Pirates are about to set sail on a 2-period journey. They have 100 bags of barley (food) and must decide how much to consume in period 1 (c1) and period 2 (c2). The pirates get all the barley in period 1 and none in period 2. Unfortunately, rats will eat 50% of any barley saved to consume in period 2. Assume the Captain, who rations the food, has the following utility function: U(c1, c2) = c1c2

C) Now, in addition, assume that the pirates have a garden on their ship. Whatever barley the Captain chooses to plant will grow into 1.5 times as much barley in period 2. Planted barley is also subject to attack by rats. What is the "real interest rate?" What levels of consumption does the Captain choose in each period?