Efficient Transfer of Public Scientific R&D to Private Firms
2.3 Efficient Choices
The issue for analysis in this section relates to the choice of the most efficient set of organizational arrangements for the transfer of informal knowledge. In this context the most efficient refers to those that maximize net value.
Assume that a scientist from a public institution discovered scientific knowledge that is expected to have an eventual commercial value. Consider the case where n such product developments can be based on this knowledge.14Suppose, in the sym- metric case, that each of the products is expected to generate a value m.15However, these developments have been subject to significant risk. The three major sources of such risk are
1. Risks of rejection by the regulators 2. Competition from non-GM varieties 3. Rejection by consumers16
It may be postulated that the actual value generated17is(m+u)with u being a random variable with expected value18E(u) =0, and variance19V(u) =σ2.
The essential choice for the scientist is the fractionαof the number of products, n, that he prefers to develop on his own. It will be assumed that the development of the remaining(1−α)n products will be licensed to private firms. Assume that production of each of the products entails a variable cost.20For the scientist it can be represented by m2/2δ∗. On the other hand, it will be assumed to be m2/2δ;δ >δ∗ for the private firm.21
Note that two different forces determine the variable costs of production. First, the level of output itself accounts for the variable costs. This can be captured by m2. That is, it is postulated that there will be diminishing returns to the use of factors of production as m increases. Second, the scientist may not be as efficient as the private firm when it comes to commercialization.δ andδ∗therefore represent the degrees of efficiency of the scientist and the private firm. Postulate that the scientist or the private firm, as the case may be, incurs the entire cost.22The private firm can compensate the scientist, for providing patented knowledge as well as the transfer of informal knowledge, by offering a fraction p of the value generated from the sale of the product.
32 T. V. S. Ramamohan Rao It is important to examine the role of the scientist in the case where a license is granted to a private firm. For all practical purposes, he has to
1. Offer informal knowledge in the use of technology
2. Monitor and control the private firm to guard against imitation and reengineer- ing23
It can be expected that these costs will increase more than proportionately with m. Similarly, the costs will increase the farther the scientific invention is to the final product. This cost will therefore be represented by km2. In general, k may be higher.24
1. The more the requirements of knowledge transfer
2. The farther away the invention is to a product of commercial value 3. The lower the IPR protection
4. The greater the costs of financing and/or financial constraints. No further attempt will be made to introduce the subtle differences in costs that each of these aspects imply25
The profit for the scientist can be written as
πs =αn(m+u) +p(1−α)n(m+u)−αnm2/2δ∗−(1−α)nkm2 It will be assumed, following the conventions of the principal-agent models of the Kawasaki and McMillan (1987) vintage, that the scientist is risk averse. Hence, the value he assigns toπswill be
Vs=αnm+p(1−α)nm−αnm2/2δ∗−(1−α)nkm2−λn2[α+p(1−α)]2σ2 whereλis the degree of risk aversion of the scientist.
In a similar fashion, the profit of the(1−α)n private firms is given by πn= (1−p)(1−α)n(m+u)−(1−α)nm2/2δ
The private firms are also involved in many other production activities. Conse- quently, they can effectively diversify their risk. That is, they will be generally risk neutral. The value of the license to them will be
Vn= (1−p)(1−α)nm−(1−α)nm2/2δ
Contract theory generally supports assigning decisions to the party with better information. Hence, the natural choice of modeling is to leave the decision regard- ing m to the private firms. For, they have better market information. Clearly, the scientist is in the best position to chooseα. Given that the scientist has a patent on knowledge, he can be expected to choose the terms of the license. In particular, he will choose the sharing fraction p as well. Each of the private firms derives a posi- tive net profit as the number of product applications increases. Hence, they may not place any limit on n. But the scientist experiences diminishing returns with respect to increases in n. Consequently he will choose the efficient n as well.
2 Efficient Transfer of Public Scientific R&D 33 Consider the efficient choice of m. It is given by m= (1−p)δ. This represents the incentive constraint of each of the agents. That is, the private firm’s output choice increases with its efficiency and the share of revenue it gets.
The principal-agent models generally postulate that the principal (in this case the scientist) maximizes the net value of the contract, viz., N=Vs+Vn, taking the participatory constraint of the agent into account.26That is, he maximizes
N =n(1−p)δ−αn(1−p)2δ2/2δ∗−(1−α)nk(1−p)2δ2
−(1−α)n(1−p)2δ/2−πn2[α+p(1−α)]2σ2
Each of the decisions of the scientist will be considered assuming the others as para- metric. Adopting this approach identifies the transitional dynamics in an efficient manner.
Ceteris paribus, the choice of n satisfies the equation (1−p)δ−α(1−p)2/2δ∗−(1−α)k(1−p)2δ2
−(1−α)(1−p)2δ/2−2λn[α+p(1−α)]2σ2=0 The following observations are pertinent.
1. ∂n/∂δ∗>0. That is, an increase in the skill level of the scientist generates more startups including the licenses granted.
2. ∂n/∂k<0. An increase in the cost of monitoring and control by the scientist will deter him from granting more licenses. In particular, any reduction in IPR protection deters the scientist from entrepreneurship.
3. ∂n/∂λσ2<0. A risk averse scientist is unlikely to grant too many licenses because that reduces his valuation of the expected returns.
Consider the choice ofα, or the willingness of the scientist to create his own startup.
The optimal choice ofαis such that
−(1−p)δ2/2δ∗+k(1−p)δ2+ (1−p)δ/2−2λσ2n[α+p(1−α)] =0 The following results can be readily verified.
1. ∂α/∂n<0. Clearly, the larger the number of possible applications the more he will contract out given his competencies for commercialization of technology.
2. ∂α/∂δ∗>0. That is, he keeps more applications to himself when he is more competent.
3. ∂α/∂δ<0 ifδ >δ∗. Greater competence of the licensee relative to his own will obviously induce the scientist to contract out more often. It should also be noted thatδ <δ∗when the scientific knowledge is in early stages and requires extensive R&D before a marketable product emerges. In such a case the scientist will prefer to startup on his own.
4. ∂α/∂k>0. That is, the more the monitoring and control necessary, and the more the requirement of informal knowledge transfer the more the scientist will prefer to create his own startup. The same applies when IPR protection is low.
34 T. V. S. Ramamohan Rao 5. ∂α/∂λσ2<0. Once again, it is plausible that a highly risk averse scientist will
not invest in his own startups.
6. ∂α/∂ p<0. It is expected that the scientist will license out more often if his share of revenues increases.
It can also be inferred that the scientist will be the sole entrepreneur ifδ is fairly large in comparison toλσ2and n, and/or k is fairly large.27
Consider the issue of the relationship between the number of startups (including licenses) and the net value generated by the process of commercialization. Ceteris paribus, it can be verified that ∂N/∂δ∗>0 and ∂n/∂δ∗>0. Consequently, an increase in the competence of the scientist will improve N as n increases. However, it cannot generally be shown that∂N/∂n>0 in all contexts. This is not surprising.
For, entrepreneurial success in generating a higher value of N is contingent on the entrepreneurs being supported by the availability of capital, finances, and so on.
It can be surmised that this result will hold even in the steady state. Hence, the entrepreneurship and growth nexus cannot be taken for granted.