Question

3.a. Define elasticity of supply and find the price from the given statement:

If Es of a good is 2 and a firm supplies 200 units at price of Rs 8 per unit, then at what price will the firm supply 250 units. (5 Marks)

b. Calculate the elasticity of supply if a 15 %increase in the price of soya bean oil increases its supply from 300 to 345 units 

Answer 1

(a) The price elasticity of supply can be found as follows:

$$E_s=\dfrac{\%\Delta Q}{\%\Delta P}=\dfrac{\dfrac{Q_2-Q_1}{0.5(Q_2+Q_1)}}{\dfrac{P_2-P_1}{0.5(P_2+P_1)}},$$ $$\dfrac{P_2-P_1}{0.5(P_2+P_1)}=\dfrac{\dfrac{Q_2-Q_1}{0.5(Q_2+Q_1)}}{E_s},$$ $$\dfrac{P_2-8}{0.5(P_2+8)}=\dfrac{\dfrac{250-200}{0.5(250+200)}}{2},$$ $$\dfrac{P_2-8}{0.5(P_2+8)}=0.11,$$ $$P_2=Rs\ 8.93.$$

(b)

$$E_s=\dfrac{\%\Delta Q}{\%\Delta P}=\dfrac{\dfrac{Q_2-Q_1}{0.5(Q_2+Q_1)}}{\%\Delta P},$$ $$E_s=\dfrac{\%\Delta Q}{\%\Delta P}=\dfrac{\dfrac{345-300}{0.5(345+300)}}{0.15}=0.93$$