Optimal normative policies for marketing of products with limited availability

We develop optimal normative policies for pricing and advertising of products with limited availability by including the traditional product diffusion parameters – innovation and imitation, and the scarcity effects generated due to limited product availability. 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.