Question

given the demand function Pd=25-Q²and supply function Ps = 2Q+1. Assuming pure competition, find the consumer and producer surplus.

Answer 1

At equilibrium, P_d = P_s.

$25−Q^{2}= 2Q+1.$

On solving, we get Q* = 4, and P* = 9.

Consumer surplus is calculated as

$∫^{q}_0d(Q) dQ − P*Q*$

Putting values

$CS= ∫^{4}_025−Q^{2} dQ − (9)(4)$

$= [25Q − \frac{Q^{3}}{3}] − 36.$

Since Q = 4

$= [100 − 21.33] − 36$

=$ $42.67.$

Now, producer surplus is calculated as

$P*Q* −∫^{q*}_0s(Q) dQ.$

Putting values

$PS = (9)(4) − ∫^{4}_02Q+1 dQ$

$= 36 − [\frac{2Q^{2}}{2}+ Q].$

Since Q = 4,

$PS = 36 − 16 − 4$

=$$16$