reduce adoption costs in the semiconductor industry and enhance technological advancement. Furthermore, it helped bridge the gap between designing new chips and implementing them on production assembly lines (Van Atta, Reed, & Seitchman, 1991; Miller, 2023) ^[1].

These examples support Jovanovic’s proposal (1997), whereby the primary engine of growth hinges on the decision to adopt existing technologies, a factor he claimed has been underemphasized in growth modeling. The key takeaway from this literature is that the adoption of new technologies entails significant costs, which should be embedded in models of learning and diffusion as being essential variables in the process of catching up. Jovanovic (1997) estimated that in the US, the loss in GDP due to technology adoption is around 10%. In addition, the adoption process may be twenty times more costly than innovation. It is therefore possible to suppose that this issue is even more critical in developing countries.

Adopting new technology entails that the timing of its introduction varies across firms and countries. First, some technologies may be human- and physical-specific, i.e. vintage-specific. The introduction of a new capital good may require on-the-job training, new investments in the educational system or physical modifications to the assembly line. These elements, plus the fact that technological progress is embodied in machines, could account for some of the productivity slowdown observed in economies following the adoption of new technology. The well-established argument in the literature posits that adopting new ideas is costly and that it also takes time for innovations to diffuse throughout an economy. Recent research on the relationship between negative growth and the introduction of information and communication technology (ICT) has demonstrated a significant initial reduction in production, reaching as much as 28%. However, as the economy learns about and diffuses this technology, long-term growth may increase by 18% (Ayerst, 2022).

Greenwood and Jovanovic (2001) observed that incorporating adoption costs and learning curves into vintage models could enhance the explanations on productivity slowdown. However, despite extensive research into new technologies, few studies have examined the dynamic relationship between adoption costs, learning and diffusion and embodied technological progress. The model presented in this paper addresses these issues by illustrating how negative growth and nonlinear dynamics in optimal growth rates can arise. The model also facilitates a comparison of different types of interventions for designing development policies aimed at fostering growth and catch-up processes. Governments may consider subsidizing capital accumulation, promoting the adoption of more complex technologies, reducing adoption costs (as exemplified by the DARPA case) or accelerating the diffusion of new technologies. Furthermore, the structure of the model enables the welfare analysis of each instrument to be evaluated, thereby enabling governments to formulate a combination of policies to foster growth and development ^[2].

The model addresses a gap in the discussion on technology adoption in economies that need to learn and diffuse technology, particularly when technology is embodied in new machines. Technically, we have utilized embodied technology in an AK endogenous growth model and a Nelson-Phelps catch-up equation to demonstrate that the inclusion of adoption costs can lead to negative growth (Nelson & Phelps, 1966; Abramovitz, 1986). The AK structure enables us to thoroughly describe the welfare and link it to policy variables. The model generates intriguing transitional dynamics and displays leapfrogging opportunities contingent upon the technology and learning parameters. The convergence of output growth toward long-run growth may even exhibit non-monotonic behavior when there is a steep learning and diffusion curve. The model enables an explicit path for capital and consumption dynamics, thereby comprehensively facilitating welfare analysis.

The policy implications suggest that, similar to Schumpeterian models, learning and diffusion may serve as significant drivers of growth and welfare enhancement, especially in developing economies. While the adoption of new technology may take time to translate into productivity gains, it ultimately contributes to long-run growth and welfare, despite any initial delays. Moreover, the complexity level of the adopted technology may also impact welfare outcomes. A U-shaped relationship exists between technological complexity and welfare, in which very simple technologies may lead to lower long-run growth, albeit with lower adoption costs. Thus, economies face a trade-off between achieving higher long-run growth and a experiencing a short-run reduction in growth and may even result in negative growth.

The paper is organized as follows: the next section presents a literature review, illustrating how the model may fill some of the gaps observed in the current literature on growth. Section 3 presents the model and the balanced growth path, while the following section reveals the conditions for negative growth and the relationship of the welfare function with learning and diffusion as well as welfare and the level of technological complexity. Lastly, Section 5 presents the possibility of leapfrogging and catching up.

