Question

1. A market is described by the following system of equations: 300 - 5P and 60 + P. A tax of $6 is placed on the seller. The new equilibrium quantity AFTER the imposition of the tax is?

2. A market is described by the following system of equations: 300 - 5P and 60 + P. Suppose a tax of $6 is placed on the seller. The price paid by buyers AFTER the imposition of the tax is?

Answer 1

Demand Function

Q = 300 - 5P

Supply Function

Q = 60 + P

Equating both demand and supply to find equilibrium price and quantity

300 - 5P = 60 + P

240 = 6P

P = 40

Q = 100

Hence the equilibrium price is $40 and the equilibrium quantity is 100 units

Now the tax is imposed of $6 hence the supply function will change but first, we need to change both the equations in terms of price.

Demand

P = 300 - Q / 5

Supply Function

P = Q - 60

After the tax, the supply function will change hence the new supply function will be

P = Q - 60 + 6

P = Q - 54

Now to find the equilibrium after the tax we will equate the demand function and new supply function.

Q - 54 = 300 - Q / 5

5Q - 270 = 300 - Q

6Q = 570

Q = 95

Hence the new equilibrium quantity AFTER the imposition of the tax is 95 units.

The price paid by buyers after the imposition of the tax can be calculated by using the above quantity in any of the above two equations (new supply function or demand function)

P = Q - 54

P = (95) - 54

P = 41

Hence the price paid by buyers AFTER the imposition of the tax is $41