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What is more price elastic in the short run? supply of hotel accommodations or demand for hotel accommodation? Say the next world cup world cup there will be millions of people flying into Brazil, what would be more price elastic in the short run for hotel accommodations, supply or demand? i was thinking in the short run demand is inelastic and so is supply? im so confused. because can they even be both?

Dear Simon,

Thank you for posing a question on the price elasticity of both demand and supply relating to aspects of a temporary yet weighty real-life situation such as short-run hotel accommodation. You have good reason to assume on a first view that both demand and supply in such a case tend to be inelastic. Since there are some hidden splices of reasoning not obvious to offhand examination, you are also right to think that intricacies may elude a first observer like you and may cause some confusion. Let me spell that out.

YOUR THINKING

First, given elasticity of demand as a measure of responsiveness of the number of hotel occupancy demanded by lodgers to changes in the rental charged by the hotels, “demand is inelastic” means the percentage change in the rental charged by hotels (a lowering or raising of room/bed rents per night) is “less than” the percentage change in the occupancy change (an increased or decreased number of room/bed occupancy).

Second, with this definition, we can safely say elasticity of demand for hotel occupancy is inelastic. This is because, people would go for hotel accommodation for a short duration either when they are vacationing, attending seminars or parties, newly arriving and looking for longer-term residential accommodation or apartments. This demand therefore springs from requirements or exigency, and people simply want that many rooms or beds for that many days or so –nothing more, nothing less. Rental of occupation has very little, if at all any, effect on their demand.

On the supplier side, we also see hotel management in the short run has a limited leeway to increase or decrease accommodation. Rooms cannot be built on short notice, nor can rooms be turned into shopping boutiques or offices on short notice. Therefore, in the short run, a small increase or decrease in the rents that could be charged from the occupants or a small increase or decrease in the offers of rental made by the new arrivals will have little impact on the offer of rooms or beds. Thus elasticity of supply in hotel occupancy in the short run is also inelastic.

TECHNICAL EXPLANATION: THE RATIONALE AND APPARATUS

The above arguments could be put to technical verification, using mathematical methods. If we assume nonlinear demand and supply curves – with exponential demand and supply curves (where “exponents” to the variable price would be “elasticity”) – we could explain the matter with an econometrically oriented analysis. This would require advanced mathematical techniques which may probably be beyond your present level of education and would also require mathematical writing with fonts not admissible on this website.

So, to make a compromise, let’s assume these nonlinear demand and supply equations are transformed into loglinear equations: so we get linear demand and supply functions in terms of logarithms of prices and quantities (occupancies) on a quadrant of log(quantity),log(price) plane. That’s simple and acceptable, and econometricians also use these manipulations with time-series data, using normal (regression) equations. To further simplify, without any loss of analytical rigour, let us consider each “logarithm of value” just a “value” and consider these on a quadrant of “quantity, price” plane. So, assuming our figures are actually logs of values, we may have two simple straight-line equations of demand and supply as under:

Demand equation: D=a-bP

Supply equation: S=c+dP

In the above equations, as you know, a=demand intercept, c=supply intercept, b=slope of the demand curve, and d=slope of the supply curve. Two things I believe you know (if you are to refresh your memory look up an intermediate-level microeconomics textbook –or just take for granted what I am explaining):

A) The midpoint of the demand curve a-bP shows unit elasticity; below the midpoint at any point on the curve we have inelasticity (elasticity<1 or what we are interested in) and above the midpoint at any point on the curve we have elasticity (e>1 or what we want to disagree with or refute). [Elasticity is then defined as lower segment of the demand curve divided by upper segment of the demand curve]

B) At each and every point on the supply curve we have inelasticity if the intercept (c) is on the horizontal P-axis; and at each and every point on the supply curve we have elasticity if the intercept is on the vertical Q-axis

C) Slope of the demand curve (b) and slope of the supply curve (d), by themselves explain NOTHING about elasticities; these slopes, together with the ratio of P to Q (multiplied with slopes), DOES explain elasticities

D) For simplicity, we restrict our analysis to geometry (and algebraic implications are subsumed)