One of the major concerns relating to growth for developing economies arises in countries that have fallen into the so-called middle-income trap. After experiencing a period of successful growth, countries that could have progressed beyond an extremely low level of income find themselves stuck at this intermediate income level. The World Bank and other institutions have recognized this fact and claim that there has been a “practice gap” between the Solow (1956) and endogenous growth models ^[3]. While the former is useful for addressing growth issues and shaping policies in low-income countries, its key feature, the exogeneity of technology, poses challenges for discussing the prospects of middle-income countries. While endogenous growth models delve into technology, they are more focused on creating innovative technology for advanced economies than on helping middle-income countries adapt and diffuse technology to facilitate their catch-up (Gills & Kharas, 2015).

The main proposal of this paper is to address this issue by developing a simple growth model that focuses on the adoption and diffusion of new technology within an embodied technology framework. Learning and the slow diffusion from leading to laggard firms have been used in the endogenous literature to explain the reduced growth in developed economies (Akcigit & Ates, 2021). Recently, robust empirical evidence has indicated that lower levels of learning and the diffusion of new technologies are partially responsible for a decline in productivity growth among OECD countries. For example, firms have faced significant costs in order to access digitalization, and the slowdown in diffusion rates has played a significant role in explaining the global reduction of growth. Furthermore, the literature has also demonstrated that even if policymakers stimulate the expansion of technological frontiers, diffusion to lagging firms will not necessarily be automatic. In conclusion, it is possible that intervention to promote diffusion and learning in the economy may enhance productivity and reduce the barriers to access new technologies (Andrews, Criscuolo, & Gal, 2016). Ferraz, Kupfer, Torracca, and Britto (2020) estimated the cost and the willingness to adopt new technologies and digitalization in the Brazilian economy and demonstrated that digitalization in Brazil moves at a very slow pace and that a very small number of firms have plans to climb the technological ladder. There is extensive literature on learning curves and the costly adoption of new technologies. Bahk and Gort (1993) estimated a learning curve and reported that productivity gains are about 15% over the first 14 years after implementing new technology. An excellent discussion on the implications of learning and diffusion may also be found in Stiglitz and Greenwald (2015). Learning and diffusion appear to be an important part of the picture and are linked to successful strategies for growth.

Another debate regarding the recent stagnation of growth in Latin American countries, in comparison to those in East Asia, has concerned the relatively low investment rate hindering a steady, persistent growth in the GDP, preventing escape from the middle-income trap. Some policy responses have been aimed at stimulating capital accumulation. Nonetheless, there has been substantial debate regarding the lack of positive impacts on productivity following the investment boom in the 2010s, shortly after the 2008 financial crisis. Some studies have reported either insignificant or even negative relationships between investment and firm-level productivity (e.g. Messa, 2015; Vasconcelos, 2017). The growing body of literature has also indicated the misallocation of capital, which is to say, incentives and policies that boost low-productive firms or sectors. Consequently, inefficient firms or sectors have been artificially sustained within the economy due to the wrong incentives. These factors contribute to the low productivity growth observed. While this may be the case, this paper posits a second possibility, i.e. that negative growth could be an optimal response in a developing economy when the country faces adoption costs. Even if the economy faces negative growth, the process of learning and diffusion can ultimately lead the economy to higher future growth. As noted by Restuccia and Rogerson (2017), the discussion on misallocation needs to be refined in order to achieve a dynamic effect. In short, this paper contributes to the discussion on growth strategies, demonstrating that a drop in the levels of consumption and capital can be an optimal response to the process of technology adoption.

