question_answer

The price elasticity of supply of a commodity is 2.0. A firm supplies 200 units of it at a price of Rs. 8 per unit. At what price will it supply 250 units?

Answer:

Given, \[{{E}_{s}}\]= 2, P = Rs. 8, Q = 200 units, \[{{Q}_{1}}\] = 250 units

\[\therefore \,\,\Delta Q={{Q}_{1}}-Q=250-200=50\,\,units\]

Let the change in price, \[\Delta P=x\]

We know that,

\[{{E}_{s}}=\frac{\Delta Q}{\Delta P}\times \frac{P}{Q}\] or \[\,2=\frac{50}{x}\,\,\times \,\,\frac{8}{200}=\frac{2}{x}\]

or         \[2x=2\]            \[\Rightarrow \] \[x=1\] or \[\Delta P=1\]

New price,  \[{{P}_{1}}=P+\Delta P=8+1\] = Rs. 9