Exploring Causality Between Artificial Intelligence and Economic Capacity

Introduction

Artificial Intelligence (AI) has emerged as a transformative General Purpose Technology (GPT) with the potential to significantly enhance economic capacity across various sectors. GPTs are technologies that have broad applications, lead to substantial impacts on productivity, and drive economic growth. The Production Possibility Frontier (PPF) illustrates the maximum feasible production combinations of two goods or services an economy can achieve with its available resources and technology.

This article explicates the causal and potential causal relationship between AI and economic capacity as illustrated by the PPF. It utilizes historical data and comparative analysis of diverse economies to evidence the findings. Furthermore, it provides a comparative analysis of the impact of AI relative to other GPTs, such as the computer, the router, and the AC electrical transformer, including numeric analysis in specific economies. Mathematical models, proofs, numeric evidence, and references to economic, historical, technical, engineering, and scientific literature are provided to substantiate the analysis.

Artificial Intelligence as a General Purpose Technology

Artificial Intelligence refers to simulation of human intelligence processes by machines, especially computer systems. These processes include learning, reasoning, problem-solving, perception, and language understanding. AI encompasses various sub-fields such as machine learning, natural language processing, robotics, and computer vision.

AI exhibits the key characteristics of a GPT that is pervasiveness; technological dynamism; and innovation complementarity. AI technologies are applicable across numerous sectors, including healthcare, finance, manufacturing, transportation, and education. Continuous advancements in algorithms, computational power, and data availability drive improvements in AI capabilities. AI enables and stimulates innovations by enhancing processes, creating new products, and facilitating research and development. ^{1 2}

The production possibility frontier (PPF) and AI

The production possibility frontier represents the maximum possible output combinations of two goods or services that an economy can produce, given its resources and technology. An example can be seen in figure 1.³

An outward shift of the PPF indicates an increase in an economy’s productive capacity, allowing for higher output levels. A shift can be caused by technological advancements, for example AI; increases in resource availability; or efficiency improvements and productivity.

AI automates tasks, optimizes processes, and augments human capabilities, leading to higher output with the same inputs; facilitates research and development, leading to new products, services, and industries; improves allocation and utilization of resources through data-driven decision-making; and enables better resource allocation and process optimization, increasing output. AI-based tools increase workers’ productivity by assisting in complex decision-making and knowledge-intensive tasks. The cumulative effect of AI across sectors contributes to overall economic expansion.

Mathematical representation of AI’s impact on TFP and the PPF

Using the Solow Growth Model with AI as a factor influencing total factor productivity (TFP):

$$Y = A \cdot F(K,L)$$

where $Y$ represents output; $A$ is TFP, influenced by AI; $K$ is capital; and $L$represents labor.

Assuming A grows as a function of AI advancements:

$$A = A_{0}e^{\gamma \cdot AI(t)}$$

where $A_{0}$ is the initial TFP level; $\gamma$ is a parameter representing the impact of AI on $TFP$; and $AI(t)$ is the level of AI adoption at time $t$. An increase in $A$ shifts the $PPF$ outward, signifying enhanced production potential.

Historical data and comparative analysis

AI’s economic impact in various economies

Benefits of AI vary in different industrial sectors but are universally applicable to all countries. In manufacturing, AI-driven automation can increase output and reduces costs. In healthcare, AI can enhance diagnostic accuracy and patient care efficiency. In retail and e-commerce, AI can optimize inventory management and personalized marketing, boosting sales and reducing waste.

United States

AI is projected to contribute an additional $3.7 trillion to the U.S. economy by 2030. An assessment from the U.S. Bureau of Economic Analysis and PwC (Price-waterhouse Coopers) estimated that AI could contribute up to 14% to U.S. GDP growth in the same time-frame. AI adoption can potentially boost labor productivity by up to 40%. ^{4 5}

China

AI is expected to add $7 trillion to China’s GDP by 2030 and could boost China’s GDP growth rate by 1.6 percentage points annually. In manufacturing, AI applications could increase productivity in the long term by 25% or more given recent developments with DeepSeek AI. In agriculture, AI-driven precision farming can enhance crop yields and resource efficiency. ^{6 7}

European Union

In 2018 the European Commission estimated that AI has the potential to increase EU GDP by 19% by 2030 and could lead to a 20% increase in labor productivity. ⁸

Comparative analysis with other GPTs

AI primarily builds upon the impact of computers, which have revolutionized data processing, communication, and automation since they became ubiquitous throughout society. The 1990s productivity boom driven by computers contributing to a surge in productivity, particularly in the U.S, led to Information and Communication Technology (ICT) accounting for approximately 0.5 percentage points of annual GDP growth.