The model used in this study is an AK model with a central planner that maximizes a constant relative risk aversion (CRRA) utility function, represented by a logarithmic function for simplicity. The use of the AK model, which employs capital in a broader context, facilitates an explicit welfare analysis, provides a comprehensive view of the dynamics of consumption and capital and presents the entire economic transition. Consequently, policy implications and the choices of new interventions become significantly clearer in these models ^[4].

It is assumed that a gap exists between leading countries and a developing economy, where the former is at the technological frontier while the latter lags behind on the technological ladder. In accordance with the literature, it is possible to infer the presence of a technological gap in developing countries. This phenomenon, as outlined by Greenwood and Jovanovic (2001), implies the existence of a disparity in technology adoption; hence, developing countries are located below the technological frontier. Furthermore, this gap widens in proportion to the complexity or to the “amount to be learned.” In essence, a given developing country not only lags behind in the comprehensive utilization of technology but also experiences an increasing divergence or distance from optimal use as the technological complexity grows. Parameter A(t) is employed to quantify and assess the current deviation from the technological frontier, which, for simplicity, is normalized to 1. Parameter q represents the complexity of the technology adopted by the country and serves as the relative price of capital with respect to consumption goods ^[5]. A simple interpretation of parameter q is that it reflects the level of complexity of a general-purpose technology, as discussed by David (1975, 1990). This new technology would only be internalized with the acquisition of new machinery and equipment, as, for example, in the dynamo era or the recent ICT revolution with the acquisition of the most recent computers. The adoption of new technologies from the ICT revolution would entail the purchase of new machinery and equipment. On the other hand, there would also be a need to invest in training and redesigning the production lines. In this article, the simplifying hypothesis is that the adoption costs of this technology are proportional to parameter q. Thus, parameter q has a key role in the present model, since it stands for the complexity level of the embodied technology but also represents the amount to be learned (q), the gap between the technological edge and the current knowledge in the economy of the technology. The assumption enables us to account for the fact that the more complex the technology, the higher the technological gap, and thus, higher adoption costs. A second process is particularly important in the dynamics of this model. As time passes, the economy learns how to master technology and diffuses best practices throughout the economy. As diffusion and learning occur, the technological gap is reduced at a rate of λ. Production, Y(t), is defined as follows, incorporating these features ^[6]:

The complete optimization problem for this optimal growth model is given by:

The objective of the central planner is to maximize the discounted amount of instantaneous utility, where parameter ρ represents the discount factor, C(t) the consumption of the final good. The model includes two sectors, the final and capital goods, respectively, C(t) and K(t). Investment in this economy is measured by the term I(t), i.e. the addition to the stock of capital goods. This specification, similar to that used by Greenwood, Hercowitz, and Krusell (1997), captures the fact that new technologies are embodied in new machines via the law of motion for capital. In other words, technological progress is also realized through the acquisition of new capital goods and parameter q acts as a measure of the efficiency of the production of capital goods. It is assumed that this stock of capital suffers depreciation at a depreciation rate of $δ$⁠.

Proof: See the supplementary material, ^[7].

The output growth rate is equal to the sum of the marginal productivity gains through learning, plus the accumulation of capital:

The balanced growth path rate is:

Consumption growth comprises two components. The first is determined by the long-run growth rate, while the second reflects the impact of the learning curve on the expanding capacity of the economy to obtain a better mastering of the adopted technology. It is evident that the faster the diffusion and learning parameter λ, the faster the economy will reach the technological frontier or optimize the current technology. It should be noted that q appears squared in the equation. The role of q is two-fold: it represents the level of embodied technological progress and also affects the amount that needs to be learned, i.e. the adoption cost, which impacts the entire economy. In other words, as the complexity of the technology (q) increases, so too do the adoption costs. The economy must exert greater effort to adopt this more complex technologies, due to a higher q. An increase in the adoption costs may be considered as a disembodied impact because it affects the marginal productivity of the total installed capital stock. This finding is consistent with Boucekkine, Del Rio, and Licandro (2003), whose model demonstrates that the growth rate of an economy is influenced by the disembodied technological parameter, multiplied by the embodied technological parameter weighted by the capital share. In this AK model, the share is equal to one. The squared parameter q accounts for both the disembodied (adoption cost) and the embodied impact. It should be observed that q also has an impact on the long-run growth in the first component and states that a more complex technology, a higher q, implies higher long-run growth. The following subsection analyzes this process in greater detail.

