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Abstract

In 2007 the EC introduced pre-commercial procurement (PCP) to endow the EU public sector with a legal instrument for procuring innovative solutions, unavailable in the market. To induce firms to participate in a PCP, the EC suggests contracting authorities to leave the intellectual property rights (IPR) of the new solution with the firms. Based on the perspective of a possible commercial success, the IPR should work as a major incentive for companies to engage in a PCP. As important as the EC seems to consider the IPR, for a successful PCP, so far no guidelines have been provided on how to estimate their economic value. This paper proposes a methodology for such evaluation, discussing its advantages and limitations. A main message of the paper is that IPR economic value should be based on the expected profits coming from commercialisation of the would-be innovative solution. Moreover, the value should change across the different development phases of the PCP. The findings could be useful for a broad audience of PCP potential participants, contracting authorities intending to promote a PCP and third parties interested in buying the IPR.

Keywords

Intellectual property rights public procurement pre-commercial procurement

Introduction

In this paper we consider the role of patents in pre-commercial procurement (PCP) of innovation (European Commission Communication, 2007), a legal instrument introduced to provide the EU public sector with a purchasing procedure for procuring innovative solutions, otherwise unavailable in the market (Edquist and Zabala-Iturriagagoitia, 2015; Brogaard, 2018; Iossa et al., 2018). In particular, we shall discuss the economic value of intellectual property rights (IPR) in such a specific environment as the PCP, which is procuring research and development (R&D) services only.

Patents are a main institutional incentive system, provided by states for inducing firms to invest in R&D, disclose and introduce innovative solutions in the society, which might be beneficial for the whole community (Scotchmer, 2004; Hall and Rosenberg, 2010). As a form of economic incentive, patents are based on a very basic principle: the patent owner is guaranteed a period of temporary monopoly over the patented invention. More explicitly, during that period the inventor could make whatever use he/she wants of the invention and/or prevent others from using it. Alternatively, the inventor could allow other subjects to use the solution, typically in return for financial compensation. Such compensation could be given through a reward scheme as simple as a lump sum, or a stream of payments paid by the user to the inventor over a period of time, or possibly even more complex payment schemes.

Clearly patenting is not the only way to protect an innovation; indeed, secrecy is also a widely adopted method, however with an important difference. While patenting puts the new solution in the public domain, diffusing its underlying knowledge and function, secrecy does not, rather keeping the innovation in the private sphere. Therefore, patent monopoly could also be seen as the price paid by the society for public disclosure of the invention.

In recent years a debate has taken place on some issues related to the current situation of the patent system, as an effective institutional incentive device for promoting innovation. Among others, Jaffe and Lerner (2004) and Bessen and Meurer (2008) have pointed out that excess patenting, as well as beaurocracy and legal litigation, are hindering the patent system as a driver for innovation. In particular, excessive patenting introduces uncertainty over whether or not a would-be patent overlaps with already existing patents, and fear of being legally suited for this may sometimes discourage the introduction of solutions potentially beneficial for the society. Patent pools (Lerner and Tirole, 2004) represent a partial remedy for this problem, by joining a group of related patents whose use is allowed possibly at FRAND (fair, reasonable and non-discriminating) prices (Layne-Farrar et al., 2007).

For this reason rather surprisingly, and somewhat paradoxically, excess patenting could discourage, rather than encourage, innovation along lines analogous to the tragedy of the anticommons (Heller, 1998; Heller and Eisenberg, 1998). In the tragedy of the commons (Hardin, 1968), R&D investment is discouraged by the absence of well-defined property rights – that is, lack of protection – in commonly available goods. In the polar opposite tragedy of the anticommons, it is overprotection that may hinder innovation, because of an excessive number of patents.

An even more fundamental critique of the patent system has been made by Boldrin and Levine (2008), who are ‘against intellectual monopoly’ altogether, for its being a system discouraging rather than fostering innovation.

The EC 2007 PCP communication, and related documents, suggest that a contracting authority (CA) should leave with the firm the IPR protecting the solution, rather than appropriate them. The intuition is simple: IPR should work as an economic incentive for a firm to participate in a PCP. If the IPR have high economic value, then the firm would have a stronger incentive to accept the CA invitation, investing time and effort to find a solution. Alternatively, if the IPR have low economic value, a PCP might be less attractive for companies.

Therefore, based on the EC indication and above considerations, IPR should play a fundamental role in inducing creative firms to participate in a PCP, when invited by CA. However, whether or not the IPR will eventually be left with the supplier, taken by CA or sold by the supplier to a third party, the EC does not provide guidelines on how to estimate the economic value of the IPR in a PCP. This seems to be an important missing element for the analysis and sound application of PCP. Indeed, whoever is going to be the patent holder, it is crucial to have a good estimate of the IPR’s economic value. In fact, while the company will want to know how valuable is its participation in a PCP, CA will want to evaluate how economically attractive is the IPR incentive for the company. Moreover, as well as for a third party willing to buy the IPR, CA may want to know the IPR market price in case CA is interested in keeping it or purchasing it from the company.

