9.4 EFFICIENCY OF ACQUISITION AND TRANSFER OF INFORMATION BETWEEN AGENTS THAT DEPEND ON EACH OTHER TO SURVIVE

In this section we examine the efficiency of acquisition and transfer of information between two private agents where one agent provides a vital positive externality of a tangible nature to the other.

Information (e.g. technical knowledge) can be a public good (e.g. a mathematical formula) or a purely private good (e.g. the recipe for a herbal liqueur). Some information and technology is generally usable (e.g. a weather for ecast), while other knowledge may be tied to a particular product (e.g. a computer program). Both information and an intermediary service reducing a perceived lack of information can meanwhile be a private good: in this case the economic agent (decision-taker) compares the price or marginal cost with the marginal benefit and then decides whether or not to buy the information. This is a standard market mechanism involving supply and demand for an economic good — in this case information.

However, information can also be provided as a gift, i.e. free of charge, if it has the character of a positive externality where the decision-taker's economic outcome (or even economic survival) is tied to the existence of another agent. The recipient of the positive externality may then have an interest, for example, in increasing the technological level of this agent and acquiring and transferring technological information to it, perhaps even free of charge, but nonetheless in its own interest This for m of support can be better for the provider than a direct subsidy, for which there is a risk of fungibility (i.e. use for a different purpose than for the externality in question).^{[1]}

A willingness to fund the acquisition and transfer of information justified by such a positive externality is (alongside trading in intangible assets, of course) one of the possible microeconomic incentives for technology diffusion in an economic system.^{[2]} In the following section we show that the generalized microeconomics approach can be useful for describing this process.

Let us assume that the survival of two agents, namely the provider and the recipient of information as a positive externality, depends exclusively on their income. Moreover, the survival of the provider of information is conditional on the survival of the recipient of that information, which is providing it with a vital positive externality. The fate of the recipient of this externality is therefore tied to that of the recipient of the information. Consequently, if the information recipient goes out of business, so will the information provider.

We assume that the sales revenue (income) e0 of the information provider comes exclusively from the sale of quantity x0 of its product at unit price p0, i.e.

The provider's income is

where μ is the cost of acquiring and transferring the information.

9.4.1 MODEL A: INFORMATION EFFECT = INFORMATION ACQUISITION AND TRANSFER COST

Let us start by assuming an extreme situation where the cost of acquiring the information equals the benefit of the information to the recipient thereof.

We again assume that the risk of extinction of an agent with income d and subsistence level b is determined by his relative margin vis-a-vis the subsistence level

which is consistent with a first-order Pareto probability distribution as described in section 1.3.1.

We will denote the subsistence levels (extinction zone boundaries) of the two agents by b0 and b1.

100 for more on technology diffusion, see Hlavacek, M.: Modely difuze technologic WP 1ES No. 1, Praha: Fakulta socialmch ved UK, 2001.

The information recipient (threatened exclusively by low income) has income of

which corresponds to a survival probability of

By contrast, the information provider is in a situation of two threats: first due to low income of his own, and second due to the information recipient going out of business. The information provider's income is

which corresponds to a survival probability given by the product of the probability of survival of the information recipient and the probability of the information provider avoiding extinction due to low own income:

Let us assume that the two agents are — prior to the decision to acquire and transfer information — in the position of the median of the relevant set (in terms of income level), which, for the assumed Pareto distribution of income, is double the survival zone boundary level:

Let us denote the ratio of the sizes of the two agents, measured by their income, by k:

i.e. we assume that the provider's income and its extinction zone boundary are k times the corresponding variable for the information recipient.

We choose the money unit in such a way that b1 = 1. Under this assumption:

The information provider's survival probability here is:

Let us set k as the parameter of the maximization problem. Differentiating p(μ,k) with respect to p and setting this derivative equal to zero gives us the condition for a maximum in the for m of an equation with unknown p and parameter k:

In Figure 56 the root of this equation is shown on the vertical axis as a function of parameter k on the horizontal axis:

Figure 56: Information provision and transfer cost p versus parameter k (the ratio of the information provider's income to the information recipient's income) — model A

It is also interesting to look at the relationship between the share of support in the donor's income μ/d and the ratio of the sizes of the two agents k:

Figure 57: The optimal share of support in the donor's income μ/d versus the ratio of the sizes of the information provider and the information recipient — model A

It turns out that an agent with 6.5 times the income of the information recipient will donate the maximum proportion of its income for the acquisition and transfer of information. If the two agents are equal in size (i.e. if k = 1), the optimal level of support is zero. For increasing k the optimal proportion decreases, and for k → ∞ it also tends to zero. However, for k = 1000 it is still greater than 4%.

We will now conduct an analysis of sensitivity to the size of the information effect Ceteris paribus we will change the model by making the effect of the transferred information half as large as the information acquisition cost.

9.4.2 MODEL B: INFORMATION EFFECT < INFORMATION ACQUISITION AND TRANSFER COST

The information recipient (threatened exclusively by low income) now has income of

and a survival probability of

The information provider is again in a situation of two threats: first due to low income of his own, and second due to the information recipient going out of business. As in model A, his income is

The information provider's survival probability is again given by the product of the probability of survival of the information recipient and the probability of the information provider avoiding extinction due to low own income:

We again assume that the two agents are (prior to the decision to acquire and transfer information) in the position of the median of the relevant set (in terms of income level), which, for the Pareto income distribution, is double the survival zone boundary level. We also choose the money unit in the same way as in model A. The information provider's maximized survival probability is then:

Differentiating p(μ, k) with respect to p and setting this derivative equal to zero again gives us the condition for a maximum, this time in the for m:

Figures 58 and 59 show how the optimal support varies in absolute terms and in relative terms (in relation to income) as a function of parameter k, i.e. the ratio of the sizes of the two agents:

It is noteworthy that even in model B, where the effect of the information is lower than the cost of acquiring and transferring it, the acquisition and transfer of information is advantageous for both agents (advantageousness being assessed here on the basis of the agents' probability of survival).

There is another, even more surprising finding: it is not true that the greater is the information effect, the stronger is the incentive for both agents. Above a certain threshold^{[3]}, an increase in the disproportion in the two agents' sizes increases the proportion of support provided from the income of the support provider.

Figure 58: The absolute size of the provider's support for information acquisition and transfer versus parameter k (ratio of the sizes of the information provider and the information recipient) — model B

Figure 59: The share of support for information acquisition and transfer in the provider's income versus parameter k (ratio of the sizes of the information provider and the information recipient) — model B

Figure 60: Comparison of the share of support in the income of the support provider for model A (solid line) and model B (dashed line)

[1] We address this problem in more detail in the final chapter of this book, on the economically rational provision of subsidies. We also give references to relevant literature there.

[2] For more on technology diffusion, see Hlaváček, M.: Modely difuze technologií. WP IES No. 1, Praha: Fakulta sociálních věd UK, 2001.

[3] The threshold value of the parameter in our illustrative example was k = 8. For a different choice of model parameters the threshold is different.

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