question_answer

When the price of a commodity goes up by 10%, a consumer's demand falls from 500 units to 400 units. Calculate the Price Elasticity of Demand\[({{E}_{d}})\].

Answer:

Given, Percentage change in price =10%, Initial Quantity (Q) = 500 units New Quantity = 400 units Change in Quantity \[(\Delta Q)=400-500=-100\,\,units\] \[\therefore \] Percentage change in quantity demanded             \[=\frac{\Delta Q}{Q}\times 100=-\frac{100}{500}=-20%\]             \[{{E}_{d}}=(-)\frac{Percentage\,Change\,inQuantity\,Demanded}{Percentage\,Change\,in\,\Pr ice}\]             \[=(-)\frac{-20%}{10%}=\frac{20%}{10%}=2\] \[{{E}_{d=}}2\,\,[{{E}_{d.}}>1,\,\,ElasticDemand]\]