Question

Show that a straight supply curve going through the origin has the price elasticity of supply equals to 1 at every point. (Hint: assume a function of P=aQ+b where a>0 and b=0)

Answer 1

When supply function is linear and passes through origin then intercept = 0
So, P = aQ + b where b = 0
So, P = aQ
Or, Q = P/a

Elasticity of supply, Es = (dQ/dP)*(P/Q)
dQ/dP = 1/a (differentiating Q = P/a)

So, Es = (dQ/dP)*(P/Q) = (1/a)*(aQ/Q) = (1/a)*a = 1
So, Price elasticity of supply = 1
(as P = aQ)

So, Es = 1 at every point independent of values of P and corresponding Q.