# Why are inventions inevitably correlated with imperfect competition?

Romer (1990) elaborates the incompatibility of nonrival inputs with constant returns to scale: If a production function depends on rival and nonrival inputs and both inputs are productive, then the production function cannot be constant returns to scale. Romer then uses the Euler's Theorem to show that non-constant returns to scale are not compatible with perfect competition. Formally: $$F(A,X)<A \cdot \frac{\partial F(A,X)}{\partial A}+X \cdot \frac{\partial F(A,X)}{\partial X}$$ where $F(A,X)$ is an increasing return production function and $X$ and $A$ are the input factors. Romer: "If all inputs were paid their value marginal product, the firm would suffer losses." Intuitively, with increasing returns to scale one firm is able to produce every quantitiy at lower costs alone than many firms together. So the economy tends towards monopoly. Romer credits Arrow (1962) amongst others with this insight.

What Arrow said though is that in order to have incentive to innovate, inventions must be appropriable, e.g. monopoly right. This leads to textbook welfare loss through market power. Nonexcludable commodities must be made excludable otherwise nobody has incentives to invent them. Intuitively, if perfect competition would prevail after invention, the inventor would not be able to recoup the positive costs of the invention. So there would never be incentive to invent in the first place.

Both authors show how a property of certain commodities is not compatible with perfect competition. However, Romer uses nonrivalry but Arrow nonexcludability. In Romer's case a technological feature of the production function leads to imperfect competition and in Arrow's case it's an incentive problem, independent of the production function.

How are Romer's and Arrow's insight the same? For me, the consequence might be the same but the reasons leading to imperfect competition are different. I am still not able to grasp the incompatibility of inventions and perfect competition. Why are inventions (R&D) inevitably correlated with imperfect competition?

EDIT: Also, note that Arrow refers to the sector producing the invention whereas Romer's source of imperfect competition stems from using the invention (I am not yet familiar with the Romer model to actually confirm that). Furthermore, Romer's problem can be solved by using increasing return production functions but Arrow's incentive problem cannot be solved this way.

• Is your question theoretical (i.e. why econ model usually...) or empirical? The latter is not evident. Here and here are examples against it, whereas here is a mixed view. The escape-competition effect can also be used in a model, deriving opposite results to the one in the title of the question. – luchonacho Jul 4 '17 at 9:23
• It is theoretical. Thank you for the references. – Fusscreme Jul 5 '17 at 14:59