As we have the full dynamics of capital and consumption, it is possible to analyze the components of growth in this economy. Due to the AK structure, the growth rate of K(t) and C(t) are equal even in the short run. The AK model implies that the ratio $C(t)K(t)$ is constant and equal to $ρq$⁠. Over time, as the economy masters the new technology, the growth rate of consumption and capital become an increasing function of time. The great attribute of this model is that in the transition to the long run, the growth engine contains three components: the complexity level of the technology, capital accumulation and learning and diffusion.

The result allows for the possibility of negative growth, whereas the consumption and output levels may decrease. This occurs when the technology is sufficiently complex to generate a level of adoption cost, which may not be fully compensated for by an increase in marginal productivity. In short, it may be optimal for the economy to present a transitory drop in consumption and capital accumulation, not due to a misallocation of capital, but as a consequence of the adoption and learning processes. Because of the nondecreasing returns to scale, changes in capital stock do not reduce marginal productivity. In this case, negative growth occurs. As the learning and diffusion processes evolve, the marginal productivity of capital increases and the economy recovers.

This long-run growth (Equation 7) is exactly that of a traditional AK model. In the long run, the gap is closed and the economy has fully learned how to master the technology. However, the long-run growth will depend on the level of technology that the country has adopted. As $A(t)→1$⁠, when $t→∞$⁠, the learning and diffusion processes have no impact on the rate of the long-run growth, given that the economy, in the long run, knows how to fully master the adopted technology q. The economy converges to the usual growth rate of the AK model ^[8]. It should be noted, however, that a more complex technology, i.e. a higher q, signifies a higher long-run growth.

The central question, therefore, is under which conditions does the economy present a negative growth, and thus, what are the welfare implications of this negative short-run drop in consumption and capital? Given the optimal rate of growth in this model, it is relatively easy to derive the conditions for observing a negative growth in the economy. Proposition 2 summarizes all the cases. The first step is to determine the level of negative growth. The second step, given the structural parameters of the economy, is to determine how long this negative growth will last. It should be noted that the diffusion rate plays a key role in the duration of the negative growth. The level of the technology, q, greatly affects the magnitude of the negative growth.

Define $t̅$ as the time interval that the negative growth lasts, i.e. the duration of the negative growth rate. Then the higher the diffusion parameter lambda, the shorter the duration of the negative growth, $∂t̅∂λ<0.$

Our analysis demonstrates that when (ρ + δ) > 0.25, technology adoption costs generate significant economic friction, manifested in negative growth rates for both consumption and capital accumulation (Proposition 3). This occurs because higher discount rates (ρ) reflect stronger present-bias preferences, while elevated depreciation rates (δ) compound the initial adjustment costs and very high initial adoption cost – consistent with the welfare effects in Corollary 3, ^[9].

Output growth dynamics are driven by the sum of productivity gains from the adoption and diffusion of new technology as well as capital accumulation. In some cases, productivity gains may dominate, leading to positive growth rates above the long-run level. Even when capital growth rates are negative, output growth rates may remain positive and exceed the long-run value. Rearranging Equation (6), may observe this:

The first term on the right-hand side converges to zero and the output growth rate is equal to the long-run growth rate. However, the economy may present an output rate above this long-run growth level if the productivity gains offset the adoption cost. Another interesting feature is that the economy may present a non-monotonic convergence toward the AK level of long-run growth, depending on the diffusion parameter, q. Indeed, the derivative of the output growth rate with respect to time is defined as:

The sign of this derivative might well change. This leads to the possibility of a non-monotonic transition. For example, an economy may present a non-monotonic transition when marginal productivity, A(t), is low, which leads to a negative growth rate in consumption and capital stock. An A(t) decreasing level of total capital stock might imply a decrease in output growth. If the learning and diffusion curve is very steep, the output may have a positive growth rate. Again, as capital accumulation increases, so the economy recovers, and the output rate rises.

