Hi there

I'm taking introductory economics and our professor has given us a
specific example/formula to calculate the equilibrium price, taking
into account elasticity, etc. However, the formula he has given is
different from the regular "linear" formulas that we were all used to
- i.e. Q = a + bD. He illustrates the new way in an example below:

Assuming constant elasticity

Demand: Q = AP ^ (-0.3)  
Supply: Q = BP ^ (0.1)

*where -0.3 and 0.1 are their respective elasticities

Substitute P and Q into equations to find A and B

My question is, how is this different from a regular linear
supply/demand formula, and how does it actually work? Why the
exponent? How do we use it? i.e how do we represent structural
increases in demand, or structural decreases in supply, etc. Are there
any examples online?

This rather worries me.

It looks as if he wants you to differentiate the equations.

What really concerns me, is what the heck has that to do with Economics ?

- I studied the subject at one of the two better known UK Universities
about 30 years ago, at a college that taught mathematical economics,
also I was pretty competent at pure maths, yet it became obvious to me
that arithmetical conundrums (sic) were about as relevant to economics
as crosswords are to English literature.

I think you might be well advised to publicly ask your tutor 
  'what is Goodhart's Law' 

If you do not get a quick and cogent answer, then you are in the wrong class.

It is an interesting subject, actually rather useful in a rather
slideways manner, in the real world, but reducing concepts to
numerology or pilpul indicates that you have a profoundly dim tutor.

Mostly economics is a modelling of 'common sense', common sense is
quite rare, so modelling it is not entirely daft.

Basically whoever set you that is an idiot
- but more importantly, /not/ a person who can show you how to think
like an economist

Too bad I can't collect the money, but you might try log-linearizing
the equations. Not wanting to take too much away from the other
comment, this is a standard way of manipulating equations which for
some economist becomes second nature.

frde-ga this is the best answer of all great my friend.if I have a
question to ask I will ask you first is there anyway to read your
other comments or answers please.

Demian,
If you want to see comments by a user, just enter the user name in the
box below and search.  If you want to check out a G-A Researcher, just
click on their blue name, which is a hyperlink.
Cheers, Myoarin

@demianunique-ga 

MyOarin has given you the method of finding posts

I'm not a GA researcher, just a member of the 'peanut gallery'
- sometimes I run into questions that make me foam at the mouth
- this one rattled my cage

The point is to teach you the form for a formula with constant
elasticity.  The difference between this and a linear form is that a
linear form never has constant elasticity - the formula for elasticity
is d(Q)/d(P)*P/Q or the first derivative at a given point.  In a
linear formula, Q=a+bP, d(Q)/d(P)*P/Q is b*(P/a+bP) - so at any given
P , the elasticity is different.  But in the form Q=2P^(.3) the result
is (.6/p^.7)*P/(2P^.3) = .3.  So in an exponential function, the curve
demonstrates constant elasticity.

Also, while economists are notorious for 'assuming' many things, we
never assume constant elasticity when it is so easy to prove.  The
formulas you prove demonstrate constant elasticity, you do not need to
assume it.

A structural increase or decrease in demand or supply is a shift in
the curve up or down without changing the shape of the graph itself.
This is called a monotonic transformation.  So the upward sloping
supply fuction is Q=5P^.3 then a monotonic shift in supply without a
drastic change in technologies would be Q=5P^.3+X where X is the
factor of the improvement (or reduction in the case of a negative X).

@CrimsonDan

Ok, assuming that the function of an economist is to observe,
understand, and explain things to other people, please do the
following :-

Explain, in simple terms the implications of different price
elasticities of demand, but do it in a way that child could understand
it.

Price elasticity of demand is the percent change in Q that comes with
a percent change in P.  When elasticity is zero, you have a vertical
demand line and the demand curve is perfectly inelastic.  No matter
what change in P you have, the quantity demanded will not change.

The other extreme is a horizontal demand curve.  For any change in
price, there is a complete loss of demand.

@CrimsonDan

Well that is not how I would explain it to a child, or the MD of a large company.

This is how I would go about it :-

As we all know, when you put the price of a product up, then people
generally buy less of it.

