Long Term Dynamics of Firm R&D Investment in Plant Breeding under Plant Breeders Rights

1. Long Term Dynamics of Firm R&D Investment in Plant Breeding under Plant Breeders Rights Mehdi Arzandeh Derek G. Brewin The 16th ICABR Conference – 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

2. Underinvestment in Plant breeding • The self-pollinating nature of some crops makes crop research output non-excludable. • Farmer saved seed can present a serious problem in capturing the benefits of breeding which contributes to the underinvestment in breeding. (Mallaet al. 2004) • Therefore, innovators in plant breeding industry without a regulated market, due to this non-excludability feature, are not able to capture their innovation outcome. The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

3. Intellectual Property rights • International agreements on Plant Breeders Rights (PBRs) and intellectual property rights have attempted to change the nature of knowledge from non-rival to rival and provide some return to breeding investment. • PBRs and patents provide the owner with exclusive commercial rights for a limited period of time. However, PBRs provide “farmer’s exemption” that allows farmers to save the seed for subsequent reproduction. (Galushko, 2008) The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

4. Is Canada falling behind? The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

5. Previous Models • A theoretical model of plant breeding was already developed by Galushko (2008). • Her three-stage static model does not account for the dynamics of producing R&D innovation since in that model, she only considers a one-shot game for R&D producing. • It is commonly modeled that in each stage, the private firm decides on the optimal number of research trials used to search for the highest yielding off-spring, which creates an improved variety with a specific expected yield. • This does not account for the lag between research expenditures and change in average yield nor it does for the fact that a rise in expected yield occurs as a result of a continuum process of R&D efforts. The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

6. Process of creating a new variety • Alston et al. 1998: The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

7. Law of motion for R&D investment • The lag between research expenditures and change in average yield is critical for the return on investment. Increments to the stock of knowledge occur through development and adoption of new higher-yielding varieties. (Malla et al; 2004) • Capital budgeting is a crucial issue in studying the important and complex capital investment decision of R&D programs (Childs and Triantis; 1999) and thus is accounted for in our model as well. The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

8. Product and Process Innovation • We also distinguish between two types of innovation so called innovation in process and innovation in product and try to account for dynamics of each type and their effect on the R&D outcome of the breeding firm. • The theoretical basis for a complementary relationship between innovation in the product and process dimensions has been espoused by other researchers (Athey and Schmutzler, 1995; Mantovani, 2006) with some empirical support (Brewin et al. 2009). The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

9. The Study’s Aim • Trying to develop a model for BPR’s regime proposing a dynamic version of a model first introduced in a static framework by Galushko (2008) to incorporate the effect of stock of knowledge on the rise in yield as well as accounting for the complementary relationship between process and product innovations. The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

10. The Model Set up • A Deterministic Optimization Problem. • At the beginning of each period, the R&D firm decides to how much invest in the process and in the product innovation research which together improve its ability to develop new varieties with lower cost in next periods. • At the end of each period, the firm introduces a new seed that improves the productivity of planting the crop and the portion of the heterogeneous farmers who are assumed to be uniformly distributed in the range [0, 1], buy it at price wnor continue using the existing generic seed at price we. The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

11. Farmers’ Profit Function • Farmer’s profit function planting the existing variety at time t: (1) • Farmer’s profit function planting new varieties at time t: (2) The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

12. New Variety Demand • Comparing the two profits, demand for development of a new variety is given by: (3) • Under PBR’s, once farmers buy the new seed, they use their own seed for replanting. It is assumed that they do not upgrade their seed to the Firm’s newer biotechnology variety. It implies that the R&D firm will not have the part of the market in the next periods, once it sells the new variety to it. The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

13. Dynamic Optimization Problem • The general form of the dynamic programing problem, the reformulated Bellman equation and the constraints facing by the firm at time t can be written as (4) The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

14. Modeling Complementarities • Brewin et al. (2009) assumed that the ex post realization of product () and process innovations () depend on both types of ex ante research: • If process and product innovation research are complementary, then > 0 and > 0, where subscripts represent partial derivatives with respect to that argument. The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

15. Modeling Complementarities • profit function of the firm for time t (5) • equations of law of motion for Z and C • (6) • (7) The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

16. Dynamic Optimization Problem • the problem in the second period (t=1) + (8) The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

17. Optimal Policy Functions • The optimal policy functions for period 1 • (9) • (10) The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

18. Dynamic Optimization Problem • The problem in the first period (t=0) (12) The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

19. Optimal Policy Functions • the optimal policy functions for period zero (13) (14) The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

20. Propositions • Proposition1. A decrease in the unitcost of innovation in product and in process or/and an increase in the amount of capital accessible for the R&D firm increases both R&D investment on innovation in process and in product which further increases the profitability of producing the new biotechnology seed for the R&D firm and planting it for the farmers. • Corollary1.A government policy that reduces the firm's unit cost of R&D research, such as a government subsidy on the cost of innovation, and a policy to increase the capital availability for the firm will enhance R&D firms' research activity. The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

21. Propositions • Proposition2. An increase in the difference between the prices of biotechnology seed and that of the existing generic seed will reduce the demand for the new variety. • Corollary2. Since increase in the new variety seed price raises the optimal amount of innovation in product and in process, the overall effect of an increase in the biotechnology variety price on the R&D profits and the level of investment on R&D depends on the elasticity of demand of the growers. The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

22. Propositions • Proposition3. Increase in the number of heterogeneous farmers increases the demand for the new variety and consequently stimulates investment on R&D in plant breeding. • Corollary3. Increase in the planted area of a crop (or size of the final product industry) raises the R&D investment. The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

23. Propositions • Proposition4. Increase in the costs of adopting a new variety decreases the demand for the biotechnology seed and decreases the benefits of R&D and investment on research. • Corollary4. A government policy such as a subsidy on the costs that reduces the farmers’ costs of adopting the new variety will enhance R&D firms' research activity. The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

24. Propositions • Proposition5. Increase in the unit cost of capital used in producing innovation in process or in product decreases the investment in the same innovation but the effect of it on the other type of innovation is ambiguous. • Corollary5. Over time, the type of innovation with more efficiency in using limited resources of the R&D firm will receive more investment. This might cause over-investment on one type and under-investment on the other one. If so, a government policy such as a subsidy on the costs of the type of innovation with a lower efficiency might enhance the outcome of R&D investment. The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

25. What Next… • A dynamic model of R&D investment has a lot of other advantages besides those pointed out in this study. • Once we upgrade this simple two period model to a model with infinite horizon, we can answer some other very important issues raised in the literature. • Some of these concerns that can be addressed by such a dynamic models are: • Falling in the IRR to investment in R&D • Overcapitalization of investment in R&D • Optimal amount of investment in R&D • And so on. The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

26. Dynamic Optimization Problem • Plugging the farmers’ demand for the new seed and the constraints into value function, it will be equivalent to The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

27. Value Function • The value function for period 1 (11) The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

28. Dynamic Optimization Problem • This problem is equivalent to The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.

29. Proposition 5 Proof • The effect of change in alpha and beta on the process innovation expenditure will be shown in this section as an example. The same argument holds for their effect on the product innovation. • Thus the effect of a change in the coefficient of innovation in product on the process innovation is ambiguous. • Therefore, the effect of a change in the coefficient of innovation in process on the amount of expenditure in process innovation is negative. The 16th ICABR Conference - 128th EAAE Seminar, June 24-27, 2012, Ravello, Italy.