Abstract
We describe a model examining how a firm might choose the package size and price for a product that deteriorates over time. Our model considers four factors: (1) the usable life of the product; (2) the rates at which consumers use the product; (3) the relation between package size and the variable cost of the product; and (4) the minimum quantities consumers seek to consume for each dollar they spend (we call these reservation quantities). We allow heterogeneity in the usage rates and reservation quantities for the consumers. We show that when the cost increases as a linear or convex function of the package size, the firm should make packages of the smallest possible size. Smaller packages reduce waste and allow consumers to more closely match their purchases with desired consumption. This in turn allows the firm to charge a higher unit price and also sell more unit volume. The results imply that in a market with multiple package sizes (produced by the same or competing firms), at least one of the packages must have the smallest possible size, provided the fixed cost of making the product is sufficiently low. For concave cost functions, the firm may find it optimal to make larger than smallest-size packages.