Optimal Advertising and Product Durability Decisions in New Product Diffusion

Abstract

This paper studies the optimal advertising policy over the product life cycle of a semi-durable good whose failure rate is a design decision. The product adoption process draws from three sources of consumers: innovators who find the product directly, consumers influenced by advertising, and loyal customers making replacements. The revenue stream is composed of sales of new products, revenue from maintenance fees, and sales of replacement products. We propose a product diffusion model with both durable and non-durable properties and solve using optimal control. The guidelines for advertising during new product diffusion are simple to implement due to near-explicit solutions. We make recommendations for the design of product durability and note cases where the failure rate should be increased.

Keywords: Advertising; Dynamic Optimization; Product Failure; Planned Obsolescence; Durable Goods

JEL Classification: M37, C61, M30