On the planet Stinko, the principal industry is turnip growing. For centuries the turnip fields have been fertilized by guano which was deposited by the now-extinct giant scissor-billed kiki-bird. It costs $5 per ton to mine kiki-bird guano and deliver it to the fields. Unfortunately, the country’s stock of kiki-bird guano is about to be exhausted. Fortunately the scientists on Stinko have devised a way of synthesizing kiki-guano from political science textbooks and swamp water. This method of production makes it possible to produce a product indistinguishable from kiki-guano and to deliver it to the turnip fields at a cost of $30 per ton. The interest rate on Stinko is 10%. There are perfectly competitive markets for all commodities.
(a) Given the current price and the demand function for kiki-guano, the last of the deposits on Stinko will be exhausted exactly one year from now. Next year, the price of kiki-guano delivered to the fields will have to be $30, so that the synthetic kiki-guano industry will just break even. The owners of the guano deposits know that next year, they would get a net return of $25 a ton for any guano they have left to sell. In equilibrium, what must be the current price of kiki-guano delivered to the turnip fields?
(b) Suppose that everything is as we have said previously except that the deposits of kiki-guano will be exhausted 10 years from now. What must be the current price of kiki-guano? (1.110 = 2.59.)