Question

Consider a market where demand is given by P = 50 - Qd and supply is given by P = 10 + Qs. After a tax of t = 4 is placed on producers

		Producer surplus is between 180 and 200
		Producer surplus is between 220 and 240
		Producer surplus is between 160 and 180
		Producer surplus is between 200 and 220

Answer 1

Answer: Producer surplus is between 160 and 180

The demand equation is as follows,

P = 50 - Qd

Or, Qd = 50 - P.........................(1)

The supply equation is as follows,

P = 10 + Qs

Or, Qs = P - 10.............................(2)

Let us now find the equilibrium price and quantity,

When the market is in equilibrium,

Qd = Qs

50 - P =  P - 10\

Or, - P - P = -10 - 50

Or, - 2P = -60

Or, P = 30

Putting P = 30 in equation(1), we get,

Qd = 50 - 30

Or, Qd = 20

Now, putting P = 30 in equation(2), we get,

Qs = 30 - 10

Or, Qs = 20

So, Qd = Qs = 20

So, the equilibrium price is '30' and the equilibrium quantity is '20'.

After a tax of t = 4 is placed on producers, the supply equation will be,

P = 10 + Qs + 4

Or, P = 14 + Qs

Or, Qs = P - 14...............(3)

The demand equation remains same as before. Let us now find the new equilibrium price and corresponding quantity demanded and supplied in market,

50 - P = P - 14

Or, - P - P = - 14 - 50

Or, - 2P = - 64

Or, P = 32

At price , P = 32, the quantity demanded will be,

Qd = 50 - 32

Or, Qd = 18

The new equilibrium price is '32' and the new market demand and supply is '18'. When tax of '4' is imposed on producers, the burden on consumer is '2' and the burden on producer is '2'. So , the consumer is paying the price of 32 but producer actually gets price of '28'.

So, the new producer surplus after the tax is as below,

New Producer Surplus = 1 / 2 * (28 - 10) * 18

Or, New Producer Surplus = 1 / 2 * 18 * 18

Or, New Producer Surplus = 9 * 18 = 162

Hence, the producer surplus is between 160 and 180.

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