Profit of a colluding firm, is always an increasing function of technological improvement, i.e., a cost reducing technological improvement (a reduction in \(s\)), always enhances an individual firm’s profit under collusion. However, the same may not hold under Cournot competition.
Proposition 1
A technological improvement that reduces :
(i). unambiguously increases a firm’s profit under collusion;
(ii). increases a firm’ profit under Cournot oligopoly iff \(n\le s+3\).
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)
The above proposition shows that under collusion, technological improvement always increases an individual firm’s profit. However, when Cournot oligopoly is the market structure with quadratic costs, cost cutting technological improvement would not necessarily always increase an individual firm’s profit. In this case a decline in \(s\) raises a firm’s profit if and only if the number of firms is restricted to \(n<s+3\) or technology is as per the following relationship \(s>n-3\). If \(n\le 3\) then a cost cutting technological improvement increases an individual firm’s profit with certainty. However, a cost cutting technological improvement would not increase an individual firm’s profit with certainty if \(n>3\). Thus, in our set up, there would be conditional innovation by the firms, i.e., innovation contingent upon the number of firms in the market, as per the required condition of \(n<s+3\). This is very different from a Cournot model with constant marginal cost where cost cutting innovation is always profitable.
As stated above, the above condition, \(s>n-3\), also impacts innovation incentives of the firms, which we attempt to analyze. Let \(s\in \left[0, S\right]\), \(0\) being the most efficient and \(S\) being the least. Clearly, \(s\left(n\right)=n-3\) is the profit – neutral technology line (from investment perspective) and as is straight forward that \({s}^{{\prime }}>0\). A/ny arbitrary \({n}_{o}\in \left(3\right., \left.N\right]\) corresponds to a specific \({s}_{o}\) on the profit – neutral technology line, such that \(\forall s\in \left({s}_{o}\right., \left.S\right]\) innovation is profit enhancing and hence rewarding and \(\forall s\in \left(0\right., \left.{s}_{o}\right]\) destruction is profit enhancing and hence rewarding. Thus, it can generally be said that, for the number of firms greater than 3 the profit neutral line clearly indicates the regions of innovation, \(A\), and destruction, \(B\), as shown in Fig. 1.
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Proof
See above discussion and Fig. 1. Q.E.D.
Given \(n\in \left(3\right., \left.N\right]\), region \(A\) is the region of un/conditional innovation while \(B\) is the region of un/conditional destruction of technology. In our model, innovation/destruction of technology depends upon both the actual level of prevailing technology, \({s}^{a}\) and the number of firms in the market, \(n\). As stated earlier, for any arbitrarily chosen \(n\), say \({n}_{i}\) there is a corresponding technology level on the profit – neutral technology line, \({s}_{i}\). However, given \(n={n}_{i}\), \({s}_{i}^{a}\) can be anywhere in the range from \(0\) to \(S\), i.e., \({s}_{i}^{a}\in \left(0\right., \left.S\right]\). The actual location of \({s}_{i}^{a}\) determines whether innovation or technological destruction would be undertaken by the firms. If \({s}^{a}\in \left({s}_{o}\right., \left.S\right]\), then \(A\) is the region of innovation where innovation is undertaken by firms with certainty. However, in general, innovation is undertaken by firms iff \({s}^{a}\in \left({s}_{i}\right., \left.S\right]\); hence \(A\) can also be thought of as the region of conditional innovation. Similarly, region \(B\) can be interpreted with respect to technological destruction.
![](data:image/png;base64,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)
Proof
See above discussion and Fig. 1. Q.E.D.
When \(n<3\), innovation is unconditionally and with certainty undertaken by firms. Here, innovation by firms is independent of the level of technology. The same is not true for the case(s) when \(n>3\). For \(n>3\), as the number of firms increases, the probability of unconditional innovation, \(\rho =\frac{\theta }{S}; \theta =(S-{s}_{o})\), shrinks and ultimately converges with zero. However, unconditional innovation and technological destruction are mutually exclusive, and given an arbitrary \({n}_{o}\in \left(3\right., N)\) depend upon \({s}_{0}^{a}\). \(\forall {s}_{0}^{a}\in \left({s}_{o}\right., \left.S\right]\), unconditional innovation is undertaken while unconditional technological destruction is undertaken \(\forall {s}_{0}^{a}\notin \left({s}_{o}\right., \left.S\right]\). Thus, the location of \({s}_{0}^{a}\in \left(0\right., \left.S\right]\) dictates one of the said outcomes (of innovation or technological destruction).
