Question

Suppose the demand curve is linear and is given by the equation P = a – bQ where P is price and Q is quantity. What is the consumer surplus if the equilibrium price is P* and equilibrium quantity is Q*?

Answer 1

Consumer Surplus = Total Utility – (Price x Quantity)

$Demand is given by : p = a - bQ$

$Marginal revenue(MR) = \frac{d(TR)}{dQ}$

$where TR = p×Q = (a - bQ)×Q$

$= aQ - bQ^2$

$Thus, MR = \frac{d(TR)}{dQ} = a - 2bQ$

$Hence, MR = a - 2bQ$

$When Q = 0 ,$

$then, P = a - b×0 = a$

$MR = a - 2b×0 = a$

Consumer surplus;

$aQ−bQ ^ 2 - (a × 0)$

$= aQ−bQ ^ 2$

= 0-0 = 0