# Why, theoretically, is economic growth exponential? [closed]

Despite the experimentally well-observed exponential nature of GDP growth, I've never actually seen a theoretical reason or "prediction" why it should be so.

(Even if the answer is "actually, it isn't exponential, growth rates increase/decrease ever so slightly", the question "why is it almost exponential?" still remains.)

Similarly, what is the standard economic explanations for the big "breaks" in economic growth rates ~10,000 BC and ~1700 AD? Historians explain it to be the result of specific technologies, but this seems to be a post-hoc explanation to me (i.e. you couldn't actually predict the effect on GDP growth from just information about technological changes -- is there any theoretical reason why "agriculture" and "the steam engine" would create a break in economic growth rates but "the assembly line", "3D printing", "computers" or "women entering the workplace" wouldn't?). What is the economists' explanation? Changes in political/economic systems?

• These seem to be very different questions. Please post them separately. (Take one out and post it as a new question.) – Giskard Jul 28 at 11:17

There are two main theories of economic growth, the Solow-Swan growth model and Romer endogenous growth model. Both of these models allow for exponential growth.

The economic output (GDP) can be modeled through standard Cobb-Douglas production function. For example, a classical production function is given by:

$$F(K,L) = AK^{\alpha}L ^{(1-\alpha)},$$

where, $$F(K,L)$$ is the output (which we can measure by GDP), $$A$$ is a stock of technology, $$K$$ stock of capital and $$L$$ is a stock of labor.

In the standard Solow-Swan model we can show that in the steady state the GDP will grow at the combined rate of growth of technology and population $$(g_A + g_L)$$, and GDP per capita at the growth rate of technology $$g_A$$ (I omitted all derivations of this result for brevity but you can see it in Romer's Advanced Macroeconomics chapter 1). Hence Solow-Swan model offers solid theoretical reasons why growth should be exponential in approximately last 200 years.

According to Gordon's The Rise and Fall of American Growth the technology in last few centuries grew extremely rapidly and had more profound effect until the recent decade which he argues can explain both the unprecedented U.S. growth since industrialization and recent decline of U.S. growth. Gordon's work focuses on US but cited therein you will find sources that discuss other countries. Furthermore, population also grown rapidly in last few hundred years so if you care only about GDP not GDP per capita the growth of world's population is also part of the story.

Next we can also look at growth through the lenses of the endogenous growth theory. The main distinction between the above Solow-Swan exogenous growth model and endogenous growth model is that in the latter the rate at which technology itself grows is not just exogenously determined by outside forces (i.e. the inevitable march of human knowledge) but also endogenously determined within the model depending on how many resources are devoted to the discovery of new knowledge.

As with the Solow-Swan model I will skip any formal derivation, which you can review at your leisure in Romer's Advanced Macroeconomics chapter 3. In this model the relationship between technology and economic growth is more complex and depending on what parameters you assume for the model (especially how new technology is produced) the theoretical predictions can be virtually identical with Solow-Swan model or they can also suggest various positive feedback loops that can accelerate growth. For example, in one version of endogenous growth theory if world's population increases the number of people devoted to producing new knowledge (i.e. scientists) also increases further boosting growth. This offers some additional explanation in sense that it also tries to explain where the technologies come from instead of treating them as just exogenous shocks to the system.

The Solow-Swan model and its predictions have been rigorously tested in the past and especially the newer augmented versions of the theory (e.g. Mankiw, Romer and Weil (1992) augmented Solow model) are empirically quite successful (see the discussion of this in Romers's Advanced Macroeconomics). The endogenous growth theory is not well empirically tested, as it is difficult to do so, but it is becoming more popular. Paul Romer even recently earned Nobel prize for his contributions to endogenous growth theory.

Furthermore, aside from the above growth theory when we talk about economic development from historical perspective it is also important to acknowledge the role of institutions. One reason why prior to industrial revolution so little progress was done was that most countries had practiced extractive institutions. For example, countries without secure property rights where warlords can just take any possession of their subjects at will create environment in which people have no incentives to spend time creating new technologies, as doing so takes a lot of time and effort and without having secure property rights why would anyone bother if their inventions can easily be expropriated. Hence as argued by Acemoglu and Robinson (see their book Why Nations Fail), technological and economic growth could really start to grow rapidly only once proper inclusive institutions were adopted (i.e. secure property right, ban on slavery/serfdom/unfree labor, free entry into occupations, lift of arbitrary restrictions on commerce etc.).

Hence those historians are more or less correct that the growth can be attributed to technology, with a necessary caveat that having proper institutions is a pre-requisite for sustainable growth. The historians might explain the growth in post-hoc fashion because they might have no economic training but the above mentioned economic models offer both clear mechanisms of how growth depends on technology and offer testable predictions that can be applied equally to past, present and future. Also it is possible that historian's are actually aware of this (at least economic historians definitely are) and you just misread them - since you never provide any citation for your assertion it is hard to judge.

In addition the assertion in your title that growth is exponential is not generally valid. It has been so in recent history, but it wasn’t always exponential and it might not be exponential in the future if technological progress slows or countries start adopting worse institutions or if you buy into endogenous growth theory if people start investing less in new technologies and as population growth halts or even if it declines in the future.