Briefly, the dynamics of output growth depends on the gains of these two components in total output through an improved A and capital stock growth rates. It is possible to derive the full dynamics of capital and consumption depending on the level of diffusion and the complexity of the technology. The question that should be asked is can there be a negative growth in total output? Alternatively, which q values yield a negative output growth rate?

In summary, it is possible to achieve an optimal reduction in output, consumption and capital accumulation due to the adoption costs associated with very complex technologies. This occurs when the learning and diffusion rate (λ) is insufficient to compensate for the initial adoption expenses, leading to a net decline in economic performance in the short run. Furthermore, it is also possible to derive the time that this negative growth will last. The period of negative output growth diminishes over time as learning and diffusion advance. Although the complexity parameter (q) has an ambiguous initial effect – imposing higher upfront adoption costs – it compensates by enabling stronger long-run growth once diffusion gains momentum ^[10]. The model may also present a non-monotonic behavior on the output growth, capital and consumption. It is therefore crucial to discover what the welfare implications are for all these cases.

The different cases that the model may present spark a discussion regarding which optimal choices policymakers must make. Given that there is an explicit solution for consumption, it is also possible to obtain an explicit welfare function.

Interpreting this welfare function is a very simple, direct task. It is the sum of the present value of the long-run steady state given by the two first terms on the right-hand side of the welfare Equation (13), plus the discounted impact of growth on total welfare. Due to the transition toward the long run, the total impact of the growth rate may be decomposed into the long-run discounted rate, given by $q−ρ−δρ2$⁠, plus a convergence toward the long run, given by $q2λ(λ+ρ)$⁠. From the welfare function, it is possible to derive some comparative statics, whereby the main aim is to define the impacts of learning and diffusion, $λ$, and the complexity level, q.

The impact of λ on welfare is unambiguously positive. The faster the diffusion or the learning parameter, the higher the welfare gains. Parameter q has a much richer impact on V(t). On the one hand, it increases the long-run growth, although on the other, a greater amount to be learned signifies a greater distance to the frontier. The sign of the derivative is ambiguous and is dependent on the value of other parameters.

To study the impact of a new technology on the economy, q, some comparative statics may be used to study the marginal impact of implementing an improved technology.

In the long run, an improvement in technology brings an unambiguous positive impact on the growth rate:

However, in the short run, the introduction of more complex technology may reduce growth, since the adoption cost will play a role in reducing the initial output:

If q < 0.5, then the derivative will always be positive, and the marginal impact of an improved technology is positive for t > 0. However, for more complex technologies $q≥0.5$⁠, the marginal impact on growth may be negative in the time interval $0<t<−1λln12q$⁠.

The negative impact of adopting more complex technology over the short run can lead to a reduction in welfare. This is because despite the long-term increase in growth, society incurs an initial cost to implement the new technology. Therefore, a very complex technology may not necessarily improve welfare, since it depends on the parameters of the utility function and how fast the economy learns.

In order to illustrate the flexibility of the model, two simulations are presented. The first simulation compares how different levels of initial capital and income affect the trajectory of some endogenous variable, notably welfare. As the model allows for the full dynamics of capital, consumption and welfare, the simulations are presented along with the trajectory of the level of the variables. Figure 1 illustrates this impact on welfare when a higher level of technology is introduced into the economy. In this first simulation, there are two economies, and the structural parameters remain the same, as follows: ρ = 0.1; δ = 0.1 and λ = 0.03. The only distinction between the two economies lies in their initial capital, whereby K(0) is set at 550 for the baseline economy and a lower initial capital of 450 for Series 2. The values are chosen just to demonstrate the flexibility of the model and to illustrate the implicit dynamics. The second simulation aims to study the impact of learning on welfare, comparing two countries with the same level of initial capital.