So if we want to plot the relationship between Price and Quantity sold
on a graph, we can put Price on the vertical axis and and Quantity on
the horizontal axis [Draw axes on the whiteboard].

The Demand curve is then a line or curve sloping down from top left to
bottom right.

If we set a Price, then we get a 'box' between the two axes and the
point on the Demand line.  The area of that box is P x Q which is
Total Revenue at that price.

Now, if we increase the price a bit, then we want to know whether the
area of the box ( Total Revenue ) will increase or decrease.

If a 5% increase in Price results in a 10% decrease in Quantity then
we can see that Total Revenue will decrease, Economists call the ratio
between :-
 ( Percentage Change in Q ) divided by ( Percentage Change in P )  'Elasticity'

If Total Revenue goes up, when Price goes up, then the Demand is
relatively 'InElastic', if Total Revenue goes down when Price goes up
then Demand is relatively Elastic.

The formula is:  [(dQ * 100) / Q ] / [(dP * 100) / P]
or :   dQ/Q * P/dP
or :   dQ/dP * P/Q

If Elasticity is below 1 then we can get more revenue by hiking the price
If Elasticity is above 1 then a price hike will reduce total revenue

There is a special case, where Total Revenue remains the same whether
you raise or lower the price - in other words the Elasticity is One.

If that happens all over the Demand Curve, then the curve has to be
'asymptotic', and will look like this [here one draws a curve on the
whiteboard].

The other special cases are a vertical line, which is totally InElastic
- and a horizontal line which is totally Elastic.

The real thing to watch out for is whether the Elasticity is less or
equal to One, if it is, then you can increase (or not reduce) Total
Revenue by hiking the Price.

If the Elasticity is greater than one, then it might be an idea
decreasing the Price, as that will increase Total Revenue, but that
might involve buying new machinery, and could increase our average
cost.

Since nobody really knows what the Elasticity of Demand really is in
the real world, it is really only useful as a 'concept' rather than a
'fact'.

Economists want to build models, so that they can explain things, and
play with 'what ifs'.  As a result, they import a little pure
mathematics to make equations that they can then 'solve'.

Of course, since they invented the equations in the first place, they
aren't doing much more than proving that the colour of a Black Cat is
... amazingly ... Black.

In the beginning, this was used to give Economics a veneer of
scientific respectability, fairly harmless, a bit like doctors using
Latin names (or pompous phrases) to cover up the fact that they
havem't a clue what is wrong.

For example a doctor will tell someone that they have 'Irritable Bowel
Syndrome', then talk about it as IBS - when all it means is that the
patient has a 'pain in the gut' - which the patient knew anyway.

Similarly, in Economics, the b*ll sh*t merchants have got in, and
instead of  Simplifying and Explaining things, they produce horribly
complicated mathematical puzzles in the hope that they will impress
the gullible.

A side effect of this 'Witch Doctoring' is horrible mistakes like the
crunch of the Hedge Fund - Long Term Capital Management - which used
Nobel prize winners to baffle and confuse people into not realizing
that it was neither Long Term, nor Hedging.

Similarly the blind followers of Milton Friedman devastated a fair
number of economies because he produced Economic 'theories' that were
sufficiently 'mathematical' to sound convincing, yet simple enough for
people to think that they understood - when they did not, and nor did
he.

Should Economics become the last resort of failed mathematicians and
failed theoretical physicists, then it would be time to abolish the
subject and re-invent it under another name - probably as a branch of
psychology.

The general rule is that, when people start talking mumbo jumbo, then
don't trust a word they say. If you can't understand them, they are
either fools, or trying to pull a con.

Assuming constant elasticity

Demand: Q = AP ^ (-0.3)  
Supply: Q = BP ^ (0.1)

Is utterly meaningless as we have three assumptions, none of which
have any bearing on Economics or the real world. Few people know their
Supply curve, and nobody knows their customers Demand curve.

  dQ/Q * P/dP = -0.3   

But all that is testing is that one knows the mathematical
representation of the measure of 'Elasticity'.

Pilpul !