This information is from the Windows Steam version circa August 2016. If it seems different since then on other platforms, please update this information, stating your platform and what's different. However if differences were seen prior to that date, please re-check to make sure all platforms were not updated.
The game has three distinct shortage events which occur on a playthrough, as broadcast on the Radio. There are suggestions that other patterns exist, so feel free to add them if you find one:
|Pattern 1||Pattern 2||Pattern 3|
So if your current game is following Pattern 1, on Day 8 there will be a warning on your radio that coffee is starting to be in short supply, and so on. These patterns can be clearly seen (in retrospect) by looking at your radio log near the end of a game. Warnings appear to last 3 days, shortages 4. You can start collecting supplies or making workshops accordingly.
If you don't check on a given day, your log will show it as of the day you check. For example if a coffee warning was slated for Day 8 but you did not check the radio until Day 10, the log will show the warning occurring on Day 10. (If your log shows something later than the table, are you sure you checked your radio every day?) The shortage will start on Day 11, regardless of checking the radio.
The cigarette shortage talks about cigarettes and tobacco, but no actual spike in tobacco prices has been observed. (Tobacco, Homegrown Tobacco, and Herbs were checked.) But all three types of cigarette might be double (see Effect, below).
If you have seen anything else doubled (e.g., alcohol), please add your pattern to the table above. There are hints on the internet that alcohol has been subject to shortages, but the current editor has not witnessed it.
The effect of a shortage is a doubling in price, but it only occurs randomly - traders (includng Franko) might pay double the regular price, or they might only pay as normal. In other words, being able to sell at a markup is very hit or miss. The probability of the price being double for a given item with a given trader (all but Central Square) seems to be very roughly fifty-fifty. In the case of cigarettes, all three types are randomly rolled; all three might be double, or none might be. Of course, one usually hopes the most expensive one (Quality Roll-Ups) is affected.
"Double" here means a doubling of the trader's usual rate. For example, if like Ciorba, Matey, or Vanya they divide all your values by 1.2 (for an effective transaction rate of .833), their "double" rate will be 1.67 (2 x 1/1.2). Franko pays 1:1, so his doubled rate is a straight-up 2:1. (With Katia versus Franko, the doubling becomes 2.4:1.)
If an item's price doubles, it's always double on both sides of the trading table. You can't buy low and sell high, pulling out the rug from a particular trader in a set of trades.
Unfortunately, the traders at Central Square appear to be completely protected against shortages. They will only ever pay normal price for shortage items, and if they sell a shortage item, they will always sell it at double price during a shortage, so you can't buy low from them, then sell high to some other trader later. (But shortages never affect the price of raw cigarette materials from any traders.)
If you want to cheeseball it, you can reload a day that Franko shows up during a shortage until he will pay double (back out to the Main Menu and use Continue to restart that day). Other traders are probably also randomly determined when their night location starts.
Profiting from Shortages
Unless you want to do cheesy reloads, spending resources in an attempt to profit from shortages is a gamble. If you can't be sure you can sell at double price, spending a night making a trip to a trader to prepare for a shortage might be largely wasted. As a result, some think the better bet is to simply ignore shortages and go collect more (free) items to haul back, instead of gambling with time and money. Still, you can always stockpile when convenient, or maybe hit a trader at a location that also needs foraging, when a warning appears.
There is one huge asterisk to this: If Franko shows up at your door during a shortage and you test him (quickly!) and find he'll pay double for some cigarette you can make, then make them like crazy before the sun goes down. Some players prepare Homegrown Tobacco so they can crank out Quality Roll-Ups (QRUs) without delay. (It's the most expensive cig, with the best profit to begin with.) Especially if you have Bruno, who would otherwise smoke your product. Franko usually shows up around 10 or 11, so you might have 8-9 hours before nightfall. So have ~9 Homegrown, Components, and Tobacco ready to go, to do this. You may very well be able to buy some or all of the ingredients from Franko on the spot (but Homegrown may be your weak link in this time-crunch situation).
So that you can use your newfound profit best, make cigs all day but don't buy much from Franko until just before nightfall, then sell all the cigs you made, and buy all you can with them, thereby converting and locking all your boom-time profits into non-inflated goods. Nine hours spent making QRUs is 36 cigs at 3x2=6 each; over 216 Franko-component-equivalents in one day. (This is for a regular survivor; Katia will get 20% more.) That's enough to buy all the basics you usually want from Franko, plus much more. If Franko's QRU price is double, and you have the right ingredients, you're not gambling. You're just acting decisively.