In this post, we destroy the 'inelastic' supply curve of modern Economics and replace it with our SORAnomic supply curve derived from Adam Smith's maxims.
SORAnomics vs Economics Supply and Demand Exercise on Logic
Adam Smith’s Supply and Demand Curves (below) are the foundation our proposed science called SORAnomics and can be applied to any problem in economics in order to provide common sense answers. For example, the question below appears in Principles of Microeconomics by Mankiw:
The equilibrium price of coffee mugs rose sharply last month, but the equilibrium quantity was the same as ever. Which explanations could be right? Explain your logic.
The market price of coffee mugs rose sharply last month, but the quantity supplied was the same as ever. What is the explanation?
The supply for coffee mugs was "perfectly inelastic"
The price of the coffee mugs during the previous month was an introductory price. The price afterwards is the natural price (a concept that is not present in economics)
There is a single supplier of coffee mugs in the whole society and people have no choice but to buy from it at whatever price it wants. So the demand curve shifted to the right.
There are many suppliers of coffee mugs. The company's specific new mug however proved to be a hit among consumers. So the supply curve shifted upwards.
Economist Answer: "Demand increased but supply was totally inelastic."
Economist Fallacy (Demand): Coffee mugs are so essential to society that people won't mind paying increasingly high prices for it.
Economist Fallacy (Supply): There can only be one coffee mug supplier.
SORAnomist Answer: Based on the only information in the question, and assuming it is a realistic scenario (why would students be taught unrealistic scenarios?), we can deduce that the previous price for the coffee mugs was an introductory price (lower than usual) in order to entice buyers (four mugs were sold at $3 each). The price was raised the next month as demand was established as all the previous mugs were sold, and it was assured that the mugs were unique enough as not to invite competition. Thus, four new mugs could be sold at $6 each, with a $3 rise in profit. Production was not increased because there was no guarantee that the demand would remain.
No coffee mug, nor any product, could ever be worth an infinite value as to be a "perfectly inelastic" good.
An Established Sophistry
The marginalist elastic and inelastic supply curves are an example of sophistry. This is because supply curves ultimately have a downward slope, responding to the downward demand curve. We have called this Smith's Demand Motive, which is the opposite of Say's Law. In other words, businesses produce to meet the demands of society. In economics however, the demands of society are manipulated to increase the produce and sales of businesses (since profits, and consequently utility and pleasure, come with sales), and so infinitely high prices are possible.
Thus, in the problem, people somehow are willing or made willing to buy the same coffee mug at a much higher price. In reality, this can only happen if:
There was only one coffee mug supplier in the whole society. Following the logic of the perfectly inelastic curve, the company merely needs to advertise its mugs to increase demand or 'shift the demand curve to the right'. It can then steadily raise its prices as demand increases fearing no loss in demand. (The economist's answer leads to this)
Somehow people were made to buy more coffee mugs at higher prices, as in a special event for that month. Smith gives an example as a public mourning raising the demand for black cloth. The same thing happens for flowers during Valentine's day. But in such cases, production is increased. Since the question says production was not increased, it means the event was sudden or temporary, like rain creating a sudden demand for umbrellas on the street. Even if this were the case, competition would prevent prices from being rising arbitrarily unless there was only one umbrella supplier, which leads to the first scenario. More realistically, the event called specifically for that kind of mug from that supplier, which leads to the next scenario.
Those specific coffee mugs suddenly became so popular, for example through social media. Realistically, the mug was a new mug, first sold at an introductory price to test the market. Once demand was established, it was raised to its natural price. Unlike in scenario 1, the mug's price cannot be raised to infinite heights because this would invite competition. (The SORAnomist's answer leads to this)
Introductory pricing occurs in real life.
In a free society, a good can never be "perfectly inelastic". Even if oil prices, for example, were raised to exorbitant prices, society will switch to coal, LPG, firewood, electric cars, public transport, bicycles, etc. through their own effort. Even if a terminal cancer patient was sold a life-saving drug in exchange for all his life's present and future money and assets, as to leave him only his clothes for the rest of his life (the highest possible price for his life is his life, as in pure slavery), he will likely not do the trade. Thus, it can be observed that in economics, economic slavery* is a real possibility, as seen in rising prices and in both personal and governmental debt (US fiscal cliff, Latin American debt crisis, Greek debt crisis, etc.).
* We define slavery as a regular state of control of another's actions that produces pain. We replace the jargon 'elastic' and 'inelastic' with easy-to-understand words: 'price-sensitive' and 'price-insensitive'.
Looking back at the Wealth of Nations, I found that Smith did mention that a commodity can be 'perfectly inelastic' if it matches the following conditions:
The first kind is the rude produce which human industry cannot multiply at all. Examples are: most rare birds and fishes, different sorts of game, and almost all wild-fowl and all birds of passage, etc. Nature produces them only in certain quantities. They are very perishable. It is impossible to accumulate together such produce of different seasons. Their demand increases with the increase in wealth and luxury. Their supply cannot increase beyond this increase of the demand. The quantity of such commodities remain the same while the competition to purchase them is continually increasing Their price may rise to any unlimited height. (Book 1, Chap 11, Digression)
However, it is obvious that such goods are not only attended with immorality, but are simply illegal just as slavery is illegal. Thus, it is still consistent with the earlier conclusion.
Update 10/2016 (This post seems to get a lot of hits, so I'll update it)
Merging the old question with Smith's quote can help us create a new, more realistic question below.
The market price of Rhino horns rose in Vietnam sharply last month, but the quantity supplied was the same as ever. What is the explanation?
There was a sudden demand for rhino horns because of a rumor that it could cure cancer. Since rhinos are endangered, the production of their horns could not be increased, leading to higher prices. However, unlike the economist's vertical supply line, the supply line will still be downward sloping, to match Smith's maxim:
"The natural price is the central price, to which the prices of all commodities are continually gravitating. Different accidents may sometimes keep them suspended a good deal above it.. But.. they are constantly tending towards it"
The yellow and green lines represent the demand and supply curves before the rumor (representing natural demand and supply therefore natural price), while the blue and red lines represent those lines after the rumor.