Each month, the firm Cashco has 50% chance that an amount of $ 1,000 will be credited In its current account, and a 50% chance that the account is debited $ 1,000. As current account does not pay interest, Cashco considers that for each $ 1,000 in balance current account at the end of the month, there is a cost of $ 15 (in lost interest). In the beginning of each month, Cashco can adjust the balance of the current account by making a deposit or withdrawal (for an arbitrary amount), with a cost of $ 20 per transaction. Cashco should never leave the balance becomes negative. The company is currently reviewing both following policies for the management of its liquidity:

P1: the beginning of a month when the balance is $ 3,000, immediately lower the balance to $ 1,000. At the beginning of a month when the balance is $ 0, immediately pay back $ 1000.

P2: the beginning of a month when the balance is $ 3,000, immediately lowering the balance to $ 2,000. At the beginning of a month when the balance is $ 0, immediately back the balance to $ 2,000.

Which of the two policies P1 and P2 have the smallest total monthly cost (opportunity more transactions), on average? NB The sequence of events takes place every month as shown below:

1. Observe the balance

2. Adjust the balance (if desired)

3. The balance changes randomly

4. The opportunity cost is charged.