The implications of costs, capacity, and competition on product line selection

We consider a situation in which a manufacturer has to select the product(s) to sell as well as the selling price and production quantity of each selected product. There are two substitutable products in the consideration set, where product 2 has a higher quality and reservation price than that of product 1. By considering the cannibalization effect that depends on the selling price of each product, the manufacturer needs to evaluate the profit function associated with three different product line options: sell both products or only one of the 2 products. In order to examine the impact of costs, capacity, and competition on the optimal product line selection, optimal price, and optimal production quantity analytically, we present a stylized model in this paper so that we can determine the conditions under which a particular option is optimal.