Question

Please slove showing steps and how you got the answer.

A market has the following supply and demand curves

P = 10 + 3Q

P = 200 - 7Q

What is the deadweight loss of a $50 per unit tax on this market?

Answer 1

Equilibrium is achieved where demand and supply both are equal

Supply Function

P = 10 + 3Q

Demand Function

P = 200 - 7Q

Equating both demand and supply

10 + 3Q = 200 - 7Q

Q = 19

To find the price we will use this quantity in any of the above two equations

P = 10 + 3Q

P = 10 + 3(19)

P = 67

Now the graph will look like this and the blue area represents deadweight loss but to calculate area of this region we need to find the price at point A and B and quantity at points A and B.

In the above graph, the length of line AB is equal to tax which $50 so we can say that

Price at point A - Price at point B = 50

(200 - 7Q) - (10 + 3Q) = 50

Q = 14

At 14 units demand will be

P = 200 - 7Q

P = 200 - 7(14)

P = 102

At 14 units supply will be

P = 10 + 3Q

P = 10 + 3(14)

P = 52

Now the graph will look like this with these new values

The area of this blue triangle is the deadweight loss.

Area = 1/2 x base x height

Area = 1/2 x 50 x 5

Area = 125

Hence the deadweight loss from a tax of $50 is equal to $125