What are the first order condition? Using the focs for b1 and b2 to derive the same expression solve for using the unconstrained method above. That is, combing your two focs into one. B. (10) This is a model that has been used to determine current crude oil prices, as discussed in the Hamilton article that goes over the different models of crude oil price determination. So it should tell us what determined the current price of crude oil. Solve for 191 as a function of the other variables. What does the current price, p1 depend on, and how? That is, for example, ifs, storage costs, inuence the current price, p1, do higher storage costs cause p1 to increase or decrease? That is, is there a positive or negative correlation? C. [5) Solve this expression for the optimal b; as a function of the parameters of the model, p1. 192, B and the parameters of the model (c, s and 6). To be helpful, your answer should be in the form: b; = [l] where [l] is an expression that you need to work out. D. [5) Under what condition would b; be postiive. That is, under what conditions would the firm be willing to store crude oil from period 1 to period 2 instead of selling it all in period 1? Do your best to provide an explanation of this condition. This is a little more difficult and probably not something that you have done before. But it is standard fare for economics and finance. Hint: the sign of b; depends entirely on the term in square brackets from C. So you job is to find conditions when the term in square brackets is positive. E. [10) Is it ever rational for the producer to store crude oil in the case when the market is backwardated, or when p; > p2? If so, explain when this is so. If not, explain the reason. If you can do this referencing the \"cost of carry,\" your answer will be even better. ( This is tricky, but here's a hint: see if you can \"expand" 6p2 into an expression that is still equal to 6p2 but that includes more terms that are useful. F. [5) I am writing this on March 31, 2020, and the CME/NYMEX settlement prices for today are already available, but a preliminary. The market is in contango, with WTI selling for about $20 per barrel for delivery in May increasing to $30 and up for deliveries in the first few months afterward, and then increasing to close to $50 in the "out months" through February 2031.1 Assume that the (annualized, of course] real interest rate on a 30-day T-bill is 0.5%. We will assume a one-year planning horizon, so p1 is the price for May 2020 and p2 is the price one year later, and the choice faced by Longhorn Crude Marketing is whether to sell in May 2020 or store until May 2021. Longhorn Crude Marketing holds inventories of B = 1 00 million barrels. Storage costs $0.50 1 Although contracts are available for delivery this far out, there are no outstanding contracts at all for that month, and no volume at all today, meaning that situation continues. There is just too much uncertainty for companies to be locking in prices this far into the future. The last date for which there is any signicant "open interest," meaning someone holds the futures contract to buy and sell in that month, is December 2026 when open interest totals 2,508 contract [compared with over half a million for delivery this May). Beyond that, there are very few contracts open. However, there is one open contract for delivery in April 2030, so one buyer has offered to buy and one seller has offered to sell at $47.37 in that month
