question_answer

Suppose there are 20 consumers for a good and they have identical demand functions.\[d(p)\]\[=50-{{6}_{p}}\]for any price less than or equal to \[\frac{20}{6}\]and d(p) = 0 at any price greater 10/3. What is the market demand function? Or Consider the demand curve d (p)=\[10-{{3}_{p}}\]. What is the elasticity at price\[\frac{5}{3}\]?

Answer:

The above demand function indicates that in a market comprising of 20 consumers, the consumer willing to buy only if the price is less than or equal to. Also, all the 20 consumers have identical demand function. Accordingly, \[{{d}_{m}}(p)=20\times d\]\[p=20\times (50-{{6}_{p}})\]   =1,000 -\[{{120}_{p}}\] for any price less than or equal to\[\frac{20}{6}\] If price exceeds\[\frac{20}{6}\] , then \[{{d}_{m}}(p)\]= 0 because at this price no consumer is willing to purchase the good. Or Given demand curve\[d(p)\] =\[10-{{3}_{p}}\] Where p is the price of good.             Now,                 Price\[(p)=\frac{5}{3}\]                            \[q=10-3\times \frac{5}{3}=10-5=5\]                                     Demand (q) =5 units                                     \[d(p)=10-{{3}_{p}}\] Here, - 3 indicates the rate at which q changes in response to change in p.             \[\therefore \]\[\frac{\Delta q}{\Delta p}=-3\]             Elasticity of demand\[({{E}_{d}})=(-)\frac{p}{q}\times \frac{\Delta q}{\Delta p}=(-)\frac{\frac{5}{3}}{5}\times -3\]                                     \[{{E}_{d}}\,\,\,\,(-)\frac{5}{3}\times \frac{1}{5}-3\]                                     Ed =1 \[\therefore \]Elasticity of demand at price\[\frac{5}{3}=1\]