![](data:image/png;base64,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)
Proof See above discussion and Fig. 1. Q.E.D.
The above propositions and discussion with regard to the \(s\) and \({n}_{o}\in \left(3\right., \left.N\right]\) also convey some information with respect to the magnitude of innovation and destruction. Consider an arbitrarily chosen \({n}_{o}\in \left(3\right., \left.N\right]\). We know that this \({n}_{o}\) corresponds to a specific \({s}_{o}\) on the profit – neutral technology line. Consider \({n}_{1}\in \left(3\right., \left.{n}_{o}\right];\)where \({n}_{1}\) corresponds to the actual number of firms. As per proposition 4, given \({n}_{1}\), for \({s}_{1}^{a}\in \left({s}_{1}\right., \left.S\right]\), innovation would be undertaken by the firms. However, the actual magnitude of potential innovation may be given by \({\alpha }_{1}=({s}_{1}^{a}-{s}_{0})\), as innovation is rewarding until \({s}_{1}^{a}={s}_{0}\), hence it would be undertaken until attainment of this equality. Given a specific \(n\), once this equality is attained, further innovation is not rewarding. It can be generalized for any \({n}_{i}\in \left(3\right., \left.{n}_{o}\right]\) and corresponding \({s}_{i}^{a}\in \left({s}_{i}\right., \left.S\right]\) and be given as \({\alpha }_{i}=({s}_{i}^{a}-{s}_{i})\). It is also straight forward that in the given situation innovation would be undertaken with certainty. However, \({\alpha }_{i}={\alpha }_{i}\left({n}_{i}\right)\) and \({\alpha }_{i}^{{\prime }}<0\). Similarly, we may think of the magnitude of potential technological destruction, given by \({\delta }_{i}\). Clearly, for \({\delta }_{i}>0\), \({s}_{i}^{a}\) must \(\in \left(0\right., {s}_{i})\). \({\delta }_{i}=({s}_{i}-{s}_{i}^{a})\). \({\delta }_{i}={\delta }_{i}\left({n}_{i}\right)\) and \({\delta }_{i}^{{\prime }}>0\). \({\alpha }_{i}\left({n}_{i}\right)\in (0, \left({s}_{i}^{a}-{s}_{i}\right))\) while \({\delta }_{i}\left({n}_{i}\right)\in \left(0\right., ({s}_{i}-{s}_{i}^{a}))\). Thus, no matter where \({s}_{i}^{a}\) is located in the interval \(\left(0\right., S)\), ultimately, through innovation or technological destruction, it would converge with the profit – neutral technology line, i.e., \({s}_{i}={n}_{i}-3\).
![](data:image/png;base64,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)
(i). \(\forall {n}_{i}\in \left(3\right., \left.{n}_{o}\right]\) and corresponding \({s}_{i}^{a}\in \left({s}_{i}\right., \left.S\right]\), the magnitude of innovation is \({\alpha }_{i}=({s}_{i}^{a}-{s}_{i})\).
(ii). \({\alpha }_{i}={\alpha }_{i}\left({n}_{i}\right)\) and \({\alpha }_{i}^{{\prime }}<0\).
(iii). \(\forall {n}_{i}\in \left(3\right., \left.{n}_{o}\right]\) and corresponding \({s}_{i}^{a}\in \left(0\right., \left.{s}_{i}\right]\), the magnitude of technological destruction is \({\delta }_{i}=({s}_{i}-{s}_{i}^{a})\).
(iv). \({\delta }_{i}={\delta }_{i}\left({n}_{i}\right)\) and \({\delta }_{i}^{{\prime }}>0\).
(v). irrespective of its initial location in the interval \(\left(0\right., S)\), ultimately, \({s}_{i}^{a}\) converges with the profit – neutral technology line, i.e., \({s}_{i}={n}_{i}-3\). Thus, the profit – neutral technology line, i.e., \({s}_{i}={n}_{i}-3\) is the equilibrium outcome.
Proof See the above discussion and Fig. 1. Q.E.D.