Arrow (1959) - Economic Welfare And The Allocation Of Resources For Invention

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  • Arrow, K.J. (1958), "Economic Welfare and the Allocation of Resources for Innovation" in idem., Essays in the Theory of Risk Bearing. pdf
  title={Economic welfare and the allocation of resources for invention},
  author={Arrow, K.},


None available - this is a book chapter.


Invention is defined as the production of knowledge.

The chapter lays out and explores three classical reasons for failure of perfect competition to achieve Pareto optimality, and applies them with respect to invention:

  1. Indivisibility
  2. Inappropriability
  3. Uncertainty

Side note: Indivisibility in this context refers to the fact that information can not be divided according to efficient use (see below). This should be compared with the notion of a public good (which is non-rival and non-excludable). Non-rival means that the consumption of the good by one individual does not reduce it for another individual. Non-excludable means that no-one can be effectively excluded.

Resource Allocation under Uncertainty

Innovation is an inherently uncertain undertaking. The uncertainty in the production and ex-post valuation of an innovation leads to a need for insurance for risk-averse agents involved in the production. However, any insurance has an inherent moral hazard problem - the greater the pay off in the state of the world without the invention, the less incentive the agent has to work to produce the invention, and the less likely the invention will be realized.

Arrows states that:

  • Projects with expected positive returns should be undertaken, no matter the variance
  • Common stock, or other insurance mechanisms, reduce the return to the innovator.
    • Then managers don't recieve the full rewards, so reducing risk dulls incentives
  • Though the stock holder can diversify away they risk by holding a portfolio of investments
    • So large corporations should be associated with R&D
    • And the government is most able to bear risk, so should be funding R&D
  • Cost-plus contracts are a compromise providing some insurance with some incentives

Overall, the dulled incentives will lead to an underinvestment in risky activities.

Information as a Commodity

Supposing that innovation results in an information based invention that can be regarded as a commodity, and that the cost of transmitting the information were zero, the socially optimal allocation would be unlimited distribution at a price of zero. Further a piece of information is by definition indivisible.

If a monopolist owner of the information were to sell it, the buyer could reproduce it at little or no cost (i.e. information is non-rival). If the owner doesn't sell it but uses it, this use will be socially inefficient, as well as possibly privately inefficient (the owner may not be the best user).

Furthermore demand for information has undesirable properties:

  • Because information is indivisible, information about production possibilities, for example, may not depend on the rate of production (c.f. price discimination).
  • In addition, information transmission and payment suffers from Arrow's information paradox, that is, the buyer doesn't know the value of the information until he has it, but then doesn't want to pay, at least given complete appropriability.
                              Arrow's Information Paradox 

"the potential purchaser of the information describing a technology (or other information having some value),
needs to know the technology and what it does in sufficient detail as to understand its capabilities 
and decide whether or not to buy it. Once the customer has this detailed knowledge, however, 
the seller has in effect transferred the technology to the customer without any compensation."
                                                                            Sourced from wikipedia, June 2010

Both properties will lead to non-optimal purchase of information and non-optimal allocation.

Though it should be noted that the appropriability would help if there was no cost of transmission and the information were given away for free (as it should be from a social standpoint). Further, a socialist economy could solve this problem by rewarding invention seperately from the charge (if any) to the users of the information. In a free enterprise economy, the property rights to support invention will create an underutilization of the information.

This is clear because:

  • The price will be positive and should be zero, so demand will be below the optimum
  • At any price the nature of information will lead to lower demand

Invention as the Product of Information

Supposing that there is an interdependence of inventive activities, these problems become magnified (though no new problems are created).

The key points are:

  • The value of information that is an input to an uncertain output is itself uncertain and magnifies the uncertainties.
  • Appropriating information for research is harder than appropriating it for production of a commodity
  • It is unclear ex-ante or ex-post how to divide up the revenue from a compound product into invention royalties
  • There are benefits to having a wide range of studies early on, and a smaller range later (when the area of promise has been identified). At each stage of refinement the full set of information is needed, which is incompatible with decentralization as in a capitalist economy. Thus there are increasing returns to use.

Competition vs. Monolopy

In short, competitive markets are better than monopolies for undertaking invention, as the monopolist faces less inventive incentive. Arrow does not comment here on risk diversification.

Alternative Form of Economic Organization in Invention

Arrow comments on the complementarity between teaching and research, and says that research (in some more applied fields) has consistently been regarded as an appropriate subject for government participation, and its role has been of great importance. If the government is to compensate for the private sector failings, two problems arise:

  • How shall the amount of resources devoted to innovation be determined?
  • How shall efficient use be encouraged?

To answer the first, the social marginal benefit should be equal to the social marginal opportunity benefit, though calculation of rates of return are problematic even ex-post. For the second, cost-plus contracts provide one mechanism (ignoring inherent motives of the researchers), but suggests that we go beyond the firm as the fundamental unit of organization for invention.