本文以Symeonidis (2003)的經濟模型架構為基礎，考量一雙佔市場，產品具水平差異和垂直差異下，廠商可通過產品研發來提升自身產品的品質。在兩廠商具對稱性性質下，廠商進行兩階段的賽局博弈，第一階段廠商同時決定其研發投入，第二階段廠商同時決定產量或價格。經過分析，我們可得以下幾個重要之結果：(i) 獨佔廠商的產品研發投入為最高。(ii) 數量競爭相較於價格競爭，廠商的產品研發投入更多。(iii) 在價格競爭下，廠商研發投入與廠商間的競爭程度呈負相關。在數量競爭中卻不一定。(iv) 價格競爭相較於數量競爭模式下，因廠商間的競爭更激烈，故產量較高價格較低、消費者福利較高、廠商利潤較低、且社會總福利較高。(v) 數量競爭下產品間的可替代性與消費者福利呈負相關，價格競爭下產品間的可替代性與消費者福利呈正相關。(vi) 兩種不同競爭方式下的市場總福利與產品間的可替代性呈負相關。

In this paper, we find that in the duopoly market, firms can enhance the quality of product through product R&D and the product have horizontal and vertical differences on the basis of Symeonidis (2003) economic model structure. In case of two firms with symmetric property, there will have two-stage game. The firms will decide their product R&D simultaneously in the first stage and decide the quantity or price in the second stage. It is shown that: (i) the monopoly firms have the highest input in product R&D.(ii) The R&D input in the Cournot competition is more than in the Bertrand competition. (iii) In the Bertrand competition, the firm’s R&D input is negatively correlated with their competition level but in Cournot competition is not necessarily.(iv) Since the firms in Bertrand competition is even more competitive in the quantity competition, so the quantity, consumer surplus and total social welfare is higher but lower in price and profit.(v) The inverse measure of the degree of horizontal product differentiation is negatively correlated with the consumer surplus in the quantity competition but positively correlated in price competition.(vi) The social total welfare and inverse measure of the degree of horizontal product differentiation have a negative correlation in both Cournot and Bertrand competition .

參考文獻
1)Arrow, K.J. (1962). Economic Welfare and the Allocation of Resources for Invention. The Rate and Direction of Economic Activity, Princeton University Press, N.Y.
2)Baumol, W.J. (2002). The Free-Market Innovation Machine : Analyzing the Growth Miracle of Capitalism. Princeton: Princeton University Press, 30-54.
3) Lin, P. and Saggi, K. (2002). Product differentiation, process R&D, and the nature of market competition. European Economic Review , 46(1), 201-211.
4) Qiu, L. (1997). On the Dynamic Efficiency of Bertrand and Cournot Equilibria. Journal of Economic Theory, 75(1), 213-229.
5) Scherer, F.M. and Ross, D. (1990). Industrial Market Structure and Economic Performance. Houghton Mifflin, Boston, MA.
6) Schumpeter, J. A. (1934). The Theory of Economic Development. Cambridge, MA: Harvard University Press.
7) Schumpeter, J. A. (1942). Capitalism, Socialism and Democracy. New York, NY: Harper and Row.
8) Singh, N. and Vives, X. (1984). Price and Quantity Competition in a Differentiated Duopoly. The RAND Journal of Economics, 15(4), 546-554.
9) Sutton, J. (1997). One smart agent. Rand Journal of Economics, 28, 605-628.
10) Sutton, J. (1998). Technology and Market Structure. MIT Press, Cambridge, MA.
11)Symeonidis, G. (1999). Cartel stability in advertising-intensive and R&D-intensive industries. Economics Letters 62, 121-129.
12) Symeonidis, G. (2000). Price and non-price competition with endogenous market structure. Journal of Economics and Management Strategy 9, 53-83.
13) Symeonidis, G. (2002). Cartel stability with multiproduct firms. International Journal of Industrial Organization 20, 339-352.
14) Symeonidis, G. (2003). Quality heterogeneity and welfare. Economics Letters, 78(1), 1-7.
15) Vives, X. (1985). On the efficiency of Bertrand and Cournot equilibria with product differentiation. Journal of Economic Theory, 36, 166-175.