Q2 = quantity supplied at price P2.
?Q = change in quantity supplied from the initial supply of Q, while ?P s change in price from the initial price of P.
For infinitesimally small changes in supply and price, the price elasticity of supply can also be expressed in terms of derivatives of Q with respect to P.
Here changes in quantity and price are expressed as proportions of the average quantity and the average price along the supply curve rather than those of the initial quantity and initial price.
The expression for the point price elasticity at a point on the supply curve can be obtained geometrically as shown below.
In Figure 2.24(a), the supply curve is a straight line passing through the origin. For point price elasticity at point T (Q, P), take a point S (Q’, P”) close to it so that supply increases by AQ (= Q’ – Q) in response to a rise in price AP (= P’ – P).
Thus the price elasticity of supply at a point on it is less than unitary if the linear supply curve intersects the quantity axis (x-axis).
In Figure 2.24(c), the linear supply curve intersects the price-axis (y-axis). Proceeding likewise, the point price elasticity at point T(QJP), can be worked out as
Thus price elasticity of supply for a linear supply curve at a point on it is more than unitary if the supply curve intersects the price axis (y-axis).
Alternatively, the supply equations for the curves in Figure 2.24 (a), (b) and (c) can be identified as