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Katz (1986) - An Analysis of Cooperative Research and Development (view source)
Revision as of 21:09, 6 December 2010
, 21:09, 6 December 2010no edit summary
These have lead to three approaches:
#'''Use strong IP protection''', like patents, to maintain incentives - but this may actually reduce the efficient sharing of R&D as per Spence (1984).#Have lax property rights but '''use subsidies ''' to restore incentives - but this has dissemination problems when spillovers are weak (again see Spence), introduces monitoring problems as firms may spuriously report R&D expenses, and may have deadweight losses in the tax system.#'''Encourage cooperative R&D''', by permitting joint-ventures under anti-trust law.
The third approach is the topic of this paper and may be successful because:
*Can help avoid problems of opportunism and asymmetric information that arise in the sale of the innovations
*Monitoring R&D inputs is easy for firms
There is a moral hazard (essential a Team's Problem) effect potentially working in the other direction though. The strength of this depends upon the product market competition in the markets where the resulting innovation will be used. If firms were Bertrand competitors (in Constant Returs to Scale market) then they have no incentive to innovate (this way), however, if the innovation were used in unrelated product markets, this effect is zero.
===The Basic Set-up===
*For every <math>c\;</math> such that <math>i\;</math> is an active producer: <math>V_i^i(c) < 0\;</math>
*For every <math>c\;</math> such that <math>i\;</math> and <math>j\;</math> are active producers: <math>V_j^i(c) \ge 0, \; i\ne j\;</math>
These assumptions are satisfied by a number of standard oligopoly models including:
Where <math>0 \le \underline{\phi} \le \overline{\phi} \le 1\;</math>
A firm's R&D effort is denoted <math>r_i\;</math>, with <math>r=(r_1,\ldots,r_n)\;</math> being the vector. As we are using symmetry we use linear sharing rules, where <math>s^k\;</math> is given below. If firm <math>i \;</math> is a member then their total expenditure on R&D is:
:<math>s^k r_I + \frac{(1-s^k)}{k-1} \sum_{j \in K-\{i\}} r_j\;</math>
There is a deterministic relationship between a firm's marginal cost <math>c_i\;</math> and its effective level of R&D <math>z_i\;</math> as follows:
*<math>c \in \(\underline{c},\overline{c}\]\;</math>, where <math>\underline{c},\overline{c} \ge 0, \;\; \underline{c},\overline{c} \le \infty\;</math>
*<math>c\;</math> is C2 such that:
**<math>c' <0\;</math>
**<math>\lim_{z \to \infty}c'(z) = 0\;</math>
That is <math>c \;</math> is positive, decreasing and convex, starting from a high value of <math>\overline{c}\;</math> at <math>z = 0\;</math>, and declining asymptotically to <math>\underline{c}\;</math> as <math>z \to \infty\;</math>.
Also, we assume that:
:<math>V^i(\overline{c}) \ge 0, \quad \mbox{where }\; \overline_c = (\overline{c},\ldots,\overline{c})\;</math>
That is equilibrium profits are positive when no one does any R&D.
There are two equilibria, one in the corner where <math>z^0 = 0 = z^n\;</math> (when the term in the brackets is less than or equal to zero), and one in the interior where the sign of <math>z^n - z^0\;</math> is given by:
:<math>(1-s^n)(1 + (n-1) \phi^n \rho(c^0)) + (\phi^n - \underline{\phi}s^n(n-1)\rho(c^0)\;</math>
At this stage, firms can choose:
*<math>\phi \in [\underline{\phi},\overline{\phi}]\;</math>
*<math>s \in [0,\overline{s}]\;</math>, where it is possible that <math>\overline{s} \ge 1\;</math>
Assuming an interior solution to the development stage for all values of <math>c\;</math>, then for an industry wide cooperative agreement it must be the case that:
:<math>\phi^n = \overline{\phi} \;\mbox{and}\; s^n = \min (\overline{s}, \frac{1 + (n-1) \overline{\phi}\rho(c^n)}{(1+(n-1)\rho(c^n))(1+(n-1)\overline{\rho})}\;</math>
The proof for the first part is by strict dominance. With a positive sharing rule, and <math>\phi < \overline{\phi}\;</math>, it is always possible to raise <math>\phi\;</math> and simultaneously lower <math>s^n\;</math>, to make more profits and hold the effective level of R&D constant.
And again if full sharing is possible (i.e. <math>\overline{\phi} = 1\;</math>) then members will set <math>s^k \le \frac{1}{k}\;</math>.
