GPT and the Economics of Cognitively Costly Writing Tasks
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GPT and the Economics of Cognitively Costly Writing Tasks
Produced by GPT-4 (r) and Scott Cunningham (r) with prompts by Scott Cunningham
In this Substack, we examine the relationship between GPT-4 and human prompts, with a focus on the role of prompting in costly forms of creative writing. The substack was produced jointly by GPT-4 and Scott Cunningham using prompts (and “revision prompts”) by Scott Cunningham, an economist and professor at Baylor University. At the end, we will reveal the prompts used to produce the substack. Some minimal edits were used, but they were kept to a minimum.
Also, we will keep track of time inputs and total output measured in minutes of time spent on the substack “prompting” and final output measured in words. GPT-4 has a cap of 25 prompts per 3 hours, so we were unable to complete the substack in one sitting. We started this on Saturday March 18th at around 6:15am and reached the 25 prompt limit at 7:15am, four paragraphs into our discussion of Goldin and Katz. That was 1,693 words and 7 pages double spaced with several lines of mathematical equations using LaTeX (that we produced with prompts) in one hour, or 28 words per minute. We will update this each time we hit capacity in this introduction as well as note the final production in words and time inputs in minutes for the entire substack post.
Finished 1 hour, 50 minutes. Total produced words is 2,185 and 9 double spaced pages with 4 equations produced in LaTeX (although there were many more that we decided to delete). My prompts were 1,174 words. This means I promoted GPT with 1,174 for it to produce 2,185 words over a 1 hour and 50 minute time frame, or 20 words per minute. With more time we would have cleaned it up and sharpened the ideas I think, but I am wanting to wait on it.
Introduction
The washing machine revolutionized domestic life by slashing laundry time from a labor-intensive 20 hours per week to a mere 1-2 hours, freeing up time for other tasks and leisure. This transformation aligns with economist Dr. Gary Becker's theory of time allocation, which suggests that individuals optimize their utility by balancing market work, household production, and leisure. In the same vein, Goldin and Katz's theory of skill-biased technological change posits that advances in technology tend to benefit workers with higher skills or education, widening the gap between them and less-skilled workers.
Many overlook the role of technology in reducing production costs and altering relative input prices, which, in turn, impacts time allocation. This broader perspective helps us appreciate technology's multifaceted influence on our lives. GPT, like the washing machine, plays a vital role in producing cognitively costly writing tasks by automating and enhancing creative writing, altering input costs like time and cognitive effort. This leads to shifts in time allocation and expands creative possibilities in both professional and personal domains.
Drawing from Becker's time allocation theory and Goldin and Katz's perspective, the rise of GPT could usher in a new era of efficiency for those adept at using it. As time costs for cognitively demanding tasks decline, we may witness skilled GPT users producing more content than ever before, harnessing the power of AI to enhance their work. These individuals might lean more heavily on GPT, streamlining their writing process and freeing up time for other pursuits, whether it's market work, leisure, or even further creative endeavors. In short, GPT's transformative capabilities promise to unlock untapped potential, fostering growth and innovation across professional and personal spheres.
Our upcoming Substack post delves into the basic economics of production, shedding light on GPT's impact on complex writing tasks and its implications for time and resource allocation.
The Cost of Time and the Production of Cognitively Costly Tasks
The Cobb-Douglas production function, introduced by Charles Cobb and Paul Douglas in their 1928 paper, is a foundational concept in economics. It models the relationship between inputs, such as labor and capital, and output in the production process. Despite its simplicity, this function has been widely used to study economic growth, income distribution, and other aspects of production.
Becker's theory of time use suggests that individuals allocate their time among work, household tasks, and leisure to maximize their well-being. The cost of time is based on opportunity costs, or the value of what is given up when choosing one activity over another.
In the context of cognitively demanding writing tasks, worker time and capital are the main inputs. Advanced technology, such as GPT, can improve labor efficiency, allowing more high-quality content to be produced within the same amount of time. This efficiency lets individuals allocate their time more effectively among various activities, promoting a balance between work, household production, and leisure.
Using the Cobb-Douglas framework, we can understand the impact of improved labor efficiency on the production of cognitively costly writing tasks. As efficiency increases, output improves, leading to higher production with the same labor and capital. Technology like GPT also affects the trade-off between labor and capital, as more efficient labor encourages adjustments in input mix to optimize production.
In summary, technology that enhances labor efficiency in cognitively demanding writing tasks not only improves output quality and quantity but also profoundly influences time and resource allocation. These advancements align with Becker's theory of time use, contributing to efficient time use, improved well-being, and economic growth.