The first simulation demonstrates that the shape of the welfare is similar for both countries when the level of level of technological complexity varies. However, the country with a lower initial capital presents a lower welfare at every level of technological complexity ^[11]. The figure clearly illustrates a U-shaped relationship between the level of complexity (q) and welfare, indicating an optimal q level. While more complex technology enhances long-term growth and welfare, excessive complexity results in a decline in welfare due to increased learning and adoption costs.

In short, countries with different levels of initial capital will present a very similar dynamic behavior, although the level of welfare will differ, with a relatively wealthier country presenting a higher level of welfare. There is a non-monotonic relationship between welfare and the complexity level of technology, thus requiring economies to balance short-term costs and long-term gains.

The second simulation presents the impact of learning and is presented in Figure 2. Similar to the first simulation, there is a baseline economy and an economy with a lower learning and diffusion process, whereby the lower learning economy has the same initial capital as the baseline economy, of 550. However, there is a lower learning parameter, λ = 0.01. In the second simulation, the baseline economy is the same, but there is another economy with the same level of initial capital, 550, although λ = 0.01. This economy is called the lower learning economy. The U-shaped relationship between the level of complexity (q) and welfare is evident from Figure 2, indicating an optimal level of q. While more complex technology increases long-run growth and improves welfare, excessively complex technology leads to a welfare loss due to the learning and adoption costs. Figure 2 presents the results of the welfare level as the complexity of the technology varies.

A U-shaped relationship persists between welfare and the complexity level of the technology. However, the economy with a lower level of learning and diffusion also presents a lower optimal complexity level of technology. At any given level of technological complexity, the baseline economy achieves a higher level of welfare. Furthermore, as the level of technological complexity increases, the welfare gap between the baseline economy and the lower learning level widens. In other words, the economy with a higher level of learning and diffusion is able to enjoy higher levels of welfare with more complex technologies since it not only grows faster but is also able to offset the negative impact of adopting complex technologies more quickly. Learning thus emerges as a key variable in the model, since it improves welfare, allows the economy to adopt more complex technologies and supports higher levels of growth and output.

Despite its simple structure, the model is capable of generating complex dynamics. To illustrate this, we compared two economies with varying learning and technology parameters: Economy 1 adopts a more complex technology but has a lower learning parameter (q = 0.265) and a slower learning rate (λ = 0.15), while Economy 2 adopts a less complex technology but learns much faster (q = 0.26, λ = 0.28). Both economies share the same structural parameters, δ = 0.15 and ρ = 0.1, but present different long-run growth rates of 1.5 and 1%, respectively. Figure 3 displays the dynamics of the output growth rate for both economies. Initially, Economy 2 experiences a higher growth rate due to its faster learning capacity, while Economy 1 undergoes a temporary reduction in total output. However, by period 12, Economy 1 has caught up and ultimately surpasses Economy 2, resulting in a leapfrogging effect. It is interesting to note that the convergence dynamics are entirely different for each economy.

In both economies, consumption and capital stock accumulation initially decline as adoption costs exceed the marginal productivity of capital. During these periods, both economies exhibit negative growth rates in consumption and capital stock accumulation. However, Economy 2, with stronger learning and diffusion processes, recovers faster than Economy 1. Figure 4 illustrates this dynamic, demonstrating that a decrease in consumption and capital stock accumulation is much less severe in Economy 2 than in Economy 1, which experiences a more persistent reduction due to the higher adoption cost of more complex technology. A positive growth is only observed after ten periods. Nevertheless, due to its higher long-run growth rate, Economy 1 leapfrogs Economy 2’s growth rate of consumption and capital stock accumulation at around t = 17.

