This is mostly principles of microeconomics material, but I think it's a useful reminder about what to expect in commodity markets when there is a permanent increase in demand.
Here is a typical model of the short-run and long-run response to an outward shift in the demand curve:
The short-run supply curve (SRS) is steeper than the long-run supply curve (LRS), so at first the price rises from Pa to Pb, and this generally happens fairly quickly as shown on the second graph tracing price movements over time (i.e. the time to move from T1 to T2 is relatively short).
In the longer run, supply is more elastic because there is more time to respond (building now factories, stepping up production of existing factories, entry of new firms, etc.). But the elasticity of the LRS curve is dependent upon the commodity in question, so two different LRS curves are shown on the graph. For some goods like oil and other natural resources, we would expect the LRS to be fairly steep since new supplies are difficult to bring into production. But for other commodities like agricultural goods it is much easier to expand supply by bringing new land into production, enhancing productivity on existing farms, and so on, so the curve is more elastic.
Thus, the price path that we expect to see over time depends upon the commodity in question. For some goods, like wheat, we expect to see a price movement from a to b to c, i.e. the new long-run price will be near the old long-run price (as shown in the second diagram). However for other goods like oil or copper, we expect that the price path will move from a to b to c', i.e. the new long-run price will be much higher than the old long-run price (not shown on the second diagram, but easy to visualize).
The increase in price in the short-run depends upon the shape of the SRS, the size of the shift in demand, how much of the good is available in storage, etc. So both the size of the initial run-up in price and the the time it takes, i.e. difference between T2 and T1, will vary by commodity.
Some commodities may have a fairly flat SRS. And for some goods the peak price effect may be delayed more than others. The point is that there can be big differences in the short-run response across commodities.
Both the size of the fall in price and the time between T3 and T2 will vary across commodities as well. The size of the fall in price in the long-run was described above, it depends upon how easily new land (mines, etc.) can be brought into production and the cost of doing so. So as with the short-run response, we would expect to see quite a bit of difference across commodities in both the magnitude of the price change and the time it takes for full adjustment to occur.
I've been telling a story about trend movements in commodity prices that is based upon movements in fundamentals, a story similar to that shown in the diagrams (as opposed to alternatives such as a speculative bubble or price manipulation story). One argument I've been using against any story that relies upon particulars in, say, the oil market to explain commodity price movements is that the prices of all commodities have moved together, we see the common co-movements even in markets where speculation is outlawed or non-existent for some other reason, the inventory changes have not been consistent with a speculation story, etc. For that reason, whatever it is that is driving commodity prices, it must be common to all markets, whatever is driving prices around cannot be something unique to a particular market (unless it can somehow bleed over into other markets, e.g. if oil is an input to the production of other commodities, we would see the prices of these commodities increase after an oil price increase, though a lag in the relationship would be expected, and, notably for the points that below, the price change would differ across commodities according to relative energy intensity in production). One story out there along these lines is a change in the laws regarding speculative investment that would cause an infusion of speculative activity in all markets simultaneously. But - in addition to the other objections mentioned above - the movements in commodity prices, at least as I've observed from inspection of graphs, do not seem to be tied closely enough to the change in the laws regarding speculation for this story to hold, though I haven't looked at this evidence in detail and I'm open to more evidence on this issue.
But it also strikes me that the movement in commodity prices is too coordinated to be explained by the graph above, i.e. explained solely by fundamentals. If the graph tells the whole story, the timing of the peaks ought to differ by commodity, the magnitude of the price run-up and subsequent fall should vary across commodities, both in magnitude and timing. The price movements should be similar in character, but with noticeable individual differences. I am relying more on the difference in peaks than anything else since I'm not sure enough time has passed to observe the full long-run response, so one thing I'll be watching for, as a test of the fundamentals story, is whether we see the kind of difference in the peaks and the long-run responses that is implied by differences in industry structure. If the largest movements in prices are too coordinated across commodities, if the size of the run-up, the timing of the peaks, and the characteristics of the longer-run responses look very similar across commodities, then the fundamentals story will be hard to support as the main driver of the large movements in commodity prices we've observed.