Which Firm are willing to Pay for Damaging their Goods and How Much? Application to a Damaged Goods Theory

The paper considers a firm with a market power which produces the same good of two different qualities using two lines of production, respectively. This allows to use second-degree price discrimination as there are two types of consumers in the market for the good. One type has lower valuation and the second has higher. Suppose, that firm decides to produce on one line. Then, it produces only higher quality good which allows them to move production closer to the MES and economize. However, in that case, they cannot price-discriminate anymore. Hence, it uses technology to damage a portion of higher quality goods in order to lower its quality. By this action, the firm incurs additional costs of damage but can discriminate by price. Such practice called Damaged Goods in the economic theory. In real life, it can be found in electronics, computer parts, software and other industries. This paper consist of two parts. The first part is the model of the firm which chooses between traditional production technology or damaging, as well as, it chooses pricing scheme. Restrictions on firm's and market's characteristics are derived that imply that optimal choice of the firm is to use damaging and price discrimination. Moreover, comparative statics are used to assess influence of parameters on firm's decision. In the second part, another model is built that allows firm to choose degree of damaging rather than simply choose whether to damage portion of good or not. Restrictions on parameters are derived that imply that the optimal choice of the firm is damaging and price discrimination. In addition, optimal level of damaging is defined. Finally, comparative statics are used to assess effect of variables on optimal level of damaging and firm's decision.