AI enables machines to perform cognitive tasks and therefore has the potential to deliver higher productivity gains due to its ability to optimize complex processes and data analytics. Enhancing the foundational impact of computers by introducing advanced data analytics and machine learning boosts productivity beyond what was achieved with computers alone. ⁹

The internet transformed communication, commerce, and access to information. Network effects describe the value increased as more users connected. Internet-related activities contributed to 3-4% of GDP in advanced economies and in 2020, the Internet economy contributed an estimated $2.1 trillion to the U.S. GDP, representing over 10% of GDP.

AI leverages vast amounts of data generated via the internet and can create new services and products that were not possible with the internet alone. AI is expected to contribute significantly to global GDP growth by 2030, surpassing the internet’s peak impact due to its deeper integration across sectors. ¹⁰

AC electrical transformers enabled efficient transmission and distribution of electricity. Between 1920 and 1950, U.S. electricity consumption increased by 500%, supporting industrial growth and urbanization. Electrification transformed industries and daily life, and contributed to approximately 0.5% annual GDP growth in the early 20th century. While transformers represented a leap in energy distribution, AI’s potential impact on productivity and GDP growth is estimated to be higher due to its pervasive applications. While the transformer revolutionized energy systems, AI has a broader impact across multiple sectors. ¹¹

Mathematical models and proofs

As discussed briefly earlier, the Solow Growth Model can be extended to include AI as a factor influencing Total Factor Productivity (TFP). Taking the standard Solow model:

$$Y(t) = A(t) \cdot K(t)^{\alpha} \cdot L(t)^{1 - \alpha}$$

where $Y(t)$ represents output at time $t$; $A(t)$ is TFP at time $t$; $K(t)$ is capital stock at time $t$, $L(t)$ is labor input at time $t$; and $\alpha$represents the output elasticity of capital, we can then make the assumption that $TFP$ growth is a function of AI adoption represented by:

$$A(t) = A_{0}e^{\gamma \cdot AI(t)}$$

where $A_{0}$ is the initial TFP level; $\gamma$ is a parameter representing the impact of AI on TFP; and $AI(t)$ is the level of AI adoption at time $t$.

To model the potential impact on economic growth we take the following expression for the growth rate of output:

$$\frac{\dot{Y}}{Y} = \frac{\dot{A}}{A} + \alpha\frac{\dot{K}}{K} + (1 - \alpha)\frac{\dot{L}}{L}$$

where the “$\cdot$” over a parameter indicates the change in the value and modify $A$ to include TFP growth due to AI:

$$\frac{\dot{A}}{A} = \gamma \cdot \frac{\dot{AI}}{AI}$$

This implies that an increase in $A(t)$ due to AI adoption shifts the PPF outward, as more output can be produced with the same inputs. The higher the $\gamma$, the greater the impact of AI on TFP and economic growth.

Numerical Example

Assuming some arbitrary parameter values:

• Initial output $Y_{0} = \$ 1\text{ trillion}$

• Initial TFP $A_{0} = 1$

• Capital $K = \$ 500\text{ billion}$

• Labor $L = \$ 50\text{ million}$

• $\alpha = 0.3$

• AI adoption increases $\text{TFP by 2\%annually}\mspace{6mu}(\text{i.e. }\gamma = 0.02)$

Year 1

$$A_{1} = A_{0}e^{\gamma} = 1 \cdot e^{0.02} \approx 1.0202 \Longrightarrow Y_{1} = A_{1} \cdot K^{\alpha} \cdot L^{1 - \alpha} = 1.0202 \cdot (500 \times 10^{9})^{0.3} \cdot (50 \times 10^{6})^{0.7}$$

Calculating $Y_{1}$ and comparing it to $Y_{0}$ suggests that the output increase due to AI-driven TFP growth alone in this arbitrary example would be approximately $792 million over one year. This would be expected to compound year on year to deliver greater long-term returns.

AI’s network effects and economic capacity

AI’s benefits from a positive feedback loop from several key effects. User adoption and network effects increase data availability enhancing AI capabilities; greater access to source data and a history of results from previous queries improve the reliability of generated content. As algorithms improve public perception and trust increase, attracting more users. Shared AI platforms and open-source frameworks accelerate advancements, increasing the technology’s value with broader adoption. With accurately defined scope and precise learning models, AI can enhance other technologies, creating synergies and further boosting economic capacity.

As AI’s network effects amplify its impact, the PPF shifts outward more significantly. AI applications then become more efficient with scale, reducing marginal costs.

Mathematical representation

Let $V(n)$ represent the value of AI as a function of the number of users or data points $n$:

$$V(n) = V_{0} + \delta \cdot ln(n)$$

where $V_{0}$represents the base value and $\delta$is a parameter representing the strength of network effects.

As $n$ increases, $V(n)$ increases, enhancing economic capacity.

