question_answer

A producer supplies 80 units of a good at a price of Rs. 10 per unit. Price elasticity of supply is 4. How much will he supply at Rs. 9 per unit?

Answer:

Given: \[{{Q}_{1}}=80\] units, \[{{Q}_{2}}=?\] \[{{P}_{1}}=\] Rs. 10/unit and \[{{P}_{2}}=\] Rs. 9/unit and \[{{E}_{s}}\] = 4

Let \[{{Q}_{2}}\] be \[x\]

\[\Delta Q=({{Q}_{2}}-{{Q}_{1}})\]

\[=(x-80)\]

\[\Delta P=({{P}_{2}}-{{P}_{1}})\]

\[=(910)\]

\[=1\]

\[{{E}_{s}}=(\Delta Q\div \Delta P)\,\times \,(P\div Q)\]

\[4=(x-80\div (-1)\times (10\div 80)\]

\[4=x\div 80\div 8\]

\[-32=x-80\]

\[x=\,48\] units

Thus, a producer will supply 48 units at Rs. 9 per unit.