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

Solution:

AR function = Demand function

Edp = $\frac{P}{Q} \times \frac{\triangle Q}{\triangle P}$

Derive the inverse function of the demand function:

P = 50 – 4q

4q = 50 – P

q = 12.5 – $\frac{p}{4}$

$\frac{P}{Q} = \frac{6}{5}$

$\frac{\triangle Q}{\triangle P}$ = -0.25

Edp = $(\frac{6}{5} ) \times -0.25 = -0.3$

Edp = -0.3

Consumer surplus = $\frac{1}{2}(Qd\times \triangle P)$

Derive Qd:

Price = 6

ΔP = Price the consumer is willing to pay – equilibrium price

Q = $12.5 - \frac{P}{4} = 12.5 - \frac{6}{4} = 12.5 - 1.5 = 11$

Qd = 11

The price the consumer is willing to pay = 50

Consumer surplus = $\frac{1}{2}(11\times (50 - 6)) = \frac{1}{2}(11\times 44) = \frac{1}{2}(484 ) = 242$

Consumer surplus = 242