Question

The average revenue function for a commodity is p = 50 – 4q. Find edp when:

demand = 5 units ; price = Rs. 6. Find consumer’s surplus at price = Rs. 6

Answer 1

p is the price and q quantituy

Average revenue = $\frac{Total revenue}{q}$  

Total revenue =$p\times q$  

Then 

Average revenue $=\frac{ Pq}{q} = p$

Therefore

Average revenue function is the demand function. 

We can write inverse demand function as: 

$p = 50 - 4q$

$q =\frac {50-p}{4}$

Price elasticity of demand $=\frac{ dq}{dp} ×\frac{ p}{q}$

$\frac{dq}{dp}= \frac{-1}{4}$

Price elasticity of demand at $q = 5$ is equal to: 

$P = 50 - 4(5) = 30.$

$\frac{dq}{dp}= \frac{-1}{4}.$

Price elasticity of demand $= \frac{-1}{4} ×\frac{ 30}{5} = -1.5$

At price $= 6$  

$q =\frac{50-6}{4} =\frac{ 44}{4} = 11$

Price elasticity of demand$=\frac{ -1}{4} ×\frac{6}{11} = -0.136$

Price $= 6$

Then$q = 11$

P when q q $= 0 is 50 - 4(0) = 50$

Consumer surplus$= \frac{1}{2} × (50-6) × 11$

Consumer surplus $=\frac{1}{2} × 44 × 11$

Consumer surplus $= 242$