An economy, Shire, has two time periods. In the first period, there is only one consumer (Gandalf) and he is considering whether to buy a cottage and if so, in which period. Gandalf will live for two periods and is willing to pay a maximum price of 90per period for using a cottage. In the second period, two consumers - Bilbo and Frodo, are born. Bilbo and Frodo will only live in the second period. Each of them are willing to pay a maximum of 40 per period for using a cottage.

Suppose that in Shire, there is only one agent (Saruman) producing cottages. Further cottages are durable in the sense that if you purchase a cottage in one period, you can use it in the next period as well without repurchasing it. Also each cottage can only accommodate one person and only Saruman can sell cottages in Shire and subletting or leasing is not allowed.

Saruman and Gandalf are experts in both game theory and seeing the future - thus each of them know that Bilbo and Frodo are going to be born in period 2 and what their willingness to pay for using cottages are going to be.

Saruman is only interested in maximizing his revenue. He can only set prices for cottages (possibly different prices in different periods) and then has to supply cottages to whoever wants to purchase cottages at that price. What is the price that Saruman will set for cottages in the first period?