生產者之空間訂價及產品退還策略與零售業者間競爭行為之經濟分析

Journal of Taiwan Land Research Vol. 2, pp. 1~ 21

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Manufacturer's Spatial Pricing, Returns

Poli-cies and Retail Competition

Tao-Hsin Hsu and Ruey-Yih Lin

Abstract

The purpose of this paper is to explicitly incorporate manufacturer's returns policy incorporate into Weber's triangular location model and reexamine the effect on price and profit of manufacturer and retailers under alternative spatial pricing policies. To address this issue, the benchmark setting is there is a single upstream manufacturer provides a lim-ited shelf life product, and sells it to two downstream competitive retailers. The manufac-turer behaves like a Stackelberg leader, and the retailers must have stocks in hand before selling to consumers. Base on our results, we have the following conclusions. 1. Whether there is a returns policy or not, the equilibrium results make no difference. 2. The ranking of choice make variables under alternative pricing policies will not be influenced by retailer competition or returns policy. 3. When manufacturer accepts returns from the retailers, it intensifies the competition between retailers and benefits the manufacturer. The insight about the role of return policy is that it can be an another instrument to raise the manufacturer's profit.

Keywords: Returns policies, Spatial pricing, Retail competition

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pp. 79-98

Beckmann, M. J. (1976)
Spatial Price Policies Revisited.
Bell Journal of Economics, Vol. 7:619-630.

Greenhut, M. L. and Ohta, H. (1972)
Output under Alternative Spatial Pricing Techniques.

American Economic Review, Vol. 62:705-713.

Holahan, W. (1975)
The Welfare Effects of Spatial Price Discrimination.
American

Economic Review, Vol. 65:498-503.

Hwang, H. and Mai, C.-C. (1990)
Effects of Spatial Price Discrimination on Output, Welfare, and Location.
American Economic Review, Vol. 80:567-575.

Padmanabhan, V. and Png, I. P. L. (1995)
Returns Policies: Make Money by Making Good.
Sloan Management Review, Fall, 65-72.

Padmanabhan, V. and Png, I. P. L. (1997) Manufacturer's Returns Policies and Retail Competition. Marketing Science, Vol. 16(1):81-94.

Robinson, J. (1933), Economics of Imperfect Competition. London: Macmillian.

Schmalensee, R. (1981) Output and Welfare Implications of Monopolistic Third-Degree Price Discrimination. American Economic Review, Vol. 71:242-247.

Schwartz, M. (1990), Third-Degree Price Discrimination and Output: Generalizing a Welfare Result. American Economic Review, Vol. 80:1259-1262.

Singh, N. and Vives, X. (1984), Price and Quantity Competition in a Differentiated Duopoly.

Rand Journal of Economics, Vol. 15(4):546-554.

Varian, H. (1985), Price Discrimination and Social Welfare. American Economic Review, Vol. 75:870-875.