This is what we aim to contribute to in this paper, targeting a broad audience of PCP potential participating firms, PCP contracting authorities and interested third party buyers. More specifically, we shall discuss how the economic evaluation of the IPR may be founded on the firm’s expected profit generated by commercialising the innovative solution. Indeed, this is what the monopolistic protection over the invention could guarantee to the firm. Given this, we then argue that the economic value of an IPR – that is, the price at which the IPR could be exchanged in the market – is represented precisely by the expected profit associated with the new solution. Therefore, the IPR market value incorporates several economic elements: prospective commercial revenues as well as rewards paid by CA, costs but also probabilities to succeed across the various phases of the PCP procedure.

For this reason, the value of IPR should be computed at different phases of the procurement process, since as a firm keeps being selected for subsequent stages, the risk of project failure changes, in particular decreases. Hence a main, rather intuitive, finding of the paper is that the economic value of the IPR typically increases along the procurement procedure. However, somewhat more surprisingly, in the paper we discuss how the IPR evaluation may also decrease, rather than always increase, over subsequent phases of the PCP procedure. The sequential nature of PCP is not new in innovation procurement public programmes, based on demand from the public sector (Bhattacharya, 2018). However the changing economic value of IPR along the PCP phases is an important element to consider, to our knowledge not yet fully investigated, since it could drive the company decision on whether, and at which phase, to sell the patent under the most favourable conditions.

The paper is structured as follows. In the following section we present a methodology to estimate the economic value of IPR in a PCP. Next, we discuss a few challenges that the implementation of such methodology could face, while the final section offers some conclusions.

A methodology to estimate the economic value of IPR in a PCP

The basic model

In what follows we shall consider the typical structure of a PCP with three phases, as suggested by the EC 2007 Communication. Yet, the framework we are going to discuss could easily be generalised to any number $n \geq 3$ of PCP phases. Moreover, suppose index k, with $k = 1, 2, 3$ ,4 indicates the first three PCP phases and the fourth, commercialisation, phase for the would be innovative solution. In principle commercialisation may not take place at all, when both CA and the market are not interested in the solution, or when for whatever reason CA or the company, or both, decide to stop the PCP procedure before its completion.

Alternatively both CA and the market could be interested, or only one of them.

Despite being off the PCP procedure, indeed falling within the 2014 EC Directive on Public Procurement, the economic value of an IPR protection depends meaningfully on what may happen in phase $k = 4$ . This is because the expected profits accruing upon commercialisation of the solution crucially affect the IPR attractiveness.

Below we develop a methodology to estimate the IPR value, and then discuss some critical points for its implementation.

Our subject of analysis is a generic company, which has been invited by CA to compete in a PCP. Start assuming that CA will leave initially the IPR, for protecting the proposal, to the company. Moreover suppose $π_{k}$ , with $k = 2, 3$ is the probability that the company is selected by CA for phase k, conditional to having reached phase $k - 1$ , while $π_{4}$ instead indicates the probability that CA will decide to proceed, after a successful PCP, with procuring the needed number of units of the final product.

In what follows, for simplicity, we shall assume these probabilities to be given and constant over time. However, in reality, not only may they differ across firms, but are also likely to depend on how much in each phase a single firm and the opponents invest in R&D. Indeed, it is clear that if one firm invests in the PCP much more than the opponents, it would plausibly have higher chances of being selected than with a much lower investment. That is, the value of success probabilities could be the endogenous outcome, rather than being given exogenously, of the competitors’ strategic decision on how many R&D resources to employ in the PCP. For this reason, the value of $π_{k}$ could change when computed in different phases, just because firms may change their decision on how much to invest in such phases. This point will be discussed in the next section.

Moreover, assume $c_{k} \geq 0$ is the firm’s cost for implementing phase $k = 1, 2, 3$ of the PCP while $r_{k} \geq 0$ the reward paid by CA to the firm, for participating in phase $k = 1, 2, 3$ . For the time being, we shall consider c_k as given, although, as stated above for probabilities, their level in each phase would typically be the outcome of some decision taken by the firm. Furthermore, c_k could be affected by previous investments already made by the company, for some parts of the would-be solution. In the next section, when discussing asymmetric companies, the point will be implicitly taken into consideration. In the subsequent section we shall discuss two main goals: more specifically, expected profit maximisation and expected profit breakeven, and see how they could give rise to rather different R&D investment levels.

