Editing Cobweb model (section)

== Elasticities versus slopes ==
When supply and demand are linear functions the outcomes of the cobweb model are stated above in terms of slopes, but they are more commonly described in terms of elasticities. The ''convergent case'' requires that the slope of the (inverse) supply curve be greater than the absolute value of the slope of the (inverse) demand curve:
:<math>\frac{dP^S}{dQ^S} > \left|\frac{dP^D}{dQ^D}\right|.</math>

In standard [[microeconomics]] terminology, define the ''[[Price elasticity of supply|elasticity of supply]]'' as <math>\frac{dQ^S/Q^S}{dP^S/P^S}</math>, and the ''[[Price elasticity of demand|elasticity of demand]]'' as <math>\frac{dQ^D/Q^D}{dP^D/P^D}</math>. If we evaluate these two elasticities at the equilibrium point, that is <math>P^S=P^D=P>0</math> and <math>Q^S=Q^D=Q>0</math>, then we see that the ''convergent case'' requires
:<math>\frac{dQ^S/Q}{dP^S/P}<\left|\frac{dQ^D/Q}{dP^D/P}\right|,</math>
whereas the ''divergent case'' requires
:<math>\frac{dQ^S/Q}{dP^S/P}>\left|\frac{dQ^D/Q}{dP^D/P}\right|.</math>

In words, the ''convergent case'' occurs when the demand curve is more elastic than the supply curve, at the equilibrium point. The ''divergent case'' occurs when the supply curve is more elastic than the demand curve, at the equilibrium point (see Kaldor, 1934, page 135, propositions (i) and (ii).)