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Marxists have a very specific "profit" and "economic growth" theory. According to marxists, profit doesn't come from technology, whose cost will be reflected in the price of whatever commodity the technology owning businessman is selling. Instead, the businessman profits by paying workers low enough for their labor so that they can squeeze a profit (e.g. profit comes from living labor not dead labor (technology)). Some of this profit will in turn be used to invest in more technology which will cause capital growth (capital valorization in marxist speak).

What's the neoclassical parallel to this? It seems in neoclassical models, the market is in equilibrium so the prices reflect marginal costs and there's no "economic profit". What seems to happen is that technological advancement "happens" and this in turn creates economic growth and a new steady state/equilibrium. However, is technological innovation here merely an accident, or does it have a logic in the same way marxian "growth" has (e.g. capitalists accrue profit through living labor and then invest it in technology)?

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Have a look at the Solow Romer growth model. Also patents exist such that profits are warranted in the case of innovation (and without innovation there aren't any profits) so we have a system which is better than always or never having profit, i,e. there's profit when there should be and there isn't where there is no need. Also note that in a wide variety of models we do not necessarily have zero profit even with free entry, but the profits are not very large in most cases. – BB King Oct 30 '15 at 22:43
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If there is perfect competition, then yes, you will get zero economic profit, but even then, technology does no poof out of nowhere. Otherwise, you might find very different results.

Let's think of the nature of competition through product differentiation. (We'll get into technology later.) Imagine two firms making their own widgets in Cournot competition, but instead of the normal price function $P = X - q_1 - q_2$, we have

$$P = X - q_i - d\cdot q_{-i}$$ where $-i$ denotes the other firm that is not firm $i$, and $d \in (0,1)$, $1$ being no product differentiation, and $0$ being completely different products sold by the two companies.

If $d = 0$, then the firms aren't really competing since their products are completely different and are acting as monopolists, making economic profit. If $d = 1$, then the firms are competing through regular Cournot and still making profit (probably).

In Bertrand, we can consider product differentiation as part of determining how much of the market you will steal away by undercutting price. The way a normal Bertrand model works is that you set price and then produce (as opposed to Cournot, where you set production, which affects the price). If you have a lower price, and there is no product differentiation, you steal away the whole market, so each firm will push price down to the price under perfect competition, where both firms split the market.

With product differentiation though, you don't lose the whole market when you are undercut, since your product is still a bit different. With full differentiation $(d=0)$ then you get the same result where each firm act as monopolists.

Under each of these models, technology doesn't "just happen", but is reflected through lowering the marginal costs of the firm, which is essential for the firm to be competitive against its rivals. The less technologically advanced the firm is, the more of the market they will lose out on. Economic profit here can be used to invest into research and development or just straight up "technology" to reduce the cost of capital usage over time or other such things like that.

Even in perfect competition with no economic profit, the reason there is no economic profit will partly be because firms have to constantly update their technology to remain competitive, regardless of how differentiated the products are (as long as $d > 0$).

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This is an interesting question that I believe involves, of all things, the second law of thermodynamics.

Both marxist and neoliberal perspectives would accept that the so-called "capitalist" must innovate and adopt new technology due to the anarchic force of competition in a market system. The machine enables the firm to reduce labor costs relative to its competitors.

For marxists this is simply a temporary, relative advantage that allows a "window of opportunity." The innovating firm can for a time underprice and capture a higher market share. Of course, competitors can adopt the same machines, no matter how long they are delayed by patents and other defensive tactics. So the unending adoption of new technology is a Sisyphean task or zero sum game, from the standpoint of any set of competitors. Though, of course, many competitors cannot keep up and must "fold their hand" as the investment stakes get higher.

The point of the marxist model is that machines in themselves do not produce value. They only shift the flow of labor so as to produce temporary advantage. Obviously, labor somewhere must make the "machines" and feed, educate, etc., those who make the machines. So in terms of profit the "machine" is only a way of displacing labor to other markets, where the relative costs of producing labor are lower. The idea that "new technology produces value" is not entirely wrong, but simplified and inaccurate.

The reason I bring the second law of thermodynamics into it is this. Marxism retained certain essentialist-materialist values from the 19th century, but these do in fact reflect some more basic laws of physics. Machines are subject to the laws of entropy. They cannot interact, maintain, and reproduce themselves. There are no "perpetual motion" machines. All machines go dead within hours if all humans die. Life is the only "perpetual motion" machine. So what appears to be "value" produced by machines is actually a deferral, displacement, and mediation of hidden labor, living humans.

Thus, for marxism, the simple-minded replacement of workers by machines is necessary under market competition. But is a kind of a "death wish" in which life is channeling itself into dumb matter.The neoliberal perspective has answers to this in the calculus, but simply does not involve itself in such "meta-macroeconomic" concerns. In keeping with the empiricist tradition, it distrusts such metaphysical or speculative analyses.

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