Finally, if $0 \leq δ \leq 1$ is the firm’s time discount factor, with $δ = \frac{1}{1 + i}$ where $i \geq 0,$ is the nominal interest rate prevailing in the market, then conditional to having been invited to participate in the PCP, the present value of the firm’s profit in phase 1 is a random variable given by

Π_{1} = {\begin{matrix} (r_{1} + δ r_{2} + δ^{2} r_{3} + δ^{3} R) - (c_{1} + δ c_{2} + δ^{2} c_{3} + δ^{3} C) & w i t h p r o b a b i l i t y θ π_{2} π_{3} π_{4} \\ (r_{1} + δ r_{2} + δ^{2} r_{3}) - (c_{1} + δ c_{2} + δ^{2} c_{3}) & w i t h p r o b a b i l i t y (1 - θ) π_{2} π_{3} π_{4} \\ (r_{1} + δ r_{2} + δ^{2} r_{3} + δ^{3} R_{m}) - (c_{1} + δ c_{2} + δ^{2} c_{3} + δ^{3} C_{m}) & w i t h p r o b a b i l i t y λ π_{2} π_{3} (1 - π_{4}) \\ (r_{1} + δ r_{2} + δ^{2} r_{3}) - (c_{1} + δ c_{2} + δ^{2} c_{3}) & w i t h p r o b a b i l i t y (1 - λ) π_{2} π_{3} (1 - π_{4}) \\ (r_{1} + δ r_{2}) - (c_{1} + δ c_{2}) & w i t h p r o b a b i l i t y π_{2} (1 - π_{3}) \\ r_{1} - c_{1} & w i t h p r o b a b i l i t y (1 - π_{2}) \end{matrix}

where R is the expected revenue obtained by the firm when selling the solution to both the CA and the market, C are the related expected production and delivery costs, $R_{m} < R$ the expected revenues from selling only to the market but not to the CA and $C_{m} < C$ the associated production and delivery costs. All such revenues and costs are discounted to phase 1, are non-negative, and if the firm would not commercialise the solution after the PCP they would be equal to zero.

Finally $0 \leq θ \leq 1$ and $0 \leq λ \leq 1$ are defined, respectively, as the firm’s probability to win the procurement competition for the new solution after the PCP, conditional on CA and the market being interested in buying, and only when the market is interested.

Notice that (1) does not consider the case when a company is invited to a PCP, excluded at some phase and yet capable to win a post PCP procurement competition, with either CA and the market or only the market. Though possible, we believe this to be an event with very low plausibility and for this reason neglected.

Then, from (1), the expected profit of a firm invited to a PCP is

E_{1} = δ^{3} [θ (R - C) π_{4} + λ (R_{m} - C_{m}) (1 - π_{4})] π_{2} π_{3} + δ^{2} (r_{3} - c_{3}) π_{2} π_{3} + δ (r_{2} - c_{2}) π_{2} + (r_{1} - c_{1})

Expression (2) is what drives a firm decision on whether or not to accept the CA invitation for participating in the PCP. Indeed, if upon having received CA invitation the firm realises that $E Π_{1} < 0$ , then the company may refuse to participate in the PCP. If instead $E Π_{1} > 0$ , it may be profitable for the firm to accept the invitation.

Since there are up to four phases until commercialisation, it is not surprising that expression (2) is composed of four terms, one for each such phase. Finally, notice that it could be $E Π_{1} > 0$ even if $r_{k} < c_{k}$ , or if $[θ (R - C) π_{4} + λ (R_{m} - C_{m}) (1 - π_{4})] < 0$ as long as $r_{k} > c_{k}$ , for some or all $k = 1, 2, 3$ .

The economic value of IPR

Based on the previous paragraph, in this section we discuss a possible way to define the market price of the IPR. Indeed, what is the price s ₁ at which the company would be willing to sell the IPR in the first phase? It seems natural to say that $s_{1} \geq E Π_{1}$ , because otherwise it would be more convenient for the company to keep the IPR. Likewise, a subject interested in buying the IPR, which price b ₁ would be willing to pay? It seems that $E Π_{1} \geq b_{1}$ ; that is, the subject would be unwilling to offer more than the expected profit. Therefore, if a transaction takes place, it would probably be at a market price around $p_{1} = E Π_{1}$ , the only value which both parties accept.

The above considerations are based on the assumption that both the seller and the buyer would share the same view on $E Π_{1}$ . If their evaluation of $E Π_{1}$ differs or the buyer bases his price offer on his own willigness to pay, which may be higher than $E Π_{1}$ , then the IPR market value at phase 1 could differ from $E Π_{1}$ . In any case, it would be no lower than $E Π_{1} .$

We ask now what would be the economic value of the IPR, should the company be at phase 2 of the PCP. By following a similar reasoning, conditional to having reached phase 2 the firm profit becomes

