We are presented with the following statement:
[The researchers] studied how New York cab drivers changed their labour supply in response to the higher incomes caused by fare rises. And they found a negative elasticity, of around minus 0.2. That means a 10% rise in cabbies' revenue per mile caused them to work 2% less.
To my mind, that could be explained by simply saying that the demand for taxi rides has a price elasticity of negative 0.2 - in other words, if prices go up ten per cent, the new equilibrium quantity demanded goes down by two per cent. (I'm not saying that this is the end of the matter, but the most obvious explanation is often the correct one).
The statement does not define 'revenue per mile'. This could mean total revenue divided by miles driven with a passenger on board, or it might mean total miles driven (whether with a passenger or while driving back to the taxi rank or touting for business). The statement does not define 'work 2% less'. The fairest assumption is that this refers to total hours worked, whether driving with or without passenger or waiting. In any event, there is probably some sort of equilibrium between the three that would be unaffected by price changes.
Dr Whatson is trying to justify a completely different explanation of the original statement, namely that the supply curve slopes backwards at higher incomes, by introducing all sorts of further assumptions here
1. Assume the demand for cabs is fairly inelastic. [I did - I assumed a price elasticity of demand of negative 0.2]
2.Therefore, (say) a 10% increase in the cab fare (set by the NY Taxi Licensing Commission) will decrease quantity demanded by 5%. [Nope - it would decrease by 2%]
3.An hour of driving around after the fare change will bring 5% less customers paying a price increase of 10% (ceteris paribus). [Nope - an hour of driving or waiting around will bring 2% less customers, which is why they cut their hours worked by 2% to balance it out, that's clearly stated]
4.Therefore revenue/hour goes up. [Yes of course - it goes up 10%, that's one of the two facts we were given]
5.Therefore revenue/mile goes up (assuming the cabbie haunts the Manhattan boulevards and not the line outside the Waldorf). [Yes of course - I already assumed that there is an equilibrium in the proportion of time spend waiting, touting and carrying a passenger. If the taxi rank outside the Waldorf is the best place to find passengers before the fare increase, it will still be the best place to find passengers after the increase].
Maybe you're mistaking miles driven for miles driven with a paying passenger? [Nope - there is no doubt a fairly fixed ratio between the two, so they change in line with each other. You could just as well say that 'average revenue per hour waiting outside the Waldorf goes up 10%', which is probably true as well]
So I'll stick with my original explanation, if you don't mind.
A grim document
14 hours ago
13 comments:
I don't fully understand the point yet (my fault I have not read it carefully time wise)
But do you think the fact that a cabbie is one of the fortunate producers who does not have to find rent before he can work make a difference? Same applies to window cleaners etc
Isn't there also some sort of massive supply restriction for New York cab licences that totally distorts supply and demand and therefore devalues what can be inferred from the research and your calculations?
RS, that all depends whether there are barriers to entry - which there clearly are in this case. In which case taxi drivers collect rents; own a valuable asset (a permit) and have to pay some rent-in-advance before they can enter the market.
L, yes, there is. But as we know, you can either restrict supply (thus pushing up prices paid), or you can increase the price (thus reducing quantity demanded - although being able to put up prices does depend on having some monopoly power).
I covered another example, where barriers to entry were reduced and unsurprisingly enough prices went down and the number of taxi drivers went up, so both findings fit into the overall same pattern.
When my GP got that big pay rise a few years ago, he immediately started working a shorter week. So, at least in the context of endlessly intrusive bureaucracy undermining professional autonomy, a negative elasticity might be just what it seems. He certainly wasn't responding to demand.
D, yes of course, because there are barriers to entry. Further, their basic salary was doubled but they no longer were paid for overtime - so no incentive to work longer hours. (yes that's simplified but nonetheless true).
If there were lower barriers to entry, people would be queueing up to become a GP and the total number of hours worked by ALL GPs would go up.
(Sigh)
In your original point,
---How do they know that this is not the quantity demanded dropping by 2% in response to a 10% fare hike?---
you start badly. Nobody ever mentioned a 10% rate hike associated with a 10% increase in revenue/mile driven. The 10% rate hike is your own invention. In fact, the rate hike would be MORE than 10%(fairly obvious).
Luckily you write this;
---Nope - there is no doubt a fairly fixed ratio between the two, so they change in line with each other---
which at least reveals your confusion. The fixity of the ratio depends on the elasticity. In any single hour after the rate hike, the miles driven with our without a passenger REMAINS THE SAME.