The key message is that all these variables are interrelated, and a mix of policies may provide higher growth and improved welfare. By understanding the trade-offs and synergies among these factors, policymakers may design more effective policies that promote sustainable economic development.

Developing economies currently face significant challenges, notably the so-called middle-income trap, a reduction in the diffusion of new technologies, and a slowdown in productivity growth ^[12]. Gills and Kharas (2015) argued that traditional new neoclassical models, such as Solow (1956), are unable to address this reality. Meanwhile, endogenous growth models focus more on the generation of new ideas or technologies rather than their adoption. In addition, the economic literature emphasizes the crucial role of learning and the diffusion of new ideas and technologies in driving growth, particularly in developing countries. This paper has presented a simple model that incorporates some of these features. Using an AK model with embodied capital technology (i.e. new ideas or technologies are embodied in capital goods), the model incorporates an important characteristic of technology adoption: introducing a new technique or machine into production is costly. To encapsulate this concept, the model incorporates a Nelson-Phelps catch-up equation, yielding some intriguing findings:

1. The possibility of catching up and leapfrogging within an AK model framework.

2. The potential for negative growth and a non-monotonic transition toward a balanced growth path due to adoption costs.

3. A shorter duration of the negative growth with higher rates of learning and diffusion, although the impact of technological complexity remains ambiguous.

4. A trade-off exists for economies, whereby adopting a more complex technology enhances long-term growth but results in a short-term reduction in productivity.

The simulation and comparative statistics presented in the present paper have illustrated that the optimal pace of technology adoption creates a trade-off between short-run costs and long-run benefits. These findings are particularly relevant for policymakers in developing countries since some of the benefits of adopting technology may only materialize once the economy learns more about the new technology. Consequently, countries may face the choice of whether to adopt a more complex technology with higher short-run costs but potentially with greater long-run gains. These results are significant and provide a strong contribution to the discussion on broader industrial policies. Over recent years, the focus of the economic literature has concentrated more on how to implement these policies rather than whether to create them (Juhász, Lane, & Rodrik, 2023). The paper has also demonstrated how a mix of policies may prove to be welfare enhancing. The model enables the analysis of various policy instruments, ranging from more horizontal interventions, such as reducing the adoption cost, as undertaken by Darpa with the Mead–Conway revolution and VLSI, to a more traditional intervention, such as capital accumulation subsidies or improving learning and diffusion. One key result of the model is that when adopting a more complex technology, in order to be welfare enhancing, it is desirable to combine it with diffusion and learning improvement.

The model generates rich dynamics and multiple transitional paths toward a long-run equilibrium growth rate. The simulations illustrate that even if an economy adopts a lower level of technology, it may outperform another with a more complex technology but which is less efficient in learning and diffusing new ideas. The versatility of the model suggests a range of possible interventions that could improve welfare. One natural extension of this study would be to incorporate optimal intervention and the trajectory of government expenditures.

One other significant result of the model is the possibility of optimal negative growth. This reduction in productivity growth is an optimal response in the economy due to adoption cost and the complexity level of the adopted technology. However, the dynamics of technological diffusion and learning reduce this initial loss and translate it to positive long-run growth. These results challenge the traditional interpretation of capital misallocation ^[13]. The static inefficiency and productivity may be the result of optimal choice and the transition to a sustainable growth process.

The author is deeply grateful to the reviewers of the journal for their insightful comments and suggestions. Special thanks go to the editor, Mauro Rodrigues, for his careful reading of the text and invaluable recommendations. The author also acknowledges the feedback and contributions of the following individuals: Raouf Boucekkine, Aude Pommeret, Agustin Perez-Barahona, Carmem Camacho, Raul Fuentes, Fabio Waltenberg, Fernanda Estevan, Flávio Gonçalves, Carlos Wagner Albuquerque Oliveira and Claudio Amitrano. Any remaining errors or omissions are solely the author’s responsibility. Additionally, the author would like to thank the CAPES Foundation for its financial support of this research.

The supplementary material for this article can be found online.