Π_{2} = {\begin{matrix} (r_{2} + δ r_{3} + δ^{2} R) - (c_{2} + δ c_{3} + δ^{2} C) & w i t h p r o b a b i l i t y θ π_{3} π_{4} \\ (r_{2} + δ r_{3}) - (c_{2} + δ c_{3}) & w i t h p r o b a b i l i t y (1 - θ) π_{3} π_{4} \\ (r_{2} + δ r_{3} + δ^{2} R_{m}) - (c_{2} + δ c_{3} + δ^{2} C_{m}) & w i t h p r o b a b i l i t y λ π_{3} (1 - π_{4}) \\ (r_{2} + δ r_{3}) - (c_{2} + δ c_{3}) & w i t h p r o b a b i l i t y (1 - λ) π_{3} (1 - π_{4}) \\ r_{2} - c_{2} & w i t h p r o b a b i l i t y (1 - π_{3}) \end{matrix}

with the expected profit given by

E Π_{2} = δ^{2} [θ (R - C) π_{4} + λ (R_{m} - C_{m}) (1 - π_{4})] π_{3} + δ (r_{3} - c_{3}) π_{3} + (r_{2} - c_{2})

Putting (2) and (3) together the following recursive equation provides a relationship between $E Π_{1}$ and $E Π_{2}$ .

E Π_{2} = \frac{E Π_{1}}{δ π_{2}} - \frac{r_{1} - c_{1}}{δ π_{2}}

Hence, if $(r_{1} - c_{1}) > 0$ it is $E Π_{2} > E Π_{1}$ when $E Π_{1} > \frac{r_{1} - c_{1}}{1 - δ π_{2}}$ , while if $(r_{1} - c_{1}) \leq 0$ it would always be $E Π_{2} > E Π_{1}$ . So, in this case, the only possibility for $E Π_{1} > E Π_{2}$ is that the company would be compensated by CA more than its phase 1 costs and $E Π_{1}$ is low enough, which certainly occurs when $δ$ and $π_{2}$ are both sufficiently close to 1, namely when the firm is virtually sure to be selected for the second phase and the prevailing market interest rate is very low, almost zero. In this case, the expressions of $E Π_{1}$ and $E Π_{2}$ would tend to be the same except for the additional term $(r_{1} - c_{1})$ in $E Π_{1},$ which makes it larger than $E Π_{2}$ .

Therefore, the IPR market value at phase 2 would typically be $p_{2} = E Π_{2}$ , higher than $p_{1} = E Π_{1}$ . That $p_{2} > p_{1}$ is consistent with the intuition, since the risk of project failure in general decreases when going from phase 1 to phase 2.

Indeed when $E Π_{2} - E Π_{1} = \frac{E Π_{1} (1 - δ π_{2})}{δ π_{2}} - \frac{r_{1} - c_{1}}{δ π_{2}} > 0,$ such positive difference could be interpreted as a risk premium, for selling/buying the IPR in phase 2 rather than in phase 1.

Likewise, by analogous reasoning in phase 3 the firm’s expected profit would be

E Π_{3} = δ [θ (R - C) π_{4} + λ (R_{m} - C_{m}) (1 - π_{4})] + (r_{3} - c_{3})

hence

E Π_{3} = \frac{E Π_{2}}{δ π_{3}} - \frac{r_{2} - c_{2}}{δ π_{3}}

and similar considerations hold when comparing $E Π_{3}$ and $E Π_{2}$ . Finally,

E Π_{4} = [θ (R - C) π_{4} + λ (R_{m} - C_{m}) (1 - π_{4})]

so that

E Π_{4} = \frac{E Π_{3}}{δ} - \frac{(r_{3} - c_{3})}{δ}

The above findings are summarised by the following proposition, where we assume that $E Π_{k} > 0$ for all $k = 1, 2, 3, 4$

Proposition 1 Suppose $(r_{k} - c_{k}) < 0$ for all $k = 1, 2, 3$ . Then $E Π_{4} > E Π_{3} > E Π_{2} > E Π_{1}$ and the IPR have an increasing value along the development phases of the PCP. If instead $(r_{k} - c_{k}) > 0$ for some $E Π_{k} > 0$ , with $k = 1, 2, 3$ , then the IPR in the next phase has a larger value, that is $E Π_{k + 1} > E Π_{k}$ , if $E Π_{k}$ . is sufficiently large.

Therefore, under the conditions of the above analysis, the economic value of the IPR varies across different phases, and would always be increasing whenever the reward paid by CA to the participating firms does not cover their costs. As a consequence, the sale price of IPR should change with the phase of PCP development, and whether or not they are sold at commercialisation phase.

Methodology implementation

The above methodology may provide guidelines on how to estimate the economic value of the IPR in a PCP. However, as already hinted at, there could be problems with its implementation, as some of the quantities may not be easy to estimate or have been introduced in an oversimplified way. In the next section we discuss some such critical issues.

R&D investment and success probability as a strategic choice

The first point concerns the possible relation between the firm’s R&D investment, in a given phase of the PCP, and the firm’s probability to be selected for the next phase. In the previous section they were introduced independently of each other, as exogenous quantities, not explained in terms of a strategic choice by the firm itself. However we suggested that, perhaps, a more realistic way to look at success probabilities is to see them as related to the amount of resources invested by the firm in a particular PCP development phase, with respect to the investment made by the other competitors.