Potential causal challenges and considerations

As with many advances in automation, AI may replace certain jobs, leading to short-term unemployment. This can be offset as demand for new skills increases, necessitating workforce retraining. Labor policies and worker protections would need to be adjusted to account for this transition.

Economics incorporate labor reallocation and human capital investment into growth models. High-skilled workers may benefit more from AI, widening income gaps. The distributive nature of technological change lifts most every one in society, but not evenly. This is a non-trivial issue, recourse to history demonstrates that the human condition is subjective, emergent and relative. How we feel about it as individuals at the time matters, that our experience of life emerges from complex interactions with others intermediated by technology and as such individual experience can be highly divergent, and finally how we experience and calibrate our expectations is relative to the experience of others as we can observe it.

In that context accessibility for the less privileged individuals in society will impact on the potential for innovation and the experience of economic disparities. Proactive investment in education to prepare the workforce for AI-driven economies increases adoption velocity. This includes adult education and retraining initiatives.

Conclusion

Artificial intelligence, as a general-purpose technology, has a causal relationship with economic capacity, contributing to an outward shift in the production-possibility frontier. AI enhances productivity, fosters innovation, and optimizes resource utilization, leading to significant economic growth across diverse economies.

Comparative analyses with other GPTs, such as the computer, the router, and the AC electrical transformer, highlighting AI’s potential for a more profound impact due to its pervasive applications and ability to augment cognitive tasks. Mathematical models and numeric evidence support the conclusion that AI’s integration into various sectors can substantially increase output and efficiency.

However, potential challenges such as job displacement, inequality, and ethical considerations necessitate public debate and deeply considered policy measures to ensure sustainable growth for every one. By addressing these challenges, economies can fully harness AI’s potential to expand economic capacity and improve societal well-being.

Bibliography

Acemoglu, D., & Restrepo, P. Artificial Intelligence, Automation and Work. In The Economics of Artificial Intelligence (2018: pp. 197–236). University of Chicago Press.

References

Barton, Dominic. Artificial intelligence: implications for China. McKinsey Global Institute (2017).

Brynjolfsson, Erik, and Andrew McAfee. The second machine age: Work, progress, and prosperity in a time of brilliant technologies. WW Norton & company, 2014.

Brynjolfsson, Erik, and Andrew Mcafee. The business of artificial intelligence. Harvard business review 7.1 (2017): 1-2.

Bughin, Jacques, et al. Notes from the AI frontier: Modeling the impact of AI on the world economy. McKinsey Global Institute 4.1 (2018).

David, Paul A. The dynamo and the computer: an historical perspective on the modern productivity paradox. The American economic review 80.2 (1990): 355-361.

European Commission. Artificial Intelligence for Europe. (2018).

Goldfarb, A., & Tucker, C. Artificial Intelligence and the Future of Work. In The Economics of Artificial Intelligence (2019): pp. 17–34. University of Chicago Press.

Jorgenson, Dale W., Mun S. Ho, and Kevin J. Stiroh. A retrospective look at the US productivity growth resurgence. Journal of Economic perspectives 22.1 (2008): 3-24.

Price Waterhouse Coopers. Sizing the Prize: What’s the Real Value of AI for Your Business and How Can You Capitalise. (2017).

Shapiro, Carl. Information rules: A strategic guide to the network economy. Harvard Business School Press, 1999.

Footnotes

1. Erik Brynjolfsson and Andrew Mcafee. The business of artificial intelligence. Harvard business review 7.1 (2017): 1-2.↩︎

2. A. Goldfarb & C. Tucker Artificial Intelligence and the Future of Work. In The Economics of Artificial Intelligence (2019): pp. 17–34. University of Chicago Press.↩︎

3. Nam Tran via Wikimedia Commons.↩︎

4. Jacques Bughin et al. Notes from the AI frontier: Modeling the impact of AI on the world economy. McKinsey Global Institute 4.1 (2018).↩︎

5. Erik Brynjolfsson and Andrew McAfee. The second machine age: Work, progress, and prosperity in a time of brilliant technologies. WW Norton & company, 2014.↩︎

6. Price Waterhouse Coopers. Sizing the Prize: What’s the Real Value of AI for Your Business and How Can You Capitalise. (2017).↩︎

7. Dominic Barton. Artificial intelligence: implications for China. McKinsey Global Institute (2017).↩︎

8. European Commission. Artificial Intelligence for Europe. (2018).↩︎

9. Dale W. Jorgenson, Mun S. Ho, and Kevin J. Stiroh. A retrospective look at the US productivity growth resurgence. Journal of Economic perspectives 22.1 (2008): 3-24.↩︎

10. Carl Shapiro. Information rules: A strategic guide to the network economy. Harvard Business School Press, 1999.↩︎

11. Paul A David. The dynamo and the computer: an historical perspective on the modern productivity paradox. The American economic review 80.2 (1990): 355-361.↩︎