question_answer

A consumer buys 200 units of a good at a price of Rs. 20 per unit. Price elasticity of demand is\[(-)\,2\]. At what price will he be willing to purchase 300 units? Calculate.

Answer:

Original Price (P) = Rs. 20 per Unit

Original Quantity (\[\theta \]) = 200 Units

Elasticity of demand (\[{{E}_{d}}\]) = \[(-)\,2\]

New Qty. (\[{{\theta }_{1}}\]) = 300 Units

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

Change in Qty = New Qty. \[\] Original Qty

(\[\Delta \theta \]) \[=300200\]

= 100 Units

New Price (\[{{P}_{1}}\]) = \[\Delta PP\](Change in Price\[\]Original Price)

Utilizing the formula:

\[{{E}_{d}}=\,\,\frac{\Delta \theta }{\Delta P}\,\,X\,\,\frac{P}{Q}\]

Where,

\[{{E}_{d}}\] = Price elasticity of demand

\[\Delta \theta \]= Change in Qty.

\[\Delta P\]= Change in Price

P = Original Price

Q = Original Qty.

Change in Qty (\[\theta \]) = New Qty.\[\]Original Qty.

\[=300200\]

= 100 Units

\[(-)\,2\] =\[\frac{100}{\Delta P}\,\,\times \,\,\frac{20}{200}\]

\[(-2)\,\Delta P=10\]

\[\therefore \]     \[(-2)\,\Delta P=\frac{10}{2}=5\]

\[(-)\] sign is ignored since it tells only the inverse relationship between Price and Qty. demanded.

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

\[=Rs.\text{ }20Rs.\text{ }5=Rs.\text{ }15\]

Hence New Price (\[{{P}_{1}}\]) will be Rs. 15 at New Qty. of 300 units.                                       Ans. Rs. 15