If the demand for cabs is not completely inelastic, number of miles driven with a passenger GOES DOWN.
Once we work out the increase in revenue/mile driven (with or without a paying customer - proxy for wages), the number of miles a cabbie drives around before or after a rate hike, we work out his labour supply response.
Since you're very keen to show me up on maths (even though I specifically tried not to use the same figures to highlight your confusion), lets proceed with your mathematical example.
Price elasticity of cabs -0.2
Rate hike 10%
T/fore, cabbie wages increase by 7.8% (i.e. revenue/mile increases by 7.8%)
After you work out this wage increase, you can then work out the labour supply response.
The price elasticity you are talking about, has everything to do with determining revenue/mile after the rate hike, and nothing to say after that.
If you still have difficulty, try thinking in extremes i.e. a 10000% rate hike, think about the labour supply response, and stream of income receipts.
Dr W, fair point with the maths. To use your model, let me ask, how do we know, on the basis of the scant information supplied that it didn't work like this:
Price elasticity of cabs -0.16
Rate hike 12.24%
Quantity demanded goes down by 12.24% x 0.16 = 2%
Instead of hundred passengers @ $10, total income $100, they have ninety-eight passengers @ $12.2449 = $110 i.e. revenue/mile increases by 10%.
Therefore, cabbie wages increase by 10%.
With the numbers you give (which are realistic) that is how it worked ;)
Revenue/mile driven, and therefore revenue/hour increase by 10%. According to the study, the cabbies then decide to work 2% less.
Dr W, maybe they do, maybe they don't, but I still fail to see why the obvious answer "Demand for taxi rides has a price elasticity of negative 0.16 or negative 0.2" is not the correct one.
You're confusing two elasticities, the e of cabs w.r.t. price and the e of labour w.r.t. wages.
Its much more simple than you seem to think. Once you are told that revenue/mile driven (wage) goes up by 10% after a fare increase, the price e of cabs becomes completely irrelevant.
Dr W, no I'm not. There are two main ones:
a) Price elasticity of demand (rising prices mean lower quantity demanded, as is almost certainly the case here).
b) Price elasticity of supply (rising prices normally mean higher quantity supplied or offered - or are a symptom of constraints on supply, such as failed harvest, barriers to entry).
A higher offered wage normally means that people will work MORE in that particular job (or more people will do it, or the same number of people will do more overtime) which, according to your logic is NOT the case here.
I reckon we are looking at (a) and you reckon that we are looking at an unusual exception to (b). Remember that there are significant barriers to entry in this particular business.
This study is about labour supply.
Initially substitution effect is stronger than the income effect (the study here) and for higher incomes, the income effect dominates the substitution effect. The labour supply curve, according to the economists' best estimates, looks like a boomerang.
The barriers to entry here simplify the information gathering, b/c since the number of cabs is fixed, we can easily work out the wage increase associated with a a particular fare increase.
Maybe you confuse the axes on the different diagrams, if you think of it like that. Consumers demand cab rides, but cabbies supply labour hours driving around, not cab rides.
I will stop here; read the first couple of sections of the paper, you will most likely find their explanation clearer than mine.
Dr W, sure, on an individual level, there is a boomerang, like City traders or Premier League footballers who are burnt out millionaires by the age of 30 who then retire; or schoolteachers and policemen who retire in their early 50s because their pension is almost as good as their wage. But in turn that attracts more people to City trading, footballing, teaching or coppering.
However, with taxi drivers, the wage = the price paid by the customer (give or take a bit) so it is difficult to distinguish between demand falling and labour supply falling.
It would make more sense to look at a business where the wage paid bears little relation to the price paid by the customer*.
A good example would be bus drivers in the UK, where routes, timetables and ticket prices are centrally regulated, and one of the few free market variables is the wage that bus operators must offer drivers (this is locally negotiated between employer and employees) and, apart from getting a PSV licence, there are no barriers to entry to being a bus driver.
If anybody can come up with evidence that when bus companies need more drivers, they simply cut their wages, then I would be interested to see it, or evidence that when bus drivers wages' rise, existing bus drivers work less. Remember that if existing drivers work less, other people will be happy to take their place.
* Of course, state school teachers' and coppers' wages are in no way borne directly by 'the customer' (free at point of use etc) so we could use those as examples as well.
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