The Race Between Education and Technology: Insights from Goldin and Katz
In their groundbreaking book "The Race Between Education and Technology" (2008), economists Claudia Goldin and Lawrence F. Katz examine the link between technology, education, and income inequality. Their theory of skill-biased technological change helps us understand how innovations like the washing machine and GPT-4 impact time use, resource allocation, and the labor market.
The washing machine is a prime example of technology that has transformed household tasks, freeing up time for other activities as per Becker's time use theory. GPT-4 follows a similar pattern, increasing the efficiency of labor inputs in cognitively demanding writing tasks. According to the Cobb-Douglas production function, this efficiency results in higher output for the same amount of labor and capital.
Goldin and Katz's theory emphasizes the importance of education and skill development in adapting to technological advancements like GPT-4. As these innovations create demand for skilled labor, supplying educated workers is crucial for avoiding income inequality and promoting inclusive economic growth.
In conclusion, the interplay of the washing machine's impact, skill-biased technological change, the Cobb-Douglas production function, Becker's theory of time use, and GPT-4 underlines the significance of education in adapting to technology. These connections highlight how technology influences time allocation, labor efficiency, and income distribution.
Cobb-Douglas and Labor Efficiency
In simple terms, the Cobb-Douglas production function is a way to describe how inputs, such as labor and capital, combine to produce output. When the efficiency of labor units increases, it means that each worker can produce more than before. This improvement in labor efficiency can result from various factors, such as better technology, education, or management practices.
In this context, an increase in labor efficiency leads to higher overall production. As workers become more productive, companies can generate more output using the same amount of labor and capital. This improvement also affects the way businesses decide to balance their use of labor and capital. With more efficient labor, companies may choose to adjust the mix of labor and capital they use to optimize production.
In summary, increasing the efficiency of labor units has a positive impact on production, enabling higher output and potentially influencing the way businesses allocate their resources between labor and capital.
To incorporate labor efficiency from Goldin and Katz's theory into the Cobb-Douglas production function, we can modify the labor input term by introducing an efficiency parameter (E). The modified production function would look like this:
In this equation, Y is the output, A is the total factor productivity, K represents the input of capital, L is the labor input, E is the efficiency parameter representing the skill or human capital component of the labor input, and 0 < α < 1. The efficiency parameter (E) captures the idea that workers with higher skills or education can produce more output per unit of labor input compared to less skilled or educated workers.
The Impact of GPT-4 on Labor Efficiency and Output in Cognitively Costly Writing Tasks
To analyze the effect of GPT-4 on labor efficiency and the optimal mix of capital to labor for workers who are good at using GPT versus those who aren't when it comes to performing cognitively costly tasks, we will consider the Goldin and Katz modified Cobb-Douglas production function:
First, let's differentiate the production function with respect to capital (K) and labor (L) to obtain the marginal product of capital (MPK) and the marginal product of labor (MPL) respectively:
In equilibrium, firms set the ratio of the marginal product of capital to the marginal product of labor equal to the ratio of input prices (w for labor and r for capital):
Now let's assume GPT-4 increases labor efficiency (E).
For workers who are good at using GPT (high E), the increase in labor efficiency will lead to an increase in MPL, which means the ratio of MPL to MPK will increase. To maintain the equilibrium condition, firms will adjust the mix of capital and labor inputs. In this case, firms will increase the use of capital (K) relative to labor (L) for these highly efficient workers to take advantage of their increased productivity.
For workers who aren't good at using GPT (low E or no change in E), there won't be a significant change in their MPL. Consequently, there won't be a substantial change in the optimal mix of capital and labor inputs for these workers when performing cognitively costly tasks.
In summary, an increase in labor efficiency due to GPT-4 will lead to a higher capital-to-labor ratio for workers who are good at using GPT, allowing them to further leverage their improved productivity in cognitively costly tasks. On the other hand, workers who aren't adept at using GPT won't experience a significant change in their optimal mix of capital and labor inputs.
When we consider the effect of GPT-4 on labor efficiency and the balance between capital (like machines and tools) and labor (workers) for different types of workers, we can think of it in simpler terms.
Imagine two types of workers: those who are good at using GPT-4 and those who aren't. For workers who are skilled at using GPT-4, their efficiency in performing cognitively costly tasks increases. As a result, the value they bring to the table when performing these tasks also goes up. To make the most of this increased efficiency, businesses will invest more in capital, like technology and equipment, to complement these highly efficient workers. In other words, businesses will try to leverage the skills of GPT-4 proficient workers by giving them more advanced tools to work with, thereby maximizing their output.
