Inventory Levels in the Presence of Competitors

To develop intuition regarding the optimal inventory levels carried by retailers in the presence of competitor, consider a retailers inventory decision when faced with uncertain demand. Because the general model is 

Assume that Retailer 1 buys the product from a supplier for 1 per unit and has a retail price of 3.80 per unit. Assume that holding cost for leftover inventory is 0.2 per unit. If this were a profit-maximizing retailer, the marginal cost per unit short (Q) is 2.80 and the marginal 

su esting an inventory level of 40 units. The associated expected profit is 64, with the following calculation  

Retailer 2, in the same market region, has a similar demand distribution from a separate primary market. Assume that customers who face a stockout at Retailer 1 go to Retailer 2 and vice versa. Thus, the demand faced by Retailer 1 for a given inventory level held by Retailer 2 is obtained as the sum of Retailer Is primary demand plus spillover demand from Retailer 2. Given an inventory Q = 40 held by Retailer 2, the spillover demand received by Retailer 2 has the distribution shown in Table 3.2. 

The total demand faced by Retailer 2 is the sum of primary demand and spillover demand from Retailer 1. If the rows represent the level of 

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