As an example, consider the following simple situation. According to the EC 2007 communication, suppose CA invites five firms in the first phase, three firms in the second phase and two firms in the third phase of the PCP. Further, suppose they all accept and each firm f, with $f = 1, 2, .., 5$ , has to decide how much to invest in that phase. Moreover, $c_{f 1}$ stands for the costs in phase 1 of firm f and $C_{1} = \sum_{f = 1}^{5} c_{f 1}$ are the total costs, that is, the overall amount of monetary resources invested in phase 1 by the invited companies. Then a simple way to model each firm’s f success probability $π_{f 2}$ , namely the probability of being selected for the next phase 2, could be

π_{f 2} = {\begin{matrix} 3 \frac{c_{f 1}}{C_{1}} i f \frac{c_{f 1}}{C_{1}} \leq \frac{1}{3} \\ 1 o t h e r w i s e \end{matrix}

that is defined as in a Tullock type-of-contest (Konrad, 2009; Vojonovic, 2015) where the success probability is proportional to the own R&D investment, with respect to the total R&D investment made by all participants.

Since $\sum_{f = 1}^{5} \frac{c_{f 1}}{C_{1}} = 1$ , the reason why in (6) appears a multiplicative term 3 on the right-hand side is the following. With three firms qualifying for phase 2, out of five invited firms, there are $(\begin{matrix} 5 \\ 3 \end{matrix}) = \frac{5!}{3! 2!} = 10$ possible triples of companies selected by CA. Table 1 summarises such combinations.

Table 1.

$Possible triples of firms qualified to phase 2$ .

A	1	2	3
B	1	2	4
C	1	2	5
D	1	3	4
E	1	3	5
F	1	4	5
G	2	3	4
H	2	3	5
I	2	4	5
L	3	4	5

From Table 1 we can construct Table 2, containing the probability of qualification for each firm.

Table 2.

$Probability of qualification to phase 2.$

$C o m p a n y$
1	$π_{12} = P (A) + P (B) + P (C) + P (D) + P (E) + P (F)$
2	$π_{22} = P (A) + P (B) + P (C) + P (G) + P (H) + P (I)$
3	$π_{32} = P (A) + P (D) + P (E) + P (G) + P (H) + P (L)$
4	$π_{42} = P (B) + P (D) + P (F) + P (G) + P (I) + P (L)$
5	$π_{52} = P (C) + P (E) + P (F) + P (H) + P (I) + P (L)$

Therefore,

\sum_{f = 1}^{5} π_{f 2} = 3 (P (A) + P (B) + P (C) + P (D) + P (E) + P (F) + P (G) + P (I) + P (H) + P (L))

However

P (A) + P (B) + P (C) + P (D) + P (E) + P (F) + P (G) + P (I) + P (H) + P (L) = 1

and so

\sum_{f = 1}^{5} π_{f 2} = 3

which explains the presence of the multiplicative 3 in $π_{f 2} = 3 \frac{c_{f 1}}{C_{1}} .$

Expression (6) could be justified on the ground that qualification to phase 2 is akin to winning a lottery, where 3c_f1 is the amount of money spent by firm f to buy tickets while C ₁ is the total amount spent by participants to buy tickets. It must also be pointed out that formulation (6) considers all firms symmetric, that is, with the same ability – a point which will be discussed later. Finally, notice that a more articulated model should also take into account the possibility that company f could qualify for the second phase with either 0 or 1 competitor. Yet, without major loss of generality, to keep the argument simple we only considered the EC suggestion, with three firms qualified for phase 2. Similar considerations would hold for the following phases.

In this case, if $c_{1} = (c_{11,}, c_{21,}, \dots; c_{51,})$ is the vector of the companies’ costs and $c_{- f 1} = c_{1} - {c_{f 1}}$ then, due to firms’ symmetry, assuming $3 \frac{c_{f 1}}{C_{1}} < 1$ and that, for simplicity, each firm has the same discount factor, company first phase profit $Π_{f 1}$ could be written as

Π_{f 1} (c_{f 1}, c_{- f 1}) = {\begin{matrix} δ E Π_{f 2} + r_{1} - c_{f 1} & w i t h p r o b a b i l i t y & 3 \frac{c_{f 1}}{C_{1}} & i f c_{f 1} > 0 \\ r_{1} - c_{f 1} & w i t h p r o b a b i l i t y & 1 - 3 \frac{c_{f 1}}{C_{1}} & i f c_{f 1} > 0 \\ 0 & i f c_{f 1} = 0 \end{matrix}

and its expected profit is given by

E Π_{f 1} (c_{f 1}, c_{- f 1}) = 3 δ E Π_{f 2} \frac{c_{f 1}}{C_{1}} + r_{1} - c_{f 1}

Assuming that company f chooses its investment $c_{f 1}$ in order to maximise (7), we obtain

C_{1} = \frac{12 δ E Π_{f 2}}{5} (8 a) a n d c_{f 1} = \frac{12 δ E Π_{f 2}}{25} f o r a l l f = 1, 2.., 5

Consequenly, when investments are defined as in (8a) and (8b) the probability of firm f to qualify for the second phase is

π_{f 2} = 3 \frac{c_{f 1}}{C_{1}} = \frac{3}{5}

as if the triple selected by CA or phase 2 was chosen with uniform probability from the $10$ possible triples of Table 1. That is, all firms share the same success probability, which is what both the companies and CA may think is the case when they have no elements to believe that companies have different chances to succeed, namely they are fully uncertain of who will be selected for the next phase.