E) We also know the concept of elasticity has to be interpreted against price. Therefore, in the short run, we are concerned with the “lower segment of the demand curve” and “the supply curve with Q-intercept” [Of course, we DON’T rule out the possibility that both supply and demand could be ELASIC –you may know that, given sufficient time hotel rooms can be constructed, and given sufficiently low rental or sufficiently high rental, occupancy rate may indeed change, as people may feel like staying for a pretty long time at hotel than renting a flat with very low hotel accommodation (e.g., international experts working for few months in another country might prefer to stay at highly reduced rental at Sheraton or Hilton)

TECHNICAL EXPLANATION: USE OF GEOMETRY

Take a look at the first attachment. The green supply curve at each and every point shows elasticity<1. The demand curve is bisected into a blue segment (elastic part) and a green segment (inelastic part). Therefore, in the short run equilibrium shows an intersection where both demand and supply are inelastic as per our foregoing explanation.

Now, as we have also reasoned out, if income increases sufficiently or desire for convenient hotel accommodation increases significantly (i.e., if the parameters, or “other things,” change), the demand curve “shifts” to the right. The extreme right demand curve in the diagram shows there is a gap between the two equal segments of the demand curve, which clearly shows the segment above the intersection is smaller, hence demand now becomes elastic (please refer to the definition at (A) above).

Next, take a look at the second attachment. We also see equilibrium at elasticities of demand and supply both less than unity (<1 or inelastic). This could be a phenomenon in, say, Australia. You go from Adelaide to Sydney or to Brisbane, and you pay high rent for accommodation in a hotel (Compare that with, say, India: you go to Mumbai or Delhi, you pay much less for equivalent comforts).

Here is a typical case. As supply is elastic, demand doesn’t become elastic even if you earn more money in Queensland. There seems a paradox: You are earning more money, hotel accommodation is also getting more expensive (look at the height of the pink line). Yet the percentage increase in occupancy is less than the percentage increase in price when both parameters change.

SUMMARY

You are right. In the short run both the demand for and the supply of hotel accommodation, whether in Brazil, North America, Australia or India, are inelastic. They are so unless otherwise parameters change drastically (“Other things do not remain the same but go out of whack”)

I am very impressed by your inquisitiveness. Sorry, Simon, I was a trifle too busy with some extra teaching assignment and have had to keep you waiting. I will be happy if this satisfies your curiosity. Keep this curiosit.

Economics

Answers by Expert:

It appears some students in this website are confused about elasticity of demand and the slope of the demand curve when they are trying to figure out why rectangular hyperbola comes up in case of unitary demand curve. First, they don't know that RH can be depicted in a positive quadrant of price,quantity plane. Secondly, they make the mistake that the slope of RH is constant at -1. Two points could help them: first, e=1 at each and every point of the RH, because the tangent at any point shows lower segment=upper segment (another geometric definition of e); yet slopes at different points,dQ/dP, are different; second, e is not slope but [(Slope)(P/Q)]in absolute terms. Caveat: only if we measure (log P) along the horizontal axis and (log Q) up the vertical axis, can we then say slope equals elasticity --in which case RH on P,Q plane is transformed into a straight-line demand curve [with slope= -tan 45 deg] on (log Q),(logP) plane, and e= -d(log Q)/d(log P). [By the way, logs are not used in college textbooks --although that is helpful in econometric estimation of elasticity viewed as an exponent of P, when demand equation is transformed into log-linear form.] I have not found the geometrical explanation I have given in any textbook followed in undergraduate and college classes in Canada (including the book followed in a university where I taught for a short time and in the book followed in George Brown College, Toronto, where I teach.

About 11 years' teaching economics and business studies, and also English, history and elementary French.Practical experience in a development bank, working with international donor agencies like the World Bank and the ADB. Experience in free-lance journalism, including Canada's "National Post." **Organizations**

I teach micro- and macroeconomics at George Brown College (continuing education), Toronto, ON, Canada.**Publications**

Many articles and editorials, on different subjects, in English newspapers.
Recently an applied Major Research Paper, based on a synthesis of the Solow growth model and the Lewis two-sector model, has be accepted by Ryerson University, Toronto. Professors Thomas Barbiero and Eric Cam, Ryerson University, accepted the paper. **Education/Credentials**

Master degree in Interantional Economics and Finance and diploma with honours in Business Administration from Canada.**Awards and Honors**

Received First Prize in an inter-university Literary Contest.