Adaptive Expectations and Oil Price Instability: We mentioned in the text that trading across time is similar to trading across space in that individuals find opportunities to buy low and sell high. Unlike the case where individuals trade across space, however, speculators who trade across time has to guess what future prices will be. If they guess correctly, they will introduce greater price stability over time (just as exporters equalize prices across regions). We now ask what might happen if this is not the case. More precisely we will assume that individuals form adaptive expectations. Under such expectations, people expect prices in the future to mimic price patterns in the past.
A. Consider first the case of the oil industry. It takes some time to get additional capacity for oil production—so oil companies have to project where future oil prices will be in order to determine whether it is economically prudent to pay the large fixed costs of increasing their ability to pump more oil. They are, in essence, speculators trying to see whether to expend resources now to raise oil production in the future or whether to allow existing capacity to depreciate in anticipation of lower oil prices in the future.
(a) Begin by drawing a demand and supply graph for oil, with linear supply steeper than linear demand, and label the equilibrium price as p∗.
(b) Suppose that unexpected events have caused price to rise to p1. Next, suppose that oil companies have adaptive expectations in the sense that they believe future price will mirror the current price. Will they invest in additional capacity?
(c) If the demand curve remains unchanged but the oil industry in the future produces an amount of oil equal to the level it would produce were the price to remain at p1, indicate the actual price that would emerge in the future as p2. (Hint: After identifying how much the oil industry will produce on its supply curve at p1, find what price will have to drop to in order for oil companies to be able to sell their new output level.)
(d) Suppose again that firms have adaptive expectations and believe the price will now remain at p2. If they adjust their capacity to this new “reality” and demand remains unchanged, what will happen to price the next period? If you keep this going from period to period, will we eventually converge to p∗?
(e) Repeat (b) through (d)—but this time do it for the case where demand is steeper than supply. How does your answer change?
(f) How would your answer change if demand and supply were equally steep?
(g)While this example offers a simple setting in which speculative behavior can result in price fluctuations rather than price stability, economists are skeptical of such a simple explanation (which is not to say that they are skeptical of all explanations that involve psychological factors on how people might form incorrect expectations). To see why, imagine you are a speculator (who is not an oil producer) and you catch onto what’s going on. What will you do? What will happen to the patterns of oil prices that you identified in the different scenarios above?
B. Suppose again that the demand function for oil x is given by xd (p) = (A −p)/α and the supply function by xs (p) = (B +p)/β. Suppose throughout that B = 0 and β = 0.00001.
(a) What is the equilibrium price p∗ if A = 80 and α = 0.000006?
(b) Next, suppose that some unexpected events led to a price of p1 = 75 — but the underlying fundamentals—i.e. supply and demand curves—remain unchanged. If oil suppliers expect the price to remain at $75 in period 2, how much will they produce in period 2? What will the actual price p2 in period 2 be?
(c) Suppose period 2 unfolds as you expected in part (c)—and now oil suppliers expect prices to remain at p2. How much will they produce in period 3? What will price p3 be in period 3?
(d) If the same process continues, what will price be in period 10? In period 20?
(e) Next, suppose instead that A = 120 and α = 0.000014. What is the equilibrium price p∗.
(f) Suppose that p1 is unexpectedly 51 but the fundamentals of the economy remain unchanged. What are p2 and p3 (as defined in (c) and (d)) now? What about the prices in periods 10 and 11?
(g) Finally, suppose that A = 100 and α = 0.00001? What will be the price pattern over time if p1 is unexpectedly 75? What if it is unexpectedly 51?
(h) If you were a speculator of the type described in A(g), what would you do in period 2 in each of the three scenarios we have explored? What would be the result of this if there were other speculators who behaved similarly?