In this case, expected profit would be equal to

E Π_{f 1} (c_{f 1}, c_{- f 1}) = \frac{3 δ E Π_{f 2}}{25} + r_{1} > 0

A few comments are in order.

First, notice that expressions (8a) and (8b) depend on prospective profits $δ E Π_{f 2}$ only, and not on current reward $r_{1} .$ The intuition is simple; while in phase 1 the company is not sure whether it will obtain $δ E Π_{f 2}$ , the reward r ₁ has been modelled as a compensation received with certainty from CA. Hence, if $E Π_{f 2} = 0$ or $δ = 0$ , the company would not invest at all in the first phase. The motivation, however, would be different in the two cases: in the former case it is because the firm would expect no future revenue, while in the latter it is because for the firm it is too costly to wait for future outcomes.

Therefore, once r ₁ is received, a company maximising expected profit would choose how much to invest considering only future profits. Therefore, if firms are paid exclusively for participation, as a compensation for the R&D costs, with expected profit maximisation r ₁ would not operate as an incentive to increase R&D investments in phase 1.

Given the above considerations, if r ₁ does not increase the firm’s investment it will play no role in increasing the probability of a successful discovery, which in turn is positively related to the level of R&D investments of the firms.

Indeed with a profit maximising company, for r ₁ to act as an incentive for increasing a company’s R&D expenditures, it should be paid (at least part of it) conditionally on the company being qualified to phase 2. Indeed, in this case it is easy to see that (8a) would become $c_{f 1} = \frac{12 r_{1} δ E Π_{f 2}}{25}$ and so increasing also in $r_{1} .$ As a consequence it would be $E Π_{f 1} (c_{f 1}, c_{- f 1}) = \frac{3 r_{1} δ E Π_{f 2}}{25}$ , and if $\frac{12 δ E Π_{f 2}}{25} > 1$ then $c_{f 1} > r_{1}$ . Finally, if $r_{1} \leq 1$ then the level of profit $\frac{3 r_{1} δ E Π_{f 2}}{25}$ would be lower than the profit level $\frac{3 δ E Π_{f 2}}{25} + r_{1}$ , while if $r_{1} > 1$ it will be $\frac{3 r_{1} δ E Π_{f 2}}{25} < \frac{3 δ E Π_{f 2}}{25} + r_{1}$ if $\frac{3 δ E Π_{f 2}}{25} < \frac{r_{1}}{r_{1} - 1}$ that is if prospective profits or the discount factor are sufficiently low, otherwise would be higher.

To summarise, the criterion by which CA would pay r ₁ to an expected profit maximising company, that is, whether just for participation or conditional to qualification to subsequent phases, will affect its R&D investments and then its profits.

The investment is positively related to the discount rate $δ$ , and therefore would go to zero if $δ$ is small enough, namely if the interest rate currently prevailing in the market would be sufficiently high.

As stated above, the chosen level of investment is the same, symmetric, for each company because we assumed symmetry in the success probability function. A more general formulation of $π_{f 2}$ could be

π_{f 2} = 3 \frac{c_{f 1}^{a_{f}}}{c_{11}^{a_{1}} + c_{21}^{a_{2}} + .. + c_{51}^{a_{5}}}

where $a_{f} > 0$ with $f = 1, 2, .., 5$ is a coefficient specifying how productive is the investment made by company f in phase 1 of the PCP. In the previous symmetric case, $a_{f} = 1$ for all firms.

Finally, if the company would not pursue expected profit maximisation, but rather invest in R&D as much as possible in the first phase, up to the breakeven level of the expected profit, then the chosen level of investment solves the equation

E Π_{f 1} (c_{f 1}, c_{- f 1}) = 3 δ E Π_{f 2} \frac{c_{f 1}}{C_{1}} + r_{1} - c_{f 1} = 0

Still with symmetric investments, the solution is given by

c_{f 1} = \frac{3 δ E Π_{f 2}}{5} + r_{1}

which is larger than (8a) and increasing in r ₁.That is, expected profit maximisation would reduce the company investment in the first phase, with respect to when investment is made up to the expected profit breakeven level. In particular, in (12) firms would invest $60 %$ of the future expected profit plus the CA reward r ₁, hence more than the latter.

