Suppose each customer purchase of a product generates $10 in profi t. Each month a customer either buys 0 or 1 unit of the product. If a customer bought last month, there is a 0.5 chance she will buy next month. If she last bought two months ago, there is a 0.2 chance she will buy next month. If she last bought three months ago, there is a 0.1 chance that she will buy next month.
If a customer has not bought for four months, there is no chance she will ever buy in the future.
Determine the value of a customer who last purchased the product last month, two months ago or three months ago. Assume profi ts are discounted at 1 percent per month.