Question

The demand and supply of a commodity may be estimated by the following equations:

P=200-1.2Qd

P=20+0.60Qs

a) Calculate the equilibrium price and quantity.

b) Draw the demand and supply curves and illustrate the equilibrium price and quantity.

c) Now suppose that the government introduces a tax on producers of $27 per unit:

i) Find the new equilibrium price and quantity and illustrate it in your diagram.

ii) Calculate the deadweight loss resulting from the tax and illustrate it in your diagram.

iii) Use the pass-through fractions to determine the burden of the tax on the producer and the consumer.

Answer 1

a) Equilibrium occurs where Qd = Qs = Q

200 - 1.2Q = 20 + 0.6Q

or, 1.8Q = 180

or, Q = 100

P = 20 + 0.6 * 100 = 80

These are the equilibrium price and quantity.

b) P = 200 - 1.2Qd

The demand curve is negatively sloped

When P = 0, Q = 2000/12 = 500/3

when Q = 0, P = 200

P = 20 + 0.6Qs

The supply curve is positively sloped.

when Q = 0, P = 20

Using the above information, we plot the graph below.

c) A tax on producers will change the supply curve.

The supply curve becomes -

P - 27 = 20 + 0.6Qs or, P = 47 + 0.6Qs

The new equilibrium is then given by -

200 - 1.2Q = 47 + 0.6Q

1.8Q = 207

or, Q = 85

These are the equilibrium price and quantity.

P = 47 + 51 = 98

ii) Deadweight loss = 1/2 * 27 * 15 = 202.5