Market supply is given as Qd=200-pMarket demand is given as Os = 4P a . a...

Market supply is given as Qd=200-pMarket demand is given as Os = 4P a . a Calculate equilibrium price and quantity

If an excise tax of $ 4 per unit is imposed on sellers , calculate the price consumers pay Pc and the price sellers receive Ps .

C. Also , calculate the dead weight loss and consumer surplus after the tax .

Expert Solution

a) Equilibrium occurs when demand = supply

200 - P = 4P

5P = 200

P = 40

At this P = 40, Q = 160

b) At a tax of $4 on sellers, tax will be shared among both consumers as well as sellers which will fall in the ratio of (demand curve touching price axis - equilibrium price) to (equilibrium price - supply curve touching price axis) which is [(100 - 40) / (40 - 0]) = 1.5

Burden on consumers would be [1.5 / (1.5 + 1)] of total tax which is 60% totalling of 0.6 * 4 = $2.4 while burden on producer is [1 / (1 + 1.5)] which is 40% totaling of 0.4 * 4 = 1.6

Price seller receive falls to $38.4 while price buyer pay rises to $42.4

c) Producer surplus post tax is area of portion D whose sum is (1/2) (153.6 - 0) (38.4 - 0) = 2,949.12

Deadweight loss is area of portion E + F whose sum is area of portion (1/2) (160 - 153.6) (42.4 - 38.4) = 12.8

Rahul Sunny answered 2 years ago

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