Question

Show that any linear inverse supply that passes through the origin (i.e., an inverse supply with the functional form p=cQ with c>0) has a price elasticity of supply equal to one. Show that any linear inverse supply curve with a positive intercept (i.e., having the functional form p=k+cQ with c,k>0) must be elastic

a) p=cQ
b) p=k+cQ
c) both a and b
d) none of the above

Answer 1

a) p=cQ. A linear inverse supply curve with the functional form p=cQ (c>0) that passes through the origin has a price elasticity of supply equal to one.

Step-by-step explanation:

Inverse supply refers to the relationship between price and quantity supplied when expressed in inverse terms. A linear inverse supply with the functional form p=cQ, where c>0, passes through the origin. To show that the price elasticity of supply is equal to one for this type of inverse supply curve, we need to calculate the price elasticity using the formula:

Elasticity of Supply = (% change in quantity supplied) / (% change in price).

For a linear inverse supply with the functional form p=cQ, the percentage change in quantity supplied is equal to the percentage change in price:

Elasticity of Supply = (% change in price) / (% change in price) = 1.