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.
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"
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