Question

If the pre-tax (inverted) supply and demand curves for a good are given by P = 10 + 2Q and P = 100 – Q respectively, then a $30 per unit tax is shared equally between producers and consumers.  

Answer 1

At pre tax equilibrium, demand = supply

Or, 100 - Q = 10 + 2Q

Or, 3Q = 90

Or, Q = 30

At Q = 30, from any of the supply or demand equation we get, P = 70.

Therefore, before tax, consumers were paying and producers were receiving $70 per unit.

Now a $30 per unit tax is imposed on the market. Let, P = after tax equilibrium price. That means, consumers will pay P dollars but sellers receive (P - 30) dollars.

Therefore, after tax demand equation remains unchanged : P = 100 - Q

Supply equation changes [replace P with (P - 30)]: P - 30 = 10 + 2Q

Or, P = 40 + 2Q

At after tax equilibrium, 100 - Q = 40 + 2Q

Or, 3Q = 60

Or, Q = 20

When Q = 20, from any of the after tax demand or supply equation we get, P = 80.

It means consumers will pay $80 per unit but sellers will receive (P - 30) = $50 per unit.

Tax burden on consumers = (what they're paying after tax - what they're paying before tax) = $(80 - 70) = $10

Tax burden on producers = (what they're receiving before tax - what they're receiving after tax ) = $70 - $50 = $20.

Therefore, the $30 per unit tax is not shared equally between the consumers and the producers.