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\[\frac{5}{3}=1\]
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