On the other hand, for workers who aren't good at using GPT-4, there won't be a significant change in their efficiency, and therefore, the balance between capital and labor for these workers remains relatively unchanged. Businesses won't have the same incentive to invest more in capital for these workers, as they won't be able to make the most of the new technology.
In summary, GPT-4's introduction leads to a shift in the balance between capital and labor for workers who are proficient at using it, as businesses invest more in capital to make the most of their increased efficiency. Meanwhile, workers who aren't skilled at using GPT-4 don't experience a significant change in their optimal mix of capital and labor.
Concluding remarks
In conclusion, Becker's theory of time use and Goldin and Katz's theory of skill-biased technological change offer a comprehensive framework for understanding the implications of GPT's introduction to the realm of cognitively costly writing tasks. Becker's theory highlights the importance of time allocation in optimizing overall utility and suggests that GPT, by enhancing labor efficiency, enables individuals to reallocate their time to other productive or leisurely activities. This leads to an increase in overall output and well-being.
Goldin and Katz's theory of skill-biased technological change emphasizes that the benefits of technological advancements are unevenly distributed, with more educated and skilled workers gaining disproportionately. In the context of GPT and cognitively costly writing tasks, those who are more adept at leveraging GPT's capabilities to enhance their productivity and output are likely to benefit the most from this technological innovation.
Theoretically, using the Goldin-Katz modified Cobb-Douglas model, if the time use brought about by GPT causes a drop in relative prices while skilled labor efficiency rises, we would observe a shift in the optimal mix of capital and labor. Specifically, firms would find it more cost-effective to use a higher proportion of skilled labor in combination with GPT technology. This shift in production would lead to an increase in output for cognitively costly tasks.
At the same time, the rise in skilled labor efficiency, complemented by GPT, would reduce the time spent on cognitively costly tasks. As skilled workers become more efficient with GPT, they can produce a higher quantity and quality of output in a shorter amount of time. This change enables them to allocate their saved time to other activities, such as market work, leisure, or further household production. Consequently, the overall productivity and economic growth for both professional and personal domains would improve.
Conversely, workers who are less skilled or unable to adapt to GPT's introduction may find themselves at a disadvantage, as the demand for their labor in producing complex written content could decrease. This underscores the importance of continuous learning and skills development to remain competitive in a rapidly evolving technological landscape.
In summary, the interplay of Becker's and Goldin and Katz's theories provides a valuable lens through which to analyze the impact of GPT on the production of cognitively costly writing tasks. This framework elucidates the winners and losers in this new landscape, emphasizing the need for adaptability and skills development to ensure equitable distribution of the benefits offered by innovations like GPT.
As GPT and skilled labor join forces, the production landscape transforms, unleashing a wave of creativity and productivity. Time spent on cognitively demanding tasks plummets, freeing up valuable hours for market work, leisure, or other pursuits. Get ready for a world where skilled workers, empowered by GPT, break new ground and redefine what's possible in both professional and personal domains.
Prompts
· The following substack was written by GPT-4 using prompts by myself. I will at the end provide the prompts. The point of this essay is to help illustrate the role that prompting plays in cognitively costly forms of creative work. I will be trying to both communicate some ideas but I will also be trying to note that the correct way to describe this substack is that it was “prompted by Scott Cunningham”, not “written by Scott Cunningham”.
o Rewrite this but use fewer adjectives
· Give some basic facts about the amount of time people, mostly women, spent washing clothes before the invention of the washing machine.
· Now give some basic facts about the amount of time people spend washing clothes when they own a washing machine
· Transition the essay to introducing the reader to Dr. Gary Becker, the economist. But focus mainly on him as you introduce and explain his theory of time use. Briefly explain Becker's theory of time use abstractly and then apply his theory to explaining the effect the invention of the washing machine had one household time use and production.
o Rewrite the opening transition into Becker's theory of time use. Cite the article with title, year of publication and tell us how old Becker was when he wrote it.
o Note that people outside of economics, particularly lay people, will tend to focus mainly on productive technology's ability to make new things, but miss that by lowering costs, it also changes relative prices of inputs used to make those things, causing marginal shifts in time allocation.
· Now draw a connection between what we have just written together and GPT role in the production of what we will call "cognitively costly writing tasks". Note that we will be sketching some rough ideas in the substack post about basic economics of production.
