Comparative Statics Analysis of An Inventory Management Model with Dynamic Pricing, Market Environment Fluctuation, and Delayed Differentiation

We consider a general joint pricing and inventory management model with delayed differentiation, in which a firm serves a market with multiple products made from a generic one. The firm holds inventory for the generic product which is produced using multiple resources. Moreover, the market size, the attractiveness of each product, the firm's productivity, and the procurement cost of each resource all evolve over the planning horizon driven by an exogenous Markov process. Comparative statics analysis is essential for studying this model, offering insights on the impact of market environment fluctuation upon the firm's optimal pricing and inventory policy. Hence, we propose a new approach that combines the advantages of implicit function theorem (IFT) and monotone comparative statics (MCS) approaches to perform comparative statics analysis in our joint pricing and inventory management model under market environment fluctuation. The new approach applies to our model where the standard IFT and MCS methods are not easily amenable. Using our new comparative statics approach, we characterize the optimal pricing and production policy of the firm, and offer insights on how the firm should adaptively respond to market environment fluctuations.