When price
falls, quantity demanded rises – this is the law of demand. But when the price
of a good falls, the total consumption value of buyers toward that good may
either fall or rise. From the viewpoint of the seller, income after price
reduction may either fall or rise. The key determinant is the price elasticity
of demand.
Price
elasticity is a coefficient calculated by a simple equation. In the late
nineteenth century, some economists tried in vain to find this simple equation.
By the end of 1881, while holidaying in Sicily with his wife, Marshall enjoyed
working at the rooftop of a small hostel. One afternoon, he came down from the
rooftop and said to his wife: “I have just found the elasticity of demand!”
Today,
other than price elasticity, there are innumerable equations of other
elasticity coefficients that can be made very complicated. Unfortunately, in
respect of explaining behavior, elasticity coefficient has only limited
application, hence is not crucial. (In estimating the change in social welfare
– if you believe in this – elasticity coefficient is crucial nonetheless.)
Let’s just
focus on the price elasticity of demand. A fall in price itself leads to less
consumption; a rise in quantity demanded itself leads to more consumption.
Whether the resultant total consumption will rise or fall depends on the
relative weightings of these two. The key in Marshall’s then solution lies in
treating the relative weightings in percentage terms. The price elasticity
coefficient is calculated by having the percentage change in quantity as the
numerator and the percentage change in price the denominator. When price falls,
and the percentage increase in quantity in the numerator is greater than the
percentage decrease in price in the denominator, then the elasticity
coefficient will be greater than one, which is termed elastic. As such, any
fall in price will lead to increased consumption (increase in seller’s income).
If the elasticity coefficient is less than one, termed inelastic, consumption
will fall.
When price
is elastic (coefficient greater than one), price and consumption diverges. When
price is inelastic (coefficient less than one), price and consumption
converges. Be mindful that price elasticity coefficient is calculated at a
particular price. There are countless prices on a demand curve, and price
elasticity coefficients at different prices can be all different: elasticity
coefficients greater than one for a certain portion of the curve, and less than
one for another portion.
Price
elasticity of demand does not offer much help in explaining behavior due to our
difficulty (inability in fact) in foreseeing its ballpark figure. Even though
quantity demanded is invisible, but due to the law of demand, we know that when
price falls, quantity demanded will rise. We will not have this convenience
using price elasticity coefficient.
Let’s
quote an example. In 1997, Hong Kong’s Western Harbor Tunnel began operations.
It was privately built and its operators undoubtedly yearned for more income.
Toll at the outset was HK$30 but traffic was infrequent, resulting in several
tactics to offer discounts. Subsequently, more traffic was generated, and toll
was increased to HK$40. With a fall in income after such an increase (elasticity
coefficient larger than one), toll was then reduced to HK$35. Service costs,
repairs and maintenance, etc., are negligible for one extra car crossing the
tunnel, therefore the main goal of the tunnel is maximizing its total income.
Maybe total income would be far higher when toll were set at HK$20 than HK$35
or HK$30.
Another
example is that over the years, every time before the Hong Kong government
raises excise taxes on tobacco and alcohol, it will forecast how much
additional revenue that would bring to its Treasury. Experience tells us that
such government forecast is never accurate, with a standard not much different
from that of low-skilled laborers. Were the Hong Kong government to ask me to
forecast, my capability would at best be on a par with that of laborers! The
problem being nobody knows the price elasticity of demand for tobacco and
alcohol.
Unable to
foresee price elasticity coefficient, we can nonetheless try guessing. Not long
ago, I made two guesses for the publications of a publisher – one was right,
the other wrong – resulting in a tie.
The first
time was for the Chinese calligraphy DVD that I helped to produce for my
teacher, Zhou Huijun. Teacher Zhou’s calligraphy demonstration is so amazing
that there is no close substitute in the market, and given one lesson of
calligraphy costs close to HK$200 while Zhou’s DVD can be constantly re-read, I
believed if the price was HK$50, its elasticity coefficient should be less than
one, therefore setting the price at HK$100 should not be a problem. Little did
I know that the price was set too high. My guess of price elasticity
coefficient was wrong.
The second
time was for my two recent books on education and academia respectively that
were re-organized from former articles. These two books were diligently
compiled to my satisfaction. The publisher asked me on the pricing. After
deliberate consideration, I said HK$100, doubling the normal price. Why? With
my belief of no close substitutes in the market, price elasticity coefficient
should be less than one. This time I was right: selling price was doubled yet
sales volume was high.
One right
and one wrong, with the same inference method. Price elasticity coefficient is
largely determined by the more or less of substitutes and their prices.
Interestingly, I believe substitutes for Teacher Zhou’s calligraphy DVD are in
all likelihood even less than that of my two books. But my guess was wrong.
The
implication here is obvious. Whoever could always accurately guess beforehand
the elasticity of demand in the market must be awfully rich. Even approximately
right could have already made a fortune. No such person has ever existed in the
world, clearly reflecting that elasticity coefficient can never be foreseen.
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