question_answer

Price of a commodity rises from Rs.5 to Rs.6. As a result, its demand falls from 100 units m to 80 units. Find out Price Elasticity of Demand\[({{E}_{d}})\] by percentage method.          If a fact is given that the slope of a straight line demand curve =\[\frac{\Delta }{\Delta Q}\], how do you   if relate it to own price elasticity of demand? Also, find price elasticity of demand, if demand is perfectly elastic.                                                      

Answer:

            Here, price and quantity for the commodity are as follows:                                                        

Price (Rs.)	Quantity (Units)
5	100
6	80

Given,                                                                                        Initial Price (P)= Rs.5               Change in Price\[(\Delta P)\]=Rs. 1 (6-5)                     Initial Quantity (Q) = 100 units                  Change in Quantity\[(\Delta Q)\]= 20 units (100 ? 80)         We know that,   Elasticity of Demand  \[(Ed)=(-)\frac{\Delta Q}{\Delta P}\times \frac{P}{Q}\]                                        =\[(-)\frac{20}{1}\times \frac{5}{100}\]    \[\therefore \]                                          \[{{E}_{d}}=(-)1\]    Or We know that, price elasticity of demand\[({{E}_{d}})=\frac{\Delta Q}{\Delta P}\times \frac{P}{Q}\]= It is given that, the slope of demand curve =\[\frac{\Delta P}{\Delta Q}\] We can write that, \[{{E}_{d}}=\frac{1}{Slope\,of\,Demand\,Curve}\times \frac{P}{Q}\] Where, P = Initial Price, Q= Initial Quantity, \[\Delta \,\,P\]=Change in Price \[\Delta \,\,Q\]= Change in Quantity So it follows that, price elasticity of demand is the reciprocal of the slope of the demand curve multiplied by the ratio of price to quantity. If demand is perfectly elastic, slope of demand curve = 0 By formula, \[{{E}_{d}}=\frac{1}{Slope\,of\,Demand\,Curve}\times \frac{P}{Q}\times \frac{1}{0}\times \frac{P}{Q}=\infty \] \[\therefore \]Price elasticity of demand is at infinity, if demand is perfectly elastic.