Question

Q-2 Assume that the market for soaps in a small closed economy is initially characterized by the following domestic demand and domestic supply equations where Q is quantity and P is price.

Demand: Q = 120 – 2P & Supply: Q = 4P – 48. Find the equilibrium price, quantity, consumer surplus & producer surplus in the market for soaps.

Answer 1

At equilibrium; demand=supply

$120-2p=4p-48\\120+48=4p+2p\\168=6p\\p=28................equilibrium \space price$

$Q=120-2p\\=120-2(28)\\=120-56\\Q=64................equilibrium\space quantity$

consumer surplus = Area of triangle ABE

$CS=\frac{1}{2}(AB)(BE)\\=\frac{1}{2}(60-28)(64)=1024$

Producer surplus = area of triangle BCE

$PS=\frac{1}{2}(BC)(BE)\\=\frac{1}{2}(28-12)(64)=512$