We develop optimal normative policies for pricing and advertising of products with limited availability by including the traditional
product diffusion parameters (Bass, 1969)–innovation and imitation, and the scarcity effects generated due to limited product
availability (Swami and Khairnar, 2003). Using optimal control methodology, our
pricing policy results suggest that a profit-maximizing firm gradually increases the price as the sales approach the product availability.
The optimal normative
advertising policy recommends gradually decreasing the expenditure on the awareness advertising and increasing the expenditure on the availability
advertising as the product diffusion progresses. These results are illustrated with suitable numerical examples.
Keywords Product diffusion models - Optimal control - Marketing policies