question_answer

Price elasticity of supply of a good is 2. A producer supplies 100 units of a good at a price of Rs 20 per unit. At what price will he supply 80 units.

Answer:

Elasticity of supply \[(Es)=2\]

Quantity supplied (Q) = 100 units

Price (P) = Rs. 20/unit

New quantity \[({{Q}_{1}})\] = 80 units

New price (\[{{P}_{ & 1}}\]) =?

Change in quantity supplied

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

\[=80100\]

\[=20\text{ }units\]

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

\[2=(-\,20\div \Delta P)\times \,(20\div 100)\]

\[2=(-20/(-\Delta P)\,\times \,(1/5)\]

(\[-\Delta P\]is taken because prices are fallen splly is falling

\[2=(-\,4/(-\Delta P))\]

\[2\,\Delta P=\,-\,4\]

\[-\,\Delta P=-4/2\]

\[-\,\Delta P=-\,2\]

\[\Delta P=(P-P1)\]

\[2=(20-P1)\]

\[P1=20-2\] = Rs. units.

Hence, the seller will supply 80 units at Rs. 18 per units.