Assume, with no loss of generality, that firms qualify for phase 2. Then, analogously for a generic firm, with $f = 1, 2, 3,$ qualified for phase 2 the profit, assuming $2 \frac{c_{f 2}}{C_{2}} < 1$ , would be

Π_{f 2} (c_{f 2}, c_{- f 2}) = {\begin{matrix} δ E Π_{f 3} + r_{2} - c_{f 2} & w i t h p r o b a b i l i t y & 2 \frac{c_{f 2}}{C_{2}} & i f c_{f 2} > 0 \\ r_{2} - c_{f 2} & w i t h p r o b a b i l i t y & 1 - 2 \frac{c_{f 2}}{C_{2}} & i f c_{f 2} > 0 \\ 0 & i f c_{f 2} = 0 \end{matrix}

and its expected profit defined as

E Π_{f 2} (c_{f 2}, c_{- f 2}) = 2 δ E Π_{f 3} \frac{c_{f 2}}{C_{2}} + r_{2} - c_{f 2}

Maximising (13), and still considering symmetry of investments and of the discount factor, provides as solutions

C_{2} = \frac{4 δ E Π_{f 3}}{3} (14 a) a n d c_{f 2} = \frac{4 δ E Π_{f 3}}{9} f o r a l l f = 1, 2, 3

14b

where $C_{2} = c_{12} + c_{22} + c_{32} .$ In the second phase it would be optimal for the company to invest about $44 %$ of the future profits.

Hence

E Π_{f 2} (c_{f 2}, c_{- f 2}) = \frac{2 δ E Π_{f 3}}{9} + r_{2} > 0

Finally, assuming that only $f = 1, 2$ qualify for the third phase of the PCP, and that one of them will be awarded the procurement contract after the PCP, then for the generic firm

Π_{f 3} (c_{f 3}, c_{- f 3}) = {\begin{matrix} δ E Π_{f 4} + r_{3} - c_{f 3} & w i t h p r o b a b i l i t y & \frac{c_{f 3}}{C_{3}} & i f c_{f 3} > 0 \\ r_{3} - c_{f 3} & w i t h p r o b a b i l i t y & 1 - \frac{c_{f 3}}{C_{3}} & i f c_{f 3} > 0 \\ 0 & i f c_{f 3} = 0 \end{matrix}

where $C_{3} = c_{13} + c_{23} .$ Therefore

E Π_{f 3} (c_{f 3}, c_{- f 3}) = δ E Π_{f 4} \frac{c_{f 3}}{C_{3}} + r_{3} - c_{f 3}

and maximising (16), again with symmetric investments, we obtain

C_{3} = \frac{δ E Π_{f 4}}{2} (17 a) a n d c_{f 3} = \frac{δ E Π_{f 4}}{4} f o r a l l f = 1, 2

17b

so that

E Π_{f 3} (c_{f 3}, c_{- f 3}) = \frac{δ E Π_{f 4}}{4} + r_{3} > 0

Therefore, in the third phase it would be best for the company to invest about $25 %$ of the prospective profits.

Numerical example

To gain further insights on what the model prescribes, it could be interesting to present a simple numerical example. Suppose the interest rate is $i = 0.05 = 5 %$ hence $δ = \frac{1}{1 + i} = \frac{1}{1.05} = 0.95.$ Moreover, assume $E Π_{f 4} = 10.000.000 €$ and $r_{3} = 500.000 €$ . Then $c_{f 3} = 2.380.952 €$ and $E Π_{f 3} = 2.880.952 €$ . Moreover, suppose that $r_{2} = \frac{r_{3}}{2} = 250.000 €$ , which implies $c_{f 2} = 1.219.450 €$ and $E Π_{f 2} = 859.725 €$ . Finally, if $r_{1} = 150.000 €$ then $c_{f 1} = 393.017 €$ and $E Π_{f 1} = 248.254 € .$ In each of the three phases, the firm is investing more than the rewards obtained from CA. This is due to the fact that in the example CA is assumed to pay every firm invited in each phase, and not only those selected for the next phase. As above, while in this case $E Π_{f k}$ is increasing with r_k , the investment $c_{f k}$ is independent of r_k . Consistently with proposition 1 in the example, expected profits, and so the IPR market price, increase along the three phases.

The example shows that testing the goodness of the model, in predicting firms’ behaviour, amounts to first estimate $E Π_{f 4}$ , then solving backward for all investments and expected profits levels, that is the IPR prices.

Expected rate of return

Why should a company employ resources in a PCP? If the prevailing interest rate in the market is $i > 0$ , would it be more profitable for the company to invest in alternative projects and obtain i additional euros, for each euro invested, or spend resources in a PCP? To answer this question we need to compare the rate of return on a PCP project with i, that is, how many additional euros are expected to obtain for each euro invested in the PCP.

As well as for expected profits and costs, the PCP rate of return will vary across its different phases.

