Question

□      Exercise: 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

Solution

Consumer Surplus =

Total Utility – (Price x Quantity)

Demand is given by : p = a - bQ

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

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$Marginalrevenue(MR)= dQ$

Where TR=$P\times Q=(a−bQ)\times Q$

$=aQ - bQ^2$

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

Hence, $MR = a - 2bQ$

When Q = 0

$Then,P=a−b\times0=a$

$MR = a - 2b\times0 = a$

Consumer surplus = $aQ−bQ ^ 2 - (a\times 0) aQ−bQ 2−(a×0)$

= $aQ−bQ ^ 2=aQ−bQ^2$

= 0-0 = 0