Question

Consider two products whose demands are independent of each other. Assume that their demands are Normally distributed and they have identical cost structures. Assume we use the newsvendor model covered in the class, which gives you a framework for how one makes inventory decisions under demand uncertainty. If we combine the demands of the two products (i.e. Pool the demands) will the total inventory decrease or increase as compared to making decisions separately for the two products. Show your arguments carefully. Need to use equations to explain

Answer 1

If we consider two products whose demands are independent of each other then one of the two products can be complementary good of another good or substitute of another good.

Complementary good is a good whose demand increases with the popularity of its Complement good. Technically we can say that it displays and negative cross elastic of demand. Consider X is a complementary good to Y, if there is increase in the price of product X then there will be decrease in the price of product Y. For example:

1. Toothbrush is a complimentary good of the toothpaste. As the cost of producing a brush may be much more hirer than toothpaste but its demand totally depend on the sale of toothpaste. We have seen many of times that we get 1 toothbrush free with one packet of toothpaste.
2. Shoe brush is a complementary good of shoe polish. The cost of making shoe brush is much for hirer than the cost of making shoe polish and individually the price of Brush is much for higher than the price of shoe polish, but they are complementary products of each other. Many of time we have seen that shoe brush is free with shoe polish.

Substitute goods are having a positive cross price elasticity as the price of one good increases simultaneously the price of another good increases. for example:

1. Pepsi and Coca Cola.
2. Tea and coffee.
3. Windows operating system and LINUX operating system.