Re: About elasticity

In article <OYCdnaMlJNsq977ZRVn-rw@xxxxxxx>, "tonyp"
<tonyp@xxxxxxxxxxxxx> wrote:

"Robert Vienneau" <rvien@xxxxxxxxxxx> wrote

The price elasticity of supply is the
PROPORTIONATE increase in the quantity supplied
for an unit PROPORTIONATE increase in price.
Note that elasticity is a dimension-less number.

"Proportionate"?

Suppose we have some commodity for which
price is related to quantity by:

Y = ( X units ) * ( $.02 / unit) ,

Or X = 50 Y

(By a suitable choice of quantity and price dimensions, the slope
can be converted to unity. So 50 or 1/50 will not appear in
the final expression for price elasticity, since price elasticity
is a dimensionless number.)

so that price Y = $2 at a supply of X = 100 units,
and Y = $4 at X = 200 units, and so on.

Graphing price Y vs. quantity X, we have a straight line.

Now, what does the graph of "elasticity of supply" look like, per your
definition?

It's not MY definition.

Change in quantity, as a proportion of quantity, is dX/X.

Change in price, as a proportion of the price, is dY/Y.

Price elasticity of supply, e:

e1 = (dX/X) / (dY/Y) = (dX/dY) (Y/X) = 50 Y/(50*Y) = 1

So the quantity supplied increases 10% after a 10% rise in prices.

Suppose that the supply curve does not go through the origin. That is,
the supply curve, in the region that we are interested, is modelled
by a straight line with a non-zero intercept:

Q = a + b*P

Price elasticity:

e2 = (dQ/dP) (P/Q) = b*(P/(a + b*P)) = (b*P)/(a + b*P)

e2 = 1/( 1 + (a/b) * (1/P) )

Notice that the price elasticity of an affine supply curve is
generally not a constant. It is a function of price. And, as
I said, it is dimensionless.

Since the demand curve is downward sloping, and the relevant
part lies in the first quadrant, if the demand curve is a
straight line, its intercept is positive. Thus the price
elasticity of a straight-line demand curve is not constant.

--
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v s a Whether strength of body or of mind, or wisdom, or
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