Question

Given demand equation P=50-2Qd and supply equation P=10+2Qs calculate. 

(a) consumer surplus

(b) producer surplus

(c) total surplus

assuming pure competition

Answer 1

$P=50-2Qd\\P=10+2Qs\\50-2Q=10+2Q\\50-10=2Q+2Q\\40=4Q\\Q=10$

$P=10+2Q\\=10+92\times10)\\P=30$

consumer surplus

$\frac{1}{2}\times base \times height$

We calculate Pd when Qd=0

$P=50-2Qd$

$\frac{2Qd}{2}=\frac{50}{2}-\frac{P}{2}$

$Qd=25-\frac{1}{2}P$

$0=25-\frac{1}{2}P$

$P=50$

consumer surplus

$=\frac{1}{2}\times10\times(50-30)$

$=\frac{1}{2}\times10\times20\\=100$

producer surplus

$P=10+2Qs$

$\frac{2Qs}{2}=\frac{P}{2}-\frac{10}{2}$

$Qs=\frac{1}{2}P-5$

$0=\frac{1}{2}P-5$

$P=10$

$\frac{1}{2}\times10\times(30-10)\\=100$

Total surplus

consumer surplus + producer surplus

$=100+100\\=200$