Let us start by considering the first phase; if $ρ_{f 1}$ is the rate of return of company f in phase 1, then

ρ_{f 1} = \frac{E Π_{f 1} (c_{f 1}, c_{- f 1})}{c_{f 1}} = \frac{\frac{3 δ E Π_{f 2}}{25} + r_{1}}{\frac{12 δ E Π_{f 2}}{25}} = \frac{1}{4} + \frac{25 r_{1}}{12 δ E Π_{f 2}} > 25 %

As compared to the interest rate currently prevailing in the economy, around $2 - 4 %$ , the return rate of the PCP would be remarkably larger, which would likely compensate for the higher risk of the inititiave. It is worth noticing that $ρ_{f 1}$ decreases with the expected profits $E Π_{f 2}$ . Though perhaps counterintuitive at first, this takes place because the reward r ₁, in the model, is independent of $E Π_{f 2}$ . Hence, the higher $E Π_{f 2}$ the larger the costs, which will tend to decrease the positive effect of r ₁ on the rate of return.

Likewise, for firms qualified in the second phase, the rate of return $ρ_{f 2}$ would be

ρ_{f 2} = \frac{E Π_{f 2} (c_{f 2}, c_{- f 2})}{c_{f 2}} = \frac{\frac{2 δ E Π_{f 3}}{9} + r_{2}}{\frac{4 δ E Π_{f 3}}{9}} = \frac{1}{2} + \frac{9 r_{2}}{4 δ E Π_{f 3}} > 50 %

while in the third phase

ρ_{f 3} = \frac{E Π_{f 3} (c_{f 3}, c_{- f 3})}{c_{f 3}} = \frac{\frac{δ E Π_{f 4}}{4} + r_{3}}{\frac{δ E Π_{f 4}}{4}} = 1 + \frac{4 r_{3}}{δ E Π_{f 4}} > 100 %

an impressively high rate of return.

Therefore, according to our analysis, most probably participating in a PCP would seem to be rather convenient for an expected profit maximising company. Therefore, if the analysis is a good description of what takes place in a PCP procedure, then CA should have no major problems in attracting firms to participate in a PCP. Notice that expected return rates would be sufficiently high even if $r_{k} = 0$ , with $k = 1, 2, 3$ . However, it may be that $r_{k} < c_{k}$ prevent firms’ participation in a PCP due to lack of resources which, if unavailable, would not allow to pursue even the first phase. For this reason, CA should ensure that invited companies have enough funds at least to participate, even if not enough to pursue profit maximisation.

Expected revenue

It is clear from the previous analysis that as long as $δ > 0$ , the size of $E Π_{4}$ , namely the expected profits at commercialisation phase, is the most important driver of R&D investment in each PCP phase. Therefore, this is also what should increase the probability to find a satisfactory innovative solution to the problem of CA. However, some points are worth mentioning on this.

First, for both the companies and CA, it may not be easy to obtain a reliable estimate of future revenues and costs, once at a commercialisation phase. As the PCP proceeds along its phases, potential demand may change, similar solutions may enter the market, etc., all of which could contribute to update the estimate of prospective profits. As a result, an R&D investment level that was considered optimal in one phase may turn out to be suboptimal in retrospect because estimated profits are now different. Likewise, if in phase 1 a company plans to invest a certain amount of resources in the second phase, upon reaching phase 2 it may change decision because estimates on future profits have changed.

Based on the above considerations, as already said, the company and CA may entertain different views on prospective profits and then on the value of IPR. This might cause controversy in case CA wants to retain (at least part of) the IPR, as well as when other third parties would be willing to buy the IPR.

Conclusions

In the paper we considered the pre-commerical procurement for innovation, introduced by the EC in 2007. In it, a main economic incentive suggested by the EC to attract companies in the PCP and invest in R&D is to leave the IPR of the innovative solution with the firm. As important as it appears to be, so far a methodology for approaching the economic evaluation of the IPR seems to be missing. In this paper, we proposed such methodology and argued how the market value of IPR must be founded on prospective revenues and costs, related to potential commercialisation of the would-be innovative solution, as well as to the probabilities of being selected through the PCP phases, the R&D costs and rewards of the CA to the firms.

We also discussed that if the likelihood of finding the needed solution to the CA problem depends on how much firms would invest in R&D, then the objective function of the relevant companies, expected profit maximisation versus breakeven or others, could meaningfully affect the amount of investments and so the probability of finding a successful innovative solution in the PCP.

If the proposed methodology may have the merit of providing guidelines on how to proceed to estimate the economic value of IPR, it also has some limitations. First, as already stated, even if different subjects agree on the methodology, they may produce different estimates on some of the crucial quantities, such as success probabilities and expected future revenues and costs. This is due to the intrinsic difficulty in finding reliable estimates for R&D processes concerning new solutions whose development, by their own nature, has not yet been experienced. It would therefore be important to have a sufficiently rich data set of past projects available, for example, that of the US Department of Defence (DoD) related to the Small Business Innovation Research (SBIR) (Bhattacharya, 2018). For this reason it will be highly desirable if PCP cases would be collected, and information organised in publicly available data sets.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Nicola Dimitri

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