I THEN ASKED IT TO REWRITE THE ENTIRE ESSAY UP TO THAT POINT WITH THIS PROMPT, “Rewrite this but make it more concise and more interesting to read”.
I THEN ASKED IT REWRITE IT AGAIN BUT to “Rewrite the following introduction, but in addition to what you wrote, also briefly discuss Goldin and Katz theory of skill-biased technological change. Then in a few sentences, tie them together by noting that GPT should is like the washing machine that it will reduce time costs for producing cognitively costly tasks depending on production functions and new human capital on prompting. “
Cobb-Douglas sections
· Start a new section on production functions. Briefly describe the history of the Cobb Douglass production function.
o Give me the latex code for the equation.
· Now explain briefly the idea of marginal rate of technical substitution and give the mathematical expression for it using the Cobb Douglass production function.
o Give me the latex code for each equation separately
· How does increased efficiency of labor units change production in a Cobb Douglas production function?
· This was very technical and correct. But now summarize the basic ideas more concisely without any math in a way that a lay person without an economics background can understand. Write so that it transitions from the previous technical discussion to the simpler discussion.
· Write latex code showing that in equilibrium the firm sets ratio of marginal product of capital to marginal product of labor to ratio input prices
· Rewrite entire section but make it concise, more interesting to read, and accurate.
I then deleted a long section about Cobb-Douglas, but incredibly it was filled with comparative statics and mathematical equations in LaTeX.
New section
· Now start a new section about the cost of time based on Becker's theory of time use. Use Cobb-Douglas to describe the production of cognitively costly tasks that use both worker time and capital to create cognitively costly writing with Becker's time use theory. What is implied by the introduction of technology that allows labor inputs to become more efficient?
· Show using this equality what happens if the relative price of capital falls
· Find a picture online of this change happening using an isquant as fall in input prices causes the firm to move do a different ratio mix.
o It can’t do it, but gave me instructions to search.
· Note that with this change in relative prices, then the person who performs cognitively costly tasks will both substitute towards GPT prompting but also because of the increased time use likely increase their output overall. Explain how this happens using Cobb-Douglas
New section
· Conclude by summarizing how Becker's theory of time use and Goldin and Katz theory of skill biased technological change work together to provide a framework for understanding who is helped and who is hurt by GPT when it comes to cognitively costly writing tasks
· But what will happen theoretically using Goldin-Katz modified Cobb-Douglas model if the time use causes a drop in relative prices but skilled labor efficiency rises? What happens to output and time spent on cognitively costly tasks?
· Now summarize that in a few sentences that are catchy and provocative
New section
· Introduce a new section on Goldin and Katz book about the race between education and technology. Give a cite and note any facts about the book's impact in economics. What earlier work was it based on.
· Connect the earlier discussion about washing machines impact on time use and production to Goldin and Katz theory of skill biased technological change, our discussion of Cobb-Douglas production technology and Becker's theory of time use with the introduction of GPT-4 and its effect on the efficiency of labor inputs used to create cognitively costly tasks.
· Now perform comparative statics on Goldin and Katz modified Cobb-Douglas production function. If GPT-4 increases labor efficiency, then what effect should we expect it to have on the optimal mix of capital to labor for workers who are good at using GPT versus those who aren't when it comes to performing cognitively costly tasks. Analyze this for us.
· This is great. Now write a less technical explanation summarizing the same ideas for a more general audience
· Please recommend for me a good image that you think illustrates what our essay is about that I could post to my substack
GPT: “I suggest using an image that showcases a person working on a computer with GPT-4 or AI-driven writing software open on the screen, surrounded by books or other symbols of education and knowledge. This image would represent the intersection of skilled labor, technology, and the impact on cognitively demanding tasks. You can find various stock images or illustrations online that capture this concept, or you can have a graphic designer create a custom image tailored to your needs.
· Rewrite the following. Is there any other predictions you can think of? Will you write more than you did before, for instance, but depend more on GPT more for doing it if you are good at using GPT?
· Rewrite entire section but still accurate and interesting.
· What determines the cost of time in Becker's theory of time use. Rewrite this and make it easier to read for a non-technical audience
The ordering of producer names was randomized using a coin flip. Scott was heads and GPT-4 was tails and it came up tails.
The use of the pronoun “our” is intentional. This substack was 95% “written” by GPT-4 with guided prompts by Scott Cunningham. The concept of writing and prompting is blurred when using AI assistance, so we use the plural pronouns and emphasize the correct description is to use language like “production” and